travelling salesperson award

Now Available

Watch Travelling Salesman on iTunes

"The themes and issues it addresses have never been more relevant ... Travelling Salesman is an essential watch."

travelling salesperson award

" Travelling Salesman ’s mathematicians are all too aware of what their work will do to the world, and watching them argue how to handle the consequences offers a thriller far more cerebral than most."

travelling salesperson award

"Simply unbelievably excellent filmmaking. This is a film to seek out."

travelling salesperson award

"A trip to see this movie might become an obligatory part of all math degrees."

travelling salesperson award

Worldwide Screening Events

New York. Philadelphia. London. Cambridge. Phoenix. Washington D.C. Glasgow. Tel Aviv. Seoul. Hamburg. Hertfordshire. San Francisco. Athens. College Station. Milwaukee. Nanyang. Edinburgh. Ann Arbor.

travelling salesperson award

Winner Best Feature Film

Silicon valley film festival 2012, picture summary.

Travelling Salesman is an intellectual thriller about four mathematicians hired by the U.S. government to solve the most elusive problem in computer science history — P vs. NP. The four have jointly created a "system" which could be the next major advancement for our civilization or destroy the fabric of humanity.

The solution's immediate application would be for theoretical computer science. However, its application would soon extend to countless other disciplines. For example, by utilizing the solution to P vs. NP, a hacker could crack advanced encryption codes within seconds—a task that now takes weeks, months, or even years. He could break into La Guardia's air traffic control or China's communication grid. But the mathematical algorithm would also serve as the basis for accelerated biological research, curing diseases such as AIDS and cancer.

We begin the film with the four at a secret location waiting to meet with a high-ranking official of the United States Department of Defense. The group discusses the global implications of their solution, and they agree that they must be extremely careful with who they allow to control their discovery.

The silver-tongued DoD agent soon arrives and presents them each with an offer of 10 million dollars in exchange for their portion of the algorithmic solution. He attempts to deftly address their concerns and sway the opinions of the four.

In the end, only one mathematician speaks out against selling the solution. In pleading his case, he is forced to reveal the dark truth about his portion of the algorithm. As the mathematicians are about to sign documents that will give the U.S. government sole and private ownership of their solution, they wrestle with the moral dilemma of how this volatile discovery will be used. The math is real. The implications are real.

The Math Behind The Film

The P vs. NP problem is the most notorious unsolved problem in computer science. First introduced in 1971, it asks whether one class of problems (NP) is more difficult than another class (P).

Mathematicians group problems into classes based on how long they take to be solved and verified. " NP " is the class of problems whose answer can be verified in a reasonable amount of time. Some NP problems can also be solved quickly. Those problems are said to be in " P ", which stands for polynomial time. However, there are other problems in NP which have never been solved in polynomial time.

The question is, is it possible to solve all NP problems as quickly as P problems? To date, no one knows for sure. Some NP questions seem harder than P questions, but they may not be.

Currently, many NP problems take a long time to solve. As such, certain problems like logistics scheduling and protein structure prediction are very difficult. Likewise, many cryptosystems, which are used to secure the world's data, rely on the assumption that they cannot be solved in polynomial time.

If someone were to show that NP problems were not difficult—that P and NP problems were the same—it would would have significant practical consequences. Advances in bioinformatics and theoretical chemistry could be made. Much of modern cryptography would be rendered inert. Financial systems would be exposed, leaving the entire Western economy vulnerable.

Proving that P = NP would have enormous ramifications that would be equally enlightening, devastating, and valuable...

"Mathematical puzzles don't often get to star in feature films, but P vs NP is the subject of an upcoming thriller"

"A movie that features science and technology is always welcome, but is it not often we have one that focuses on computer science. Travelling Salesman is just such a rare movie."

"We all know that the P=NP question is truly fascinating, but now it is about to be released as a movie."

"I speak with Timothy about where he got the idea for the movie, how he made sure that the mathematics was correct, and why science movies just may be the new comic book movies."

"At last someone is taking the position that P = NP is a possibility seriously. If nothing else, the film's brain trust realize that being equal is the cool direction, the direction with the most excitement, the most worthy of a major motion picture."

"Travelling Salesman is an unusual movie: despite almost every character being a mathematician there's not a mad person in sight."

Production Stills

travelling salesperson award

$1M Prize for Solution of Traveling Salesman Problem

travelling salesperson award

"Meanwhile, the Clay Mathematics Institute is offering a $1 million prize to anyone who can show whether the Traveling Salesman Problem can be fully solved at all, which the mathematician Jordan Ellenberg recently called “the biggest open problem in complexity theory.” NYT: March 14 - The Traveling Salesman Problem

See what can be found in the Theatre Section of the New York Times? And you thought it was for egg-head liberals.

I suspect that the article may have oversimplified what is needed to win the prize, unless the Clay Institute is currently offering TWO one million dollar prizes. But that’s the NYT for you.

The diagram obviously shows a solution (not necessarily the best solution) to a problem different from the one that was a recent Car Talk Puzzler. The only point in New England appears to be Boston, which means at least four states aren’t on the route in that part of the country. It also misses both Nevada and New Mexico entirely, and has two points in California. (That’s just the parts of the country I can speak for without seeing state lines on the map.)

The diagram shows a solution for an optimal tour through 33 cities in a 1962 Procter and Gamble contest. Yes, it is optimal.

If you did not read the article, you should not criticize.

If you want someone to read the article before commenting on the difference between the graphic you posted and the recent Car Talk Puzzler, you shouldn’t have posted the graphic. If you think that was criticism, your definition of criticism is overbroad.

I forget the exact wording, but didn’t the solution to the travelling salesman puzzler offered up on the radio show require identifying a state which is only connected to one other state? I think Maine connects only to New Hampshire. All other states (contiguous) connect to at least two other states. Florida for example connects to both Georgia, and Alabama.

Way to go @George_San_Jose1 You revived a 10 year old thread.

:wink:

OK. as long as the dead have been resurrected, nice math problem but very unrealistic. I always get a charge out of these stories to simply mask a math exercise for those that like to work out math problems. At any rate it’s all academic because that’s not the way a traveling salesman would have to do it, unless all he/she/it was doing is cold calls. Then why drive all over the country doing that? You would tend to go into an area and work that area but would be going back and forth etc. depending on appointments and call backs. Of course now like with the yellow pages, you would do your driving with your fingers and computers.

This is the famous NP-Complete problem, useful in many ways List of NP-complete problems - Wikipedia , the ‘traveling salesman’ is a trivial example meant to make it seem familiar to a broad audience. Solving it is worth far more than a billion dollars. People have already spent millions trying to solve it - this prize won’t recruit any competent entrants.

Login Register

Pay calculator tool

Find wages and penalty rates for employees.

Leave calculator tool

Work out annual and personal leave

Shift calculator

Rates for your shifts

Notice and redundancy calculator  

  • Accessibility
  • Subscribe to email updates
  • Visit Fair Work on YouTube
  • Visit Fair Work on Twitter
  • Visit Fair Work on Facebook
  • Visit Fair Work on Instagram
  • Visit Fair Work on LinkedIn

Automatic translation

Our automatic translation service can be used on most of our pages and is powered by Microsoft Translator.

Language help

For professionally translated information, select your language below.

Popular searches

  • minimum wages
  • annual leave
  • long service leave

Commercial Sales Award [MA000083]

Who the commercial sales award covers.

The Commercial Sales Award covers Commercial Travellers, Merchandisers and Advertising Sales Representatives and their employers.

Commercial Travellers, Merchandisers and Advertising Sales Representatives are all people who work away (or substantially away) from the employer’s business office or location (eg. on the road).

A Commercial Traveller is someone who:

  • sells or solicits orders for articles, goods, wares, merchandise or material that is sold wholesale or resale, or will be used by the customer for producing, preparing or distributing what they will sell.

Commercial Travellers must be selling goods for wholesale sale (ie. not for retail).

An Advertising Sales Representative is someone who:

  • solicits orders, obtains sales leads or appointments, or promotes sales in other ways for  advertising space or time of any kind.

A Merchandiser is someone who:     

  • promotes the employer’s products,
  • re-orders stock
  • prepares display units and gondola ends.

They may also solicit orders for these products but only as a minor part of their work.

The Commercial Sales Award also covers labour hire businesses and their employees who work as Commercial Travellers, Advertising Sales Representatives and Merchandisers if they are placed with an employer and the employer isn’t covered by an award that has a classification for them.

Check the award for full information on who is covered and the classification descriptions.

Source reference: Commercial Sales Award [MA000083] clauses 2 and 4

Who the Commercial Sales Award doesn't cover

Commercial Travellers, Merchandisers and Advertising Sales Representatives are not covered by this award when they are employed by a business that is covered by a different modern award that has a classification for them.

The Commercial Sales Award doesn't cover employers and employees when they are covered by one of the following awards:

  • Clerks Award
  • Contract Call Centres Award
  • Graphic Arts Award
  • Retail Award.

Check the award for full information on coverage and classifications.

Not the right award?

If your industry or work isn’t covered above, you can also check:

  • Clerks Award summary
  • Contract Call Centres Award summary
  • Graphic Arts and Printing Award summary
  • Retail Award summary .

Find your pay and entitlements

  • Calculate pay
  • Calculate leave
  • Calculate notice and redundancy
  • Download the  Commercial Sales Award [MA000083] Pay Guide (DOCX) (PDF)  for a summary of pay rates, all allowances and common penalties in this award.

Pay and entitlements less than the award?

Employees must be paid at least award pay rates and entitlements.

If your pay rates are less than the award, go to Help resolving workplace issues to follow our step by step guide on how you can fix it.

Need help finding the answers to other questions about the workplace?  Get help .

Looking for another award?

If you’re looking for award coverage for multiple job roles, start our Find my Award tool again.

The Fair Work Ombudsman acknowledges the Traditional Custodians of Country throughout Australia and their continuing connection to land, waters, skies and communities. We pay our respects to them, their Cultures, and Elders past, present and future.

Thank you for your feedback. If you would like to tell us more about the information you’ve found today you can complete our feedback form .

Please note that comments aren't monitored for personal information or workplace complaints. If you have a question or concern about your job, entitlements or obligations, please Contact us .

Bookmark to My account

  • Get priority support!
  • Save results from our Pay, Shift, Leave and Notice and Redundancy Calculators
  • Bookmark your favourite pages
  • Ask us questions and save our replies
  • View tailored information relevant to you.

Log in now to save this page to your account.

  • Fair Work Online: www.fairwork.gov.au
  • Fair Work Infoline: 13 13 94

Need language help?

Contacting the Translating and Interpreting Service (TIS) on 13 14 50

Hearing & speech assistance

Call through the National Relay Service (NRS):

  • For TTY: 13 36 77 . Ask for the Fair Work Infoline 13 13 94
  • Speak & Listen: 1300 555 727 . Ask for the Fair Work Infoline 13 13 94

The Fair Work Ombudsman is committed to providing you with advice that you can rely on. The information contained in this fact sheet is general in nature. If you are unsure about how it applies to your situation you can call our Infoline on 13 13 94 or speak with a union, industry association or a workplace relations professional.

Printed from fairwork.gov.au Content last updated: 2023-06-30 © Copyright Fair Work Ombudsman

Grey Arrow in Cicler

  • Student Member
  • Corporate Partnership
  • Accreditation
  • OR Society Accreditation »
  • Become Chartered »
  • Data Science Professional Certification »
  • Continuing Professional Development CPD »
  • Awards, Medals and Scholarships
  • Beale Medal »
  • President's Medal »
  • Goodeve Medal »
  • Stafford Beer Medal »
  • Cook Medal »
  • KD Tocher Medal »
  • Griffiths Medal »
  • Ranyard Medal »
  • Lyn Thomas Impact Medal »
  • Companion of OR »
  • The Simpson Award »
  • May Hicks Award »
  • The OR Society Undergraduate Award »
  • The Doctoral Award »
  • Scholarships IFORS »
  • Donald Hicks Scholarships »
  • EURO Summer Institute Scholarships »
  • Elsie Cropper Award »
  • Assisted Places »
  • Silver Medal »
  • Master's Scholarship »
  • University Master's Courses in OR »
  • Master's Scholarships Recent Winners »
  • Analytics Summit
  • AS24 Speakers »
  • AS24 Sponsors »
  • Annual Conference
  • OR66 Streams »
  • OR66 Organising Committee »
  • OR66 Sponsors »
  • Previous Annual Conferences
  • OR64 »
  • OR63 »
  • OR62 »
  • OR61 »
  • OR65 »
  • OR65 Plenary Speakers »
  • OR65 Streams »
  • OR65 Key Dates »
  • OR65 Rates and Booking »
  • OR65 Useful Information »
  • ECR Workshop »
  • OR65 Organising Committee »
  • Annual General Meeting
  • 2018 Beale Lecture Richard Omerod »
  • 2018 Beale Lecture Dr Çagri Koç »
  • 2019 Beale Lecture Mike Jackson »
  • Beale Lecture 2020 Speakers »
  • 2021 Beale Lecture »
  • Beale 2023 »
  • Blackett Lecture
  • Previous Blackett Lectures »
  • Blackett 2022: Professor Christina Pagel »
  • Careers Open Day
  • COD 2022 Exhibitors »
  • ISMOR 40 Proceedings »
  • ISMOR 39 Proceedings »
  • Knowledge Exchange Day
  • New to OR Conference
  • Speakers »
  • Simulation Workshop
  • Scenario Planning and Foresight
  • Validate AI Conference
  • Regional Society & SIG Events
  • Non-Society Events
  • WORAN Land Lecture
  • Previous WORAN Land Lectures »
  • September Webinar »
  • November Webinar »
  • October Webinar »
  • 15 November Webinar »
  • December Webinar »
  • January 24 Webinar »
  • WISDOM Webinar »
  • February 24 webinar »
  • March 2024 »
  • April 24 »
  • May 24 »
  • May_2_2024 »
  • Joint SIG Event
  • Joint SIG Speakers 2024 »
  • Publications
  • JORS »
  • EJIS »
  • KMRP »
  • JOS »
  • JBA »
  • OR Insight »
  • Inside OR »
  • Impact Magazine »
  • Databases & Literature Searches
  • Additional Journals
  • Technology Analysis & Strategic Management »
  • Engineering Optimization »
  • Journal of Decision Systems »
  • Journal of Management Analytics »
  • International Journal of Modelling and Simulation »
  • International Journal of Management Science and Engineering Management »
  • International Journal of Systems Science: Operations & Logistics »
  • International Journal of Healthcare Management »
  • Tutors »
  • Your Learning Portal
  • Inhouse Private Courses
  • Training for PhD Students – NATCOR
  • Submit Training Bids
  • Researchers Database
  • EPSRC Peer College Review
  • Why Kerem Akartunali joined the EPSRC Peer Review College »
  • Why Alain Zemkoho is joining the EPSRC Peer Review College »
  • Why Kathy Kotiadis joined the EPSRC Peer Review College »
  • Open Funding Opportunities
  • Top Tips: Applying for Funding
  • Potential Funding Sources for Research
  • Top Tips: Reviewing a Research Proposal
  • Get Involved
  • Job Opportunities in OR
  • Volunteering Opportunities
  • OR in Education
  • University Masters Courses in OR »
  • Careers »
  • For Volunteers »
  • For Lecturers »
  • For Teachers »
  • Teaching Resources »
  • Volunteering Resources »
  • Webinars »
  • Pro Bono OR
  • Pro Bono OR Volunteering »
  • Open Pro Bono Projects »
  • Pro Bono OR for the Third Sector »
  • Case Studies »
  • Society Groups
  • Regional Societies »
  • East Midlands »
  • London & South East »
  • Midlands »
  • North East »
  • North West »
  • Scotland »
  • South Wales »
  • Southern »
  • Western »
  • Yorkshire & Humberside »
  • Special Interest Groups and Networks »
  • Analytics Network »
  • Behavioural OR »
  • Decision Analysis »
  • Defence »
  • Early Career Researchers (ECR) »
  • Health & Social Services »
  • Independent Consultants Network »
  • New to OR Network »
  • OR, Analytics, and Education »
  • OR and Strategy »
  • OR in Practice »
  • OR in the Third Sector »
  • People Analytics »
  • Problem Structuring Methods »
  • Public Policy Design »
  • Simulation OR »
  • Systems Thinking »
  • Women in OR & Analytics Network »
  • Related Organisations
  • Submit a paper to a journal
  • Become a reviewer
  • Legacy Giving
  • History of OR
  • OR in Business
  • Agent Based Modelling »
  • Bayesian Analysis »
  • Data Envelopment Analysis »
  • Data Provenance »
  • Data Warehousing »
  • Fuzzy Systems »
  • Grey Models »
  • Heuristics »
  • Multicriteria Analysis »
  • Neural Networks »
  • Optimization »
  • Performance Measurement »
  • Queueing »
  • Reliability »
  • Retail »
  • Simulation »
  • System Dynamics »
  • Vehicle Routing Problem »
  • History of The OR Society
  • 75th Anniversary

A brief History of the Travelling Salesman Problem

By nigel cummings.

In the April 2000 issue of this Newsletter I produced an article about the application of insect behavioural patterns to common OR problems. In particular I wrote about Marco Dorigo and his team at the Free University of Brussels, and their work with ant-like agents applied in that instance to the travelling salesman problem (TSP).

At this time it occurred to me that the majority of OR oriented minds had been presented with the TSP or variations of, for a very considerable time. TSP is a problem which is both short and easy to state: given a finite number of cities along with the cost of travel between each pair of them, and with the object of finding the cheapest way of visiting all the cities and returning the original point of departure. (The travel costs are symmetric from the point of view that travelling from city X to city Y costs just as much as travelling from Y to X - the manner of visiting all the cities is simply the order in which the cities are visited.)

I began to wonder when the original TSP had surfaced? Who thought of it? Was it called the Travelling Salesman Problem? Who produced the first solutions? During a period of research which I expected to be brief, I came across increasing numbers of references to the solution of the TSP and TSP like problems. I was surprised to learn that the mathematician and economist Karl Menger, perhaps best know for his interests in hyperbolic, probabilistic geometry, and the algebra of functions had publicised TSP among his colleagues in Vienna in the 1920s. It seemed then, that the TSP has spanned at least 9 decades! In 1932 Menger published "Das botenproblem", in Ergebnisse eines Mathematischen Kolloquiums (This volume contains a statement of a problem posed by Karl Menger on February 5, 1930, at a mathematical colloquium in Vienna).

Menger called it the "Messenger Problem" a problem encountered by postal messengers, as well as by many travellers he went on to define the problem as: "the task of finding, for a finite number of points whose pairwise distances are known, the shortest path connecting the points The rule, that one should first go from the starting point to the point nearest this, etc., does not in general result in the shortest path."

In the 1940s the TSP was studied by statisticians: Mahalanobis (in 1940), Jessen (in 1942), Gosh (in 1948), and Marks (in 1948)) in connection with an agricultural application. P. C. Mahalanobis's, "A sample survey of the acreage under jute in Bengal" discussed aspects of TSP solutions through randomly chosen locations in the Euclidean plane. This work was in connection with a survey of farm lands in Bengal that took place in 1938, where one of the major costs in carrying out the survey was the transportation of men and equipment from one survey point to the next.

The mathematician Merill M. Flood made the TSP popular among his colleagues at the RAND Corporation. Over the years the problem gained notoriety as the prototype of a hard problem in combinatorial optimisation - examining the tours one by one is difficult because of their large number.

TSP data consists of integer weights assigned to the edges of a finite complete graph; the objective is to find a hamiltonian cycle (that is, a cycle passing through all the vertices) of the minimum total weight. In this context, hamiltonian cycles are commonly called tours.

Julia Robinson is most famous for her work with Hilberts tenth problem, which asked for a procedure for deciding if a Diophantine equation had a solution in integers also [published a paper concerning the TSP. Published in 1949 the paper entitled "On the Hamiltonian Game" provided a method for solving a problem related to the TSP. Although the problem was well known at that time, there does not appear to be any earlier reference in the literature.

During the 1950s a number of solutions appeared from the likes of George B. Dantzig, Fulkerson, and Johnson (1954). Their approach remains the only known tool for solving nontrivial TSP instances with more than several hundred cities; over the years, it has evolved further through the work of M.Grtschel, S. Hong, M. Jnger, P. Miliotis, D. Naddef, M. Padberg, W.R. Pulleyblank, G. Reinelt, and G. Rinaldi. (George B. Dantzig is generally regarded as one of the three founders of linear programming, along with von Neumann and Kantorovich.)

In 1954 I. Heller published an 88-page report containing many basic results on the asymmetric TSP polytope. Heller described this work as "an assembly of facts and tools, hence, a working paper in the literal sense of the word."

A year later (1955) G. Morton and A.H. Land provided additional solutions, though interestingly they wrote that they originally called the TSP, the laundry van problem. The paper mainly concerns the use of linear programming for solving the TSP but there are several interesting side topics such as the authors use of their version of 3-opt. "We have developed a method for investigating the change in cost of all three-in, three-out changes which are possible without destroying the circuit." They also said that, "the TSP may be familiar to statisticians as the `Mean Minimum Distance' problem", and they give several references dating back to 1942. (G. Morton and A.H. Land, "A contribution to the `travelling-salesman' problem", Journal of the Royal Statistical Society, Series B 17, 185-194.)

In 1956 Merill M. Flood published "The travelling-salesman problem", Operations Research 4, 61-75. In which he described some heuristic methods for obtaining good tours, including the nearest-neighbour algorithm and 2-opt.

In 1957 L.L. Barachet published, "Graphic solution of the travelling-salesman problem", ( Operations Research 5, 841-845.) This paper described an enumeration scheme for computing near-optimal tours and made observations on the structure of optimal tours for geometric problems. The paper also detailed a tour for a 10-city instance which was solved by hand to demonstrate the practicality of the method for small instances.

The 1950s saw an increasing use of computers in solving such problems. 1958 saw F. Bocks , "An algorithm for solving travelling-salesman and related network optimisation problems", this paper was presented at the Operations Research Society of America, Fourteenth National Meeting, St. Louis, October 24, 1958. It described a 3-opt algorithm and an enumeration scheme for computing an optimal tour. The algorithm was tested on the examples of Robacker and Barachet, as well as on a new 10-city problem. All the tests were carried out on an IBM 650 computer.

In 1959 George.B. Dantzig, D.R. Fulkerson, and S.M. Johnson published "On a linear-programming, combinatorial approach to the travelling-salesman problem", Operations Research 7, 59-66. This provided a step-by-step application of the Dantzig-Fulkerson-Johnson for a ten city example.

At the beginning of the 1960s, R. Bellman published "Combinatorial processes and dynamic programming". In this Bellman (no stranger to computers ) used the TSP as an example of a combinatorial problem that can be solved via dynamic programming. He wrote: "It follows that with current machines it would be possible to solve problems of this type in a direct fashion for ."

<p">Around this time M. F. Dacey announced a new heuristic algorithm for the TSP. The details of the algorithm were given in a technical report from the Department of Geography, University of Washington. Dacey noted that when the heuristic was applied to 10 Robacker instances, the solutions found were on average 4.8 percent longer than the optimal solutions.

1963 saw the publication of a paper jointly by J.D.C. Little, K.G. Murty, D.W. Sweeney, and C. Karel, entitled "An algorithm for the travelling salesman problem", the authors coined the term Branch and Bound, and proceeded to illustrate a combinatorial bounding method in their algorithm, and they regarded branch on edges being either in or not in the tour. Their algorithm was implemented on an IBM 7090 computer.

In 1964 heuristics were applied to a 57 city problem among others by R.L. Karg and G.L. Thompson, their method was described in "A heuristic approach to solving travelling salesman problems", ( Management Science 10, 225-248.) The following year Shen Lin published a paper which detailed a heuristic solution for up to 105 cities.

Leaping forward to the 1970s R.M. Karp and M. Held published "The travelling-salesman problem and minimum spanning trees", a paper which introduced the 1-tree relaxation of the TSP and the idea of using node weights to improve the bound given by the optimal 1-tree. Part II was published in 1971, and detailed An iterative method for computing a good 1-tree bound (using node weights). The authors embedded this method in a branch-and-bound algorithm and solved, amongst others, the 42-city instance of Dantzig, Fulkerson, and Johnson (1954), the 57-city instance of Karg and Thompson (1964), and a 64-city random Euclidean instance.

In 1974 further improvements to the Held-Karp algorithm for the symmetric travelling-salesman problem were announced by K. Helbig Hansen and J. Krarup, who tested their version of Held-Karp on the 57-city instance of Karg and Thompson (1964) and a set of instances having random edge lengths. In 1976 P. Miliotis applied integer programming to the TSP and implemented a branch-and-cut algorithm using subtour inequalities.

1977 saw M. Grtschel's thesis which contained much of the polyhedral work on the TSP that he carried out jointly with M. Padberg. It also provided the solution for a 120-city instance by means of a cutting-plane algorithm, where cuts (subtour inequalities and comb inequalities) were detected and added by hand to the linear programming relaxation. From that time onward, further work in cutting planes methods was carried out by the likes of: P. Miliotis, "Using cutting planes to solve the symmetric travelling salesman problem", Mathematical Programming 15 , 177-188. And M.W. Padberg and S. Hong, "On the symmetric travelling salesman problem: a computational study", Mathematical Programming Study 12, 78-107. As recently as 1991 M. Grtschel collaborated with O. Holland on, "Solution of large-scale symmetric travelling salesman problems."

It will be interesting to see what further papers result from the TSP problem now we are inhabiting the 21st century.

First published to members of the Operational Research Society in Inside OR June 2000

Latest news.

Maths Summit

Maths Summit to bring political leaders together with experts from academia and industry

On 12 March 2024, the Council for Mathematical Sciences and the ‘Protect Pure Maths’ project are putting on the Maths Summit, with the support The OR Society and four other learned mathematical societies. The intention is to bring together political leaders and experts from academia and industry to discuss how the mathematical sciences can contribute better to research, innovation and prosperity.

Sophie Huiberts Wins Gijs De Leve Prize

February 2024

Sophie Huiberts wins Gijs de Leve Prize

The Dutch national network for operational research, LNMB, has awarded the prestigious Gijs de Leve Prize to Sophie Huiberts, the award’s first female winner. The prize is given to the best PhD thesis in Mathematics of Operations Research over the period of consideration.

1706603765871

Supply Chain Management Award won by Philip Morris International

This week it was announced that tobacco giant Philip Morris International (PMI) won the prestigious Supply Chain Management Award 2023 with their platform Sync Hub.

Amazon Last-Mile Routing Research Challenge

Last-mile routing research challenge awards $175,000 to three winning teams

Aug 6, 2021 | Challenge FAQ & Details

Author: Douglas Gantenbein. This article originally appeared at Amazon Science

Finding the optimal route between multiple destinations —  the traveling salesman problem  — is a challenge regularly faced by Amazon’s Last Mile team. Meeting that challenge has meant developing planning software to allow Amazon’s delivery fleet to find the most efficient routes. But what happens when drivers must deviate from those routes? Drivers have access to real-time information — road blockage, congestion, parking, etc —and other knowledge and know-how that existing optimization models don’t capture.

“Despite the tremendous advances in routing optimization over the last decade, there remains an important gap between periodic route planning and real-time route execution,” said  Beryl Tomay , Amazon vice president for Last-Mile Delivery.

That’s why  in February  Amazon collaborated with MIT’s Center for Transportation & Logistics ( MIT CTL ) to develop a competition that challenged academic teams to train machine learning models to predict the delivery routes chosen by experienced drivers.

On July 30, the winners of that contest, dubbed the  Amazon Last Mile Routing Research Challenge , were announced. “The Last Mile routing challenge is a classic problem,” said  Daniel Merchan , a senior research scientist on Amazon’s Last Mile team. “Our participants worked for more than three months to come up with innovative, data-driven solutions.”

Left to right: William Cook, professor of combinatorics and optimization at the University of Waterloo; Stephan Held, associate professor with the Research Institute for Discrete Mathematics at the University of Bonn, Germany; and Keld Helsgaun, associate professor emeritus in computer science at Roskilde University, Denmark.

Team Passing Through, comprising scholars from three separate universities, took top honors, winning $100,000. The team’s members are:

William Cook , professor of combinatorics and optimization at the University of Waterloo, Canada; Stephan Held , associate professor with the Research Institute for Discrete Mathematics at the University of Bonn, Germany; and Keld Helsgaun , associate professor emeritus in computer science at Roskilde University, Denmark.

“The challenge was a huge contribution to the research community, providing a massive collection of test instances,” the team said in a statement provided to Amazon Science. “In a single post, Amazon made publicly available more real-world examples of the traveling salesman problem than had been collected in total over the past 70 years.”

Left to right, Xiaotong Guo, Qingyi Wang, and Baichuan Mo.

The $50,000 second-place prize went to Team Permission Denied, comprising a trio of MIT Ph.D. students —  Xiaotong Guo ,  Qingyi Wang , and  Baichuan Mo  — while Team Sky is the Limit, comprising  Okan Arslan , assistant professor at HEC Montreal, and  Rasit Abay , a Ph.D. student at the University of New South Wales Canberra, won the $25,000 third-place prize.

More than 220 teams participated in the competition, with 45 competing in the final round. Overall, the teams represented 71 different universities and 22 countries. Entrants ranged in academic level from undergraduate to retired faculty.

Okan Arslan, assistant professor at HEC Montreal, and Rasit Abay, a PhD student at the University of New South Wales Canberra

Entrants were given 6,100 historical route records from five areas across the United States to use as a baseline for their project. They also were given more than 3,000 traces of driver-determined routes. Both datasets included driver knowledge. The initial dataset was used for training and testing the model, while the second dataset was utilized for evaluation using both sources of information. Contestants endeavored to build models that could identify and predict drivers’ deviations from routes computed in the traditional manner.

Participants utilized a variety of approaches, including conventional optimization models (some of them enhanced with machine learning components), and wrote short technical papers explaining their approach.

Last Mile Challenge finalists will have an opportunity to publish their research in  Transportation Science .

Call for papers A special issue of  Transportation Science  will be published in conjunction with the Last Mile Challenge.  Karthik Konduri , a senior research scientist on the Last Mile team, and  Julian Pachon , director and chief scientist for the Last Mile science team, will be co-editors for this special issue. The deadline for submissions is Nov. 30, 2021.

  • Divisions and Offices
  • Grants Search
  • Manage Your Award
  • NEH's Application Review Process
  • Professional Development
  • Grantee Communications Toolkit
  • NEH Virtual Grant Workshops
  • Awards & Honors
  • American Tapestry
  • Humanities Magazine
  • NEH Resources for Native Communities
  • Search Our Work
  • Office of Communications
  • Office of Congressional Affairs
  • Office of Data and Evaluation
  • Budget / Performance
  • Contact NEH
  • Equal Employment Opportunity
  • Human Resources
  • Information Quality
  • National Council on the Humanities
  • Office of the Inspector General
  • Privacy Program
  • State and Jurisdictional Humanities Councils
  • Office of the Chair
  • NEH-DOI Federal Indian Boarding School Initiative Partnership
  • NEH Equity Action Plan
  • GovDelivery

Traveling Man

Illinois explores the history of the profession shared by l. frank baum, benedict arnold, and johnny appleseed. .

Illustrated advertisement of a woman in a toga holding a spear-shaped fountain pen.

The Waterman fountain pen was invented in 1884 by Lewis Edison Waterman, a traveling insurance salesmen motivated by a former client who refused to sign a policy with a leaky reservoir pen.

1919 poster by Ogé; Library of Congress

When Arthur Miller’s  Death of a Salesman  appeared on stage in 1949, the traveling salesman became—and, in the minds of many, has remained—synonymous with middle-class tragedy.

But for Ronald Solberg, the traveling salesman is not so easy to define. “So many different images come to my mind with those two words,” he writes. “A peddler with a sack slung over his back, a wry teller of tales with a farmer-city slicker story,” or a hustler with “a wagon filled with ointments and elixirs.” Solberg once peddled brushes in southern Minnesota, but has since laid down his  grip —or sample case. Currently a history teacher, Solberg worked also in public relations and advertising, and was, at one point, the communications director for the Million Dollar Round Table, an international association of life insurance salesmen.

In 2002, Solberg was commissioned by Chicago’s Newberry Library to compile lesson plans on turn-of-the-century labor activity. His experiences on the road and with the MDRT were his inspiration. Seven years of research produced  The Whizbangs of Oohs and Ahs—America’s Salesmen: Their Lore, Lives and Laughs , and he now lectures on the subject through the Illinois Humanities Council’s Road Scholars program.

“There’s certainly some truth to  Death of a Salesman , but that’s only one side of it,” says Solberg. On the bright side, it is a career that has attracted multitalented individuals, who have collectively altered our culture. Former salesmen include P. T. Barnum, L. Frank Baum, Benedict Arnold, and John Chapman, who is more affectionately known as Johnny Appleseed. A more exhaustive list contains some commercial titans, from the founders of department stores to the top grossers in condiment and chewing gum sales.

The traveling salesman, Solberg writes, is uniquely American. In the eighteenth century, “peddlers were quite rare in Europe because craft guilds provided local artisans with monopolies in their territories.” The U.S., on the other hand, lacked regulations and its artisans required a class of men to dole out their products. Some salesmen became general merchants hawking small essentials that were effortlessly transported, such as pins, needles, scissors, and combs. Others became specialized dealers, limiting their wares to a single product.

In the late nineteenth century, rail hubs, like Chicago, became springboards for roaming merchants, who doubled as “walking newspapers and purveyors of information,”says Solberg. Businesses, like the Fuller Brush Company (for which Solberg’s father was a field manager), relied on the charm of their salesmen. They were armed with “leave-behinds,” encouraged to meet “stop-goals,” and, for the first time in commercial history,they could offer home trials and money-back guarantees.

Clued-in merchants, responsive to the needs of customers, became instrumental in the creation of new products. They developed goods with “built-in obsolescence—that consumers would willingly purchase over and over again,” writes Solberg. Modern shoppers may thank former salesmen as they pull on a pair of jeans, relish a potato chip, vacuum a carpet, or furtively tout a knockoff purse.

That final treat—the introduction of knockoffs—reveals a sordid reality: Life on the road brought a desire for shortcuts. In 1833, a British observer wrote, “Yankee Peddlers . . . are proverbial for dishonesty. They go forth annually in the thousands to lie, cog, cheat, [and] swindle.” Some took pride in their double-dealings. William Avery Rockefeller, a nineteenth-century salesmen and the father of John D., boasted of how he treated his sons: “I cheat my boys every chance I get. I want to make ’em sharp.” But Rockefeller and like-minded rogues were the exception, not the norm. Alfred Fuller, founder of the Fuller Brush Company, clarified, “The salesman is an idealist and an artist; in that respect he differs from the huckster, who is just out for profit.”

As Solberg is quick to remind his audiences, the traveling salesman is not a creature of the past. “Good salesmen find that they adjust to the times and use whatever systems are available to them.” They have been “responsible for developing the modes of persuasion that we now associate with modern merchandizing [and] public relations.” Television commercials—which highlight articulate, personable spokesmen—draw on door-to-door techniques. Business cards and catalogs, the former bread and butter of a successful vendor, are common fare. Boardroom jargon, too, bears their influence. “Brass tacks,” “pitch,” and “best-seller” were each coined or popularized by roving merchants.

Off the sales floor, the trials of traveling salesmen offer a universal lesson. “It’s tough work, going door to door, business to business. But it builds character. [You learn to] overlook the people who say ‘no,’ to find the ones that say ‘yes.’ It’s an important message,” says Solberg.

Corinne Zeman is an editorial intern for HUMANITIES magazine.

molded plywood chair

SUBSCRIBE FOR HUMANITIES MAGAZINE PRINT EDITION Browse all issues   Sign up for HUMANITIES Magazine newsletter

  • Cast & crew
  • User reviews

Travelling Salesman

Travelling Salesman (2012)

Four mathematicians are hired by the US government to solve the most powerful problem in computer science history. Four mathematicians are hired by the US government to solve the most powerful problem in computer science history. Four mathematicians are hired by the US government to solve the most powerful problem in computer science history.

  • Timothy Lanzone
  • Andy Lanzone
  • Danny Barclay
  • David John Cole
  • 27 User reviews
  • 5 Critic reviews

Travelling Salesman Official Trailer

  • No. 1 - Tim Horton

David John Cole

  • Professor Acuri
  • Mysterious Man

Matt Lagan

  • Number Four

Marc Raymond

  • All cast & crew
  • Production, box office & more at IMDbPro

More like this

Proof

Did you know

  • Trivia The original draft of the screenplay was written in 2009, years before leaked NSA information detailing cyber-espionage was revealed--a topic discussed directly in the film.
  • Goofs Early in the film, the character Tim Horton asks a colleague about the characteristics of a desert. The colleague replies that they are 'hot'. This is not true, since Antarctica is a desert and is not thought of as being 'hot'. There are many ways to classify an area as a desert. Two of the main methods are that total precipitation is less than 10 inches, and the evaporation being greater than precipitation. 'Hot' is too subjective a term since many people will disagree on what qualifies as 'hot'.

[last lines]

No. 1 - Tim Horton : Don't blink. You might miss something.

User reviews 27

  • Sep 14, 2013
  • How long is Travelling Salesman? Powered by Alexa
  • June 16, 2012 (United States)
  • United States
  • Official Facebook
  • Official site
  • Los Angeles, California, USA
  • Fretboard Pictures
  • See more company credits at IMDbPro

Technical specs

  • Runtime 1 hour 20 minutes
  • Dolby Digital

Related news

Contribute to this page.

Travelling Salesman (2012)

  • See more gaps
  • Learn more about contributing

More to explore

Production art

Recently viewed

web

Commercial Sales Award 2020

This Fair Work Commission consolidated modern award incorporates all amendments up to and including 9 April 2024 ( PR771359 ).

Clause(s) affected by the most recent variation(s):

18 — Superannuation

Table of Contents

[Varied by PR742720 , PR747569, PR750453 ]

Part 1— Application and Operation of this Award .............................................................. 3

1. Title and commencement ............................................................................................. 3

2. Definitions .................................................................................................................... 3

3. The National Employment Standards and this award .................................................. 4

4. Coverage ....................................................................................................................... 4

5. Individual flexibility arrangements .............................................................................. 5

6. Requests for flexible working arrangements ................................................................ 7

7. Facilitative provisions .................................................................................................. 7

Part 2— Types of Employment ............................................................................................... 8

8. Types of employment ................................................................................................... 8

9. Full-time employees ..................................................................................................... 8

10. Part-time employees ..................................................................................................... 8

11. Casual employees ......................................................................................................... 9

12. Statement and terms of engagement ............................................................................. 9

Part 3— Hours of Work ......................................................................................................... 10

13. Ordinary hours of work .............................................................................................. 10

14. Breaks ......................................................................................................................... 10

Part 4— Wages and Allowances ............................................................................................ 10

15. Classifications and minimum rates ............................................................................. 10

16. Payment of wages ....................................................................................................... 12

17. Allowances ................................................................................................................. 12

18. Superannuation ........................................................................................................... 15

Part 5— Overtime and Penalty Rates ................................................................................... 17

19. Overtime and penalty rates ......................................................................................... 17

Part 6— Leave and Public Holidays ..................................................................................... 19

20. Annual leave ............................................................................................................... 19

21. Personal/carer’s leave and compassionate leave ........................................................ 24

22. Parental leave and related entitlements ...................................................................... 24

23. Community service leave ........................................................................................... 25

24. Family and domestic violence leave .......................................................................... 25

25. Public holidays ........................................................................................................... 25

Part 7— Consultation and Dispute Resolution .................................................................... 26

26. Consultation about major workplace change ............................................................. 26

27. Consultation about changes to rosters or hours of work ............................................ 27

28. Dispute resolution ....................................................................................................... 27

Part 8— Termination of Employment and Redundancy .................................................... 29

29. Termination of employment ....................................................................................... 29

30. Redundancy ................................................................................................................ 30

Schedule A —Summary of Hourly Rates of Pay ................................................................. 32

Schedule B —Summary of Monetary Allowances ............................................................... 35

Schedule C —Supported Wage System ................................................................................ 36

Schedule D — Agreement for Time Off Instead of Payment for Overtime ....................... 39

Schedule E —Agreement to Take Annual Leave in Advance ............................................ 40

Schedule F —Agreement to Cash Out Annual Leave ......................................................... 41

Part 1— Application and Operation of this Award

1.                       Title and commencement

1.1                    This award is the Commercial Sales Award 2020.

1.2                    This modern award commenced operation on 1 January 2010. The terms of the award have been varied since that date .

1.3                    A variation to this award does not affect any right, privilege, obligation or liability that a person acquired, accrued or incurred under the award as it existed prior to that variation.

2.                       Definitions

[Varied by PR733916 ]

In this award, unless the contrary intention appears:

Act means the Fair Work Act 2009 (Cth).

Advertising Sales Representative means a person employed, substantially away from the employer’s place of business, in soliciting orders, obtaining sales leads or appointments or otherwise promoting sales for, or selling advertising space or time of any kind.

[Definition of casual employee inserted by PR733916 from 27Sep21]

casual employee has the meaning given by section 15A of the Act .

Commercial Traveller means a person employed, substantially away from the employer’s place of business, for the purpose of soliciting orders for, or selling articles, goods, wares or merchandise or material for wholesale sale, for resale, or for use in or in connection with the production and/or preparation and/or distribution of commodities for sale by the customer.

commission means any financial incentive payment, financial bonus or financial reward directly related to the soliciting or obtaining of orders or business by an individual Commercial Traveller, but will not be deemed to include any incentive payment, bonus or reward periodically made by the employer on the basis of profitability or performance of the employee, or any section, group or division thereof.

defined benefit member has the meaning given by the Superannuation Guarantee (Administration) Act 1992 (Cth).

employee means national system employee within the meaning of the Act .

employer means national system employer within the meaning of the Act .

exempt public sector superannuation scheme has the meaning given by the Superannuation Industry (Supervision) Act 1993 (Cth).

home means the employee’s usual place of residence.

Merchandiser means a person who is employed away from, or substantially away from, the employer’s place of business in promoting the employer’s products, re‑ordering stock and preparing display units and gondola ends, and who in conjunction with these principal functions may solicit orders as a minor feature of the employee’s work.

MySuper product has the meaning given by the Superannuation Industry (Supervision) Act 1993 (Cth).

NES means the National Employment Standards as contained in sections 59 to 131 of the Fair Work Act 2009 (Cth) (the Act ).

on-hire means the on-hire of an employee by their employer to a client, where such employee works under the general guidance and instruction of the client or a representative of the client.

Probationary Traveller means an Advertising Sales Representative or Commercial Traveller who has less than 3 months’ service with the employer.

standard rate means the minimum weekly rate for a Commercial Traveller in clause  15.1 .

3.                       The National Employment Standards and this award

3.1                    The National Employment Standards (NES) and this award contain the minimum conditions of employment for employees covered by this award.

3.2                    Where this award refers to a condition of employment provided for in the NES , the NES definition applies.

3.3                    The employer must ensure that copies of the award and the NES are available to all employees to whom they apply, either on a notice board which is conveniently located at or near the workplace or through accessible electronic means.

4.                       Coverage

[Varied by PR743445 ]

4.1                    This occupational award covers employers throughout Australia with respect to Commercial Travellers, Merchandisers and Advertising Sales Representatives and those employees unless any other modern award contains classifications that apply to such persons, in which case the other modern award prevails.

4.2                    This award does not cover:

[4.2(a) varied by PR743445 ppc 11Jul22]

(a)           employers and employees covered by the Clerks—Private Sector Award 2020; the Contract Call Centres Award 2020; or the Graphic Arts, Printing and Publishing Award 2020 ;

(b)          employees excluded from award coverage by the Act ;

(c)           employees who are covered by a modern enterprise award or an enterprise instrument (within the meaning of the Fair Work (Transitional Provisions and Consequential Amendments) Act 2009 (Cth)), or employers in relation to those employees; or

(d)          employees who are covered by a State reference public sector modern award or a State reference public sector transitional award (within the meaning of the Fair Work (Transitional Provisions and Consequential Amendments) Act 2009 (Cth)), or employers in relation to those employees.

4.3                    This award covers any employer which supplies on-hire employees in occupations set out in clause 4.1 and those on-hire employees, if the employer is not covered by another modern award containing a classification which is more appropriate to the work performed by the employee. Clause 4.3 operates subject to the exclusions from coverage in this award.

4.4                    This award covers employers which provide group training services for trainees engaged in any of the occupations set out at clause  4.1 and those trainees engaged by a group training service hosted by a company to perform work at a location where the activities described in clause  4.1 are being performed. Clause 4.4 operates subject to the exclusions from coverage in this award.

4.5                    Where an employer is covered by more than one award, an employee of that employer is covered by the award classification which is most appropriate to the work performed by the employee and to the environment in which the employee normally performs the work.

5.                       Individual flexibility arrangements

5.1                    Despite anything else in this award, an employer and an individual employee may agree to vary the application of the terms of this award relating to any of the following in order to meet the genuine needs of both the employee and the employer:

(a)           arrangements for when work is performed; or

(b)          overtime rates; or

(c)           penalty rates; or

(d)          allowances; or

(e)           annual leave loading.

5.2                    An agreement must be one that is genuinely made by the employer and the individual employee without coercion or duress.

5.3                    An agreement may only be made after the individual employee has commenced employment with the employer.

5.4                    An employer who wishes to initiate the making of an agreement must:

(a)           give the employee a written proposal; and

(b)          if the employer is aware that the employee has, or reasonably should be aware that the employee may have, limited understanding of written English, take reasonable steps (including providing a translation in an appropriate language) to ensure that the employee understands the proposal.

5.5                    An agreement must result in the employee being better off overall at the time the agreement is made than if the agreement had not been made.

5.6                    An agreement must do all of the following:

(a)           state the names of the employer and the employee; and

(b)          identify the award term, or award terms, the application of which is to be varied; and

(c)           set out how the application of the award term, or each award term, is varied; and

(d)          set out how the agreement results in the employee being better off overall at the time the agreement is made than if the agreement had not been made; and

(e)           state the date the agreement is to start.

5.7                    An agreement must be:

(a)           in writing; and

(b)          signed by the employer and the employee and, if the employee is under 18 years of age, by the employee’s parent or guardian.

5.8                    Except as provided in clause 5.7(b) , an agreement must not require the approval or consent of a person other than the employer and the employee.

5.9                    The employer must keep the agreement as a time and wages record and give a copy to the employee.

5.10                The employer and the employee must genuinely agree, without duress or coercion to any variation of an award provided for by an agreement.

5.11                An agreement may be terminated:

(a)           at any time, by written agreement between the employer and the employee; or

(b)          by the employer or employee giving 13 weeks’ written notice to the other party (reduced to 4 weeks if the agreement was entered into before the first full pay period starting on or after 4 December 2013).

NOTE: If an employer and employee agree to an arrangement that purports to be an individual flexibility arrangement under this award term and the arrangement does not meet a requirement set out in section 144 then the employee or the employer may terminate the arrangement by giving written notice of not more than 28 days (see section 145 of the Act ).

5.12                An agreement terminated as mentioned in clause 5.11(b) ceases to have effect at the end of the period of notice required under that clause.

5.13                The right to make an agreement under clause 5 is additional to, and does not affect, any other term of this award that provides for an agreement between an employer and an individual employee.

6.                       Requests for flexible working arrangements

[6 substituted by PR763288 ppc 01Aug23]

Requests for flexible working arrangements are provided for in the NES .

NOTE: Disputes about requests for flexible working arrangements may be dealt with under clause  28 — Dispute resolution and/or under section 65B of the Act .

7.                       Facilitative provisions

7.1                    A facilitative provision provides that the standard approach in an award provision may be departed from by agreement between an employer and an individual employee, or an employer and the majority of employees in the enterprise or part of the enterprise concerned.

7.2                    Facilitative provisions in this award are contained in the following clauses:

   

Part 2— Types of Employment

8.                       Types of employment

8.1                    Employees under this award will be employed in one of the following categories:

(a)           full-time;

(b)          part-time; or

(c)           casual.

9.                       Full-time employees

9.1                    A full-time employee is engaged to work an average of 38 hours per week.

9.2                    Any employee not specifically engaged as a part-time or casual employee is, for all purposes of this award, a full-time employee unless otherwise specified in the award.

10.                  Part-time employees

10.1                A part-time employee is engaged to work less than an average of 38 hours per week.

10.2                An employee may be employed on a regular part-time basis in any classification in this award.

10.3                Before starting part-time employment the employer and employee must agree on:

(a)           the number of hours to be worked by the employee;

(b)          the days on which they will be worked; and

(c)           the starting and finishing times for the work.

10.4                The terms of this agreement may be varied by consent and such variation will be in writing.

10.5                An employer is required to roster a part-time employee for a minimum of 3 consecutive hours on any shift.

11.                  Casual employees

[Varied by PR723885 , PR733916 ]

[11.1 deleted by PR733916 from 27Sep21]

11.1                Casual loading

[11.2 renumbered as 11.1 by PR733916 from 27Sep21]

[11.1(a) substituted by PR723885 ppc 20Nov20]

(a)           For each ordinary hour worked, a casual employee must be paid:

(i)            the minimum hourly rate for the classification in which they are employed; and

(ii)          a loading of 25% of the minimum hourly rate.

(b)          The casual loading is paid instead of entitlements to leave and other matters from which casuals are excluded by the terms of this award and the NES .

[New 11.3 inserted by PR723885 ppc 20Nov20; 11.3 renumbered as 11.2 by PR733916 from 27Sep21]

11.2                When a casual employee works overtime, they must be paid the overtime rates in clause 19.2 .

[11.3 renumbered as 11.4 by PR723885 , 11.4 renumbered as 11.3 by PR733916 from 27Sep21]

11.3                A casual employee must be engaged and paid for at least 2 consecutive hours of work on each occasion they are required to attend work.

11.4                Offers and requests for casual conversion

[11.4 renumbered as 11.5 by PR723885 ; 11.5 renumbered as 11.4 and renamed and substituted by PR733916 from 27Sep21]

Offers and requests for conversion from casual employment to full-time or part-time employment are provided for in the NES .

NOTE: Disputes about offers and requests for casual conversion under the NES are to be dealt with under clause 28 — Dispute resolution .

12.                  Statement and terms of engagement

Within 14 days from the commencement of employment, the employer will provide to each employee a written statement containing the information set out below:

(a)           the remuneration payable;

(b)          the vehicle allowance payable or car supplied;

(c)           the rate or rates of commission payable;

(d)          the conditions and terms on which commission or any part thereof is payable or not payable;

(e)           deductions, if any, which are made or may be made to the commission payable; and

(f)            if the employee has a territory, the boundaries or limits of the territory, provided that the employer may change territory boundaries or limits, or move employees from one territory to another on advice to the employee/s concerned.

Part 3— Hours of Work

13.                  Ordinary hours of work

13.1                Maximum weekly hours and requests for flexible working arrangements are provided for in the NES .

13.2                The ordinary hours of work for a full-time employee are an average of 38 per week with a maximum of 152 hours over 28 consecutive days.

13.3                The ordinary hours of work may be worked on any days of the week.

13.4                The ordinary hours of work will not exceed 10 hours on any day.

14.                  Breaks

An employer will allow an employee reasonable time to have regular and normal meals on each day of the employee’s employment.

Part 4— Wages and Allowances

15.                  Classifications and minimum rates

[Varied by PR720159 , PR723829 , PR718901 , PR726419 ; corrected by PR726293 ; varied by PR729342 , PR740768 , PR762192 ]

[15.1 varied by PR718901 ; corrected by PR726293 ; varied by PR729342 , PR740768 , PR762192 ppc 01Jul23]

15.1                An employer must pay an adult employee, other than those employees specified in clause 15.2 , the following minimum rates for ordinary hours worked by the employee:

1 The minimum weekly rate for a Probationary Traveller is based on 90% of the minimum weekly rate for a Commercial Traveller/Advertising Sales Representative.

NOTE: See Schedule A —Summary of Hourly Rates of Pay for a summary of hourly rates of pay including overtime and penalty rates.

15.2                The following employees are not entitled to the minimum rates set out in the table in clause 15.1 :

(a)           an employee receiving a supported wage (refer to Schedule C —Supported Wage System ); and

(b)          a trainee

[15.2(b)(i) varied by PR720159 ppc 18Jun20]

(i)            Schedule E to the Miscellaneous Award 2020 sets out minimum wage rates and conditions for employees undertaking traineeships.

[15.2(b)(ii) varied by PR720159 ppc 18Jun20, PR718901 ppc 01Feb21; corrected by PR726293 ; varied by PR729342 ; corrected by PR737574 ; varied by PR740768 , PR762192 ppc 01Jul23]

(ii)          This award incorporates the terms of Schedule E to the Miscellaneous Award 2020 as at 1 July 2023 . Provided that any reference to “this award” in Schedule E to the Miscellaneous Award 2020 is to be read as referring to the Commercial Sales Award 2020 and not the Miscellaneous Award 2020 .

[Note inserted by PR723829 ppc 01Nov20; deleted by PR726419 ppc 01Feb21]

15.3                Junior minimum rates

The minimum rates for a junior are the following percentages of the wage rate for Commercial Traveller/Advertising Sales Representative:

15.4                No Commercial Traveller (or Probationary Traveller) will be remunerated solely by commission payment, salary or retainer, that is lower than the minimum rate for a Commercial Traveller (or Probationary Traveller) in clause 15.1 .

16.                  Payment of wages

NOTE: Regulations 3.33(3) and 3.46(1)(g) of Fair Work Regulations 2009 set out the requirements for pay records and the content of payslips including the requirement to separately identify any allowance paid.

16.1                Employees will be paid weekly, fortnightly or monthly.

16.2                Wages will be paid by cash, cheque or electronic funds transfer into the employee’s nominated bank account.

16.3                Payment on termination of employment

(a)           The employer must pay an employee no later than 7 days after the day on which the employee’s employment terminates:

(i)            the employee’s wages under this award for any complete or incomplete pay period up to the end of the day of termination; and

(ii)          all other amounts that are due to the employee under this award and the NES .

(b)          The requirement to pay wages and other amounts under clause 16.3(a) is subject to further order of the Commission and the employer making deductions authorised by this award or the Act .

NOTE 1: Section 117(2) of the Act provides that an employer must not terminate an employee’s employment unless the employer has given the employee the required minimum period of notice or “has paid” to the employee payment instead of giving notice.

NOTE 2: Clause 16.3(b) allows the Commission to make an order delaying the requirement to make a payment under clause 16.3 . For example, the Commission could make an order delaying the requirement to pay redundancy pay if an employer makes an application under section 120 of the Act for the Commission to reduce the amount of redundancy pay an employee is entitled to under the NES .

NOTE 3: State and Territory long service leave laws or long service leave entitlements under section 113 of the Act , may require an employer to pay an employee for accrued long service leave on the day on which the employee’s employment terminates or shortly after.

17.                  Allowances

[Varied by PR719053 , PR729526 , PR740932 , PR762358 ]

17.1                An employer must pay to an employee the allowances the employee is entitled to under clause 17 .

NOTE: See Schedule B —Summary of Monetary Allowances for a summary of monetary allowances and method of adjustment.

17.2                Expense-related allowances

(a)           Weekend allowance

[17.2(a) varied by PR719053 , PR740932 , PR762358 ppc 01Jul23]

An allowance of $64.80 will be paid to an employee required by the employer to be away from home (a usual place of residence) or headquarters for any weekend.

(b)          Living away from home allowance

[17.2(b) varied by PR719053 , PR740932 , PR762358 ppc 01Jul23]

An employee required to remain away from their usual place of residence for 2 or more consecutive nights in any one week, Monday to Sunday inclusive, in servicing the employee’s allocated area will be paid an additional allowance of $81.59 per week.

(c)           Vehicle allowance

An employee required by the employer to use the employee’s motor vehicle in the performance of the employee’s duties will be paid an allowance of:

[17.2(c)(i) varied by PR729526 , PR740932 , PR762358 ppc 01Jul23]

(i)            $0.95 per kilometre, for use of the employee’s own motor car; and

[17.2(c)(ii) varied by PR729526 , PR740932 , PR762358 ppc 01Jul23]

(ii)          $0.32 per kilometre for use of the employee’s own motorcycle.

(d)          Vehicle modification reimbursement

Where the employer requires the employee to alter or modify the employee’s own vehicle, the employer will reimburse to the employee the full cost of such alterations or modifications.

(e)           Telephone allowance

(i)            Where an employee does not have a telephone, modem or broadband connection and, at the written request of the employer, the employee is required to have such equipment, the employer must reimburse the reasonable cost of purchase, installation and rental of this equipment.

(ii)          Where an employee makes telephone calls in connection with their employment on the employee’s private telephone at the direction of the employer, the employer must reimburse the reasonable cost of such calls. The employer may request details of all such calls claimed by the employee.

(f)            Expenses and accommodation reimbursement

(i)            In addition to the remuneration payable under clause 15 — Classifications and minimum rates , all reasonable expenses actually and properly incurred by the employee in the discharge of the duties will be reimbursed by the employer, including:

·    approved entertainment expenses;

·    vehicle parking fees where actually and necessarily incurred;

·    3 star class hotel/motel accommodation;

·    expenses for meals and morning or afternoon tea when the employee is required to be away overnight from the usual place of residence at the employee’s usual time for taking such meal, in the course of their employment;

·    laundry expenses incurred by the employee after they have been away from their place of residence for more than one weekend in the course of their employment;

·    first class rail tickets with sleeping accommodation (if available) on overnight journeys, and economy class airline tickets where required; and

·    the cost of garaging by an employee entitled to the living away from home allowance in clause 17.2(b) when such is required by the employer.

(ii)          Such expenses that can be reasonably anticipated will be paid in advance.

(g)           Injury or illness requiring transport

If an employee suffers an injury or illness requiring return to their usual place of residence or to a hospital or other place where the employee may receive medical care, the expenses actually incurred in travelling to any such location will be reimbursed by the employer.

(h)          Change of residence

Any employee (other than a casual) who is directed or required by the employer, in writing, to relocate the employee’s residence to another area, will be reimbursed reasonable costs for relocating personal and household effects and members of their immediate dependent family. Reasonable costs expressed in clause 17.2(h) are to be the amount agreed upon, in writing, between the employer and employee prior to any relocation.

(i)             Training program

An employee required by the employer to undertake any course of instruction or training will have all fees and expenses reimbursed by the employer.

18.                  Superannuation

[Varied by PR771359 ]

18.1                Superannuation legislation

[18.1 substituted by PR771359 ppc 09Apr24]

(a)           The NES and Superannuation legislation, including the Superannuation Guarantee (Administration) Act 1992 (Cth), the Superannuation Guarantee Charge Act 1992 (Cth), the Superannuation Industry (Supervision) Act 1993 (Cth) and the Superannuation (Resolution of Complaints) Act 1993 (Cth), deal with the superannuation rights and obligations of employers and employees.

(b)          The rights and obligations in clause 18 supplement those in superannuation legislation and the NES .

NOTE: Under superannuation legislation:

(a) Individual employees generally have the opportunity to choose their own superannuation fund.

(b) If a new employee does not choose a superannuation fund, the employer must ask the Australian Taxation Office (ATO) whether the employee is an existing member of a stapled superannuation fund and, if stapled fund details are provided by the ATO, make contributions to the stapled fund.

(c) If an employee does not choose a superannuation fund and does not have a stapled fund, the choice of superannuation fund requirements will be satisfied by contributions made to a superannuation fund nominated in the award covering the employee, provided the fund is able to accept contributions for the benefit of the employee.

(d) A fund may not be able to accept contributions for the benefit of an employee if the employee would be a new member of the fund’s MySuper product and the MySuper product is closed to new members because it has failed the performance tests of Australian Prudential Regulation Authority (APRA) for 2 consecutive years.

18.2                Employer contributions

An employer must make such superannuation contributions to a superannuation fund for the benefit of an employee as will avoid the employer being required to pay the superannuation guarantee charge under superannuation legislation with respect to that employee.

18.3                Voluntary employee contributions

(a)           Subject to the governing rules of the relevant superannuation fund, an employee may, in writing, authorise their employer to pay on behalf of the employee a specified amount from the post-taxation wages of the employee into the same superannuation fund as the employer makes the superannuation contributions provided for in clause 18.2 .

(b)          An employee may adjust the amount the employee has authorised their employer to pay from the wages of the employee from the first of the month following the giving of three months’ written notice to their employer.

(c)           The employer must pay the amount authorised under clauses 18.3(a) or 18.3(b) no later than 28 days after the end of the month in which the deduction authorised under clauses 18.3(a) or 18.3(b) was made.

18.4                Superannuation fund

[18.4 varied by PR771359 ppc 09Apr24]

Unless, to comply with superannuation legislation, the employer is required to make the superannuation contributions provided for in clause 18.2 to another superannuation fund, the employer must make the superannuation contributions provided for in clause 18.2 and pay any amount authorised under clauses 18.3(a) or 18.3(b) to one of the following superannuation funds or its successor, provided that, in respect of new employees, the fund is able to accept new beneficiaries:

(a)           AustralianSuper;

(b)          LUCRF Super;

(c)           CareSuper;

(d)          REST Superannuation;

(e)           Sunsuper;

(f)            MTAA Superannuation Fund;

(g)           any superannuation fund to which the employer was making superannuation contributions for the benefit of its employees before 12 September 2008, provided the superannuation fund is an eligible choice fund and is a fund that offers a MySuper product or is an exempt public sector superannuation scheme; or

(h)          a superannuation fund or scheme which the employee is a defined benefit member of.

18.5                Absence from work

Subject to the governing rules of the relevant superannuation fund, the employer must also make the superannuation contributions provided for in clause 18.2 and pay the amount authorised under clauses 18.3(a) or 18.3(b) :

(a)           Paid leave— while the employee is on any paid leave;

(b)          Work-related injury or illness —for the peri od of absence from work (subject to a maximum of 52 weeks) of the employee due to work-related injury or work-related illness provided that:

(i)            the employee is receiving workers compensation payments or is receiving regular payments directly from the employer in accordance with the statutory requirements; and

(ii)          the employee remains employed by the employer.

Part 5— Overtime and Penalty Rates

19.                  Overtime and penalty rates

[Varied by PR723885 , PR763288 ]

19.1                Full-time and part-time employees

[19.1—Overtime renamed as Full-time and part-time employees and substituted by PR723885 ppc 20Nov20]

(a)           Monday to Friday work

A full-time or part-time employee directed by the employer to perform any work after 6.00 pm Monday to Friday inclusive, or in excess of the ordinary hours of work provided in clause 13 — Ordinary hours of work , will be paid at a rate of 150% of the applicable minimum hourly rate set out in clause 15 — Classifications and minimum rates .

(b)          Saturday work

A full-time or part-time employee directed by the employer to perform any work on a Saturday will be paid at a rate of 150% of the applicable minimum hourly rate set out in clause 15 — Classifications and minimum rates , with a minimum payment of 2 hours.

(c)           Sunday work

A full-time or part-time employee directed by the employer to perform any work on a Sunday will be paid at a rate of 200% of the applicable minimum hourly rate set out in clause  15 — Classifications and minimum rates , with a minimum payment of 3 hours.

19.2                Casual employees

[19.2— Saturday work renamed as Casual employees and substituted by PR723885 ppc 20Nov20]

A casual employee directed by the employer to perform any work after 6.00 pm Monday to Friday inclusive, or in excess of the ordinary hours of work provided in clause 13 — Ordinary hours of work , will be paid at a rate of 175% of the applicable minimum hourly rate set out in clause 15 — Classifications and minimum rates .

A casual employee directed by the employer to perform any work on a Saturday will be paid at a rate of 175% of the applicable minimum hourly rate set out in clause 15 — Classifications and minimum rates , with a minimum payment of 2 hours.

A casual employee directed by the employer to perform any work on a Sunday will be paid at a rate of 225% of the applicable minimum hourly rate set out in clause 15 — Classifications and minimum rates , with a minimum payment of 3 hours.

NOTE: The overtime rates for casual employees have been calculated by adding the casual loading prescribed by clause 11.1(a)(ii) to the overtime rates for full-time and part-time employees prescribed by clause 19.1 .

[19.3 deleted by PR723885 ppc 20Nov20]

19.3                Time off instead of payment for overtime

[19.4 renumbered as 19.3 by PR723885 ppc 20Nov20]

(a)           An employee and employer may agree in writing to the employee taking time off instead of being paid for a particular amount of overtime that has been worked by the employee.

(b)          Any amount of overtime that has been worked by an employee in a particular pay period and that is to be taken as time off instead of the employee being paid for it must be the subject of a separate agreement under clause 19.3 .

(c)           An agreement must state each of the following:

(i)            the number of overtime hours to which it applies and when those hours were worked;

(ii)          that the employer and employee agree that the employee may take time off instead of being paid for the overtime;

(iii)        that, if the employee requests at any time, the employer must pay the employee, for overtime covered by the agreement but not taken as time off, at the overtime rate applicable to the overtime when worked;

(iv)        that any payment mentioned in clause 19.3(c)(iii) must be made in the next pay period following the request.

NOTE: An example of the type of agreement required by clause 19.3 is set out at Schedule D — Agreement for Time Off Instead of Payment for Overtime . There is no requirement to use the form of agreement set out at Schedule D — Agreement for Time Off Instead of Payment for Overtime . An agreement under clause 19.3 can also be made by an exchange of emails between the employee and employer, or by other electronic means.

(d)          The period of time off that an employee is entitled to take is the same as the number of overtime hours worked.

EXAMPLE: By making an agreement under clause 19.3 an employee who worked 2 overtime hours is entitled to 2 hours’ time off.

(e)           Time off must be taken:

(i)            within the period of 6 months after the overtime is worked; and

(ii)          at a time or times within that period of 6 months agreed by the employee and employer.

(f)            If the employee requests at any time, to be paid for overtime covered by an agreement under clause 19.3 but not taken as time off, the employer must pay the employee for the overtime, in the next pay period following the request, at the overtime rate applicable to the overtime when worked.

(g)           If time off for overtime that has been worked is not taken within the period of 6 months mentioned in clause 19.3(e) , the employer must pay the employee for the overtime, in the next pay period following those 6 months, at the overtime rate applicable to the overtime when worked.

(h)          The employer must keep a copy of any agreement under clause 19.3 as an employee record.

(i)             An employer must not exert undue influence or undue pressure on an employee in relation to a decision by the employee to make, or not make, an agreement to take time off instead of payment for overtime.

(j)            An employee may, under section 65 of the Act , request to take time off, at a time or times specified in the request or to be subsequently agreed by the employer and the employee, instead of being paid for overtime worked by the employee. If the employer agrees to the request then clause 19.3 will apply, including the requirement for separate written agreements under clause 19.3(b) for overtime that has been worked.

[Note varied by PR763288 ppc 01Aug23]

NOTE: If an employee makes a request under section 65 of the Act for a change in working arrangements, the employer may only refuse that request on reasonable business grounds (see section 65A(3) of the Act ).

(k)          If, on the termination of the employee’s employment, time off for overtime worked by the employee to which clause 19.3 applies has not been taken, the employer must pay the employee for the overtime at the overtime rate applicable to the overtime when worked.

NOTE: Under section 345(1) of the Act , a person must not knowingly or recklessly make a false or misleading representation about the workplace rights of another person under clause 19.3 .

Part 6— Leave and Public Holidays

20.                  Annual leave

[Varied by PR751092 ]

20.1                Annual leave is provided for in the NES .

20.2                Annual leave does not apply to a casual employee.

20.3                Leave loading

(a)           During a period of annual leave an employee who does not receive commission must also be paid a loading of 17.5% calculated on the employee’s minimum rate of pay as prescribed by clause 15 — Classifications and minimum rates .

(b)          Where the employee receives commission, such employee will, in addition to their ordinary pay, receive either the average of the commission payments earned over the preceding 12 months or the loading prescribed in clause  20.3(a) , whichever is the greater.

NOTE: Where an employee is receiving over-award payments such that the employee’s base rate of pay is higher than the rate specified under this award, the employee is entitled to receive the higher rate while on a period of paid annual leave (see sections 16 and 90 of the Act ).

20.4                Conversion to hourly entitlement

An employer may reach agreement with the majority of employees concerned to convert the annual leave entitlement in section 87 of the Act to an hourly entitlement for administrative ease.

20.5                Annual leave in advance

(a)           An employer and employee may agree in writing to the employee taking a period of paid annual leave before the employee has accrued an entitlement to the leave.

(b)          An agreement must:

(i)            state the amount of leave to be taken in advance and the date on which leave is to commence; and

(ii)          be signed by the employer and employee and, if the employee is under 18 years of age, by the employee’s parent or guardian.

NOTE: An example of the type of agreement required by clause 20.5 is set out at Schedule E —Agreement to Take Annual Leave in Advance . There is no requirement to use the form of agreement set out at Schedule E —Agreement to Take Annual Leave in Advance .

(c)           The employer must keep a copy of any agreement under clause 20.5 as an employee record.

(d)          If, on the termination of the employee’s employment, the employee has not accrued an entitlement to all of a period of paid annual leave already taken in accordance with an agreement under clause 20.5 , the employer may deduct from any money due to the employee on termination an amount equal to the amount that was paid to the employee in respect of any part of the period of annual leave taken in advance to which an entitlement has not been accrued.

20.6                Direction to take annual leave during shutdown

[20.6 renamed and substituted by PR751092 ppc 01May23]

(a)           Clause 20.6 applies if an employer:

(i)            intends to shut down all or part of its operation for a particular period ( temporary shutdown period ); and

(ii)          wishes to require affected employees to take paid annual leave during that period.

(b)          The employer must give the affected employees 28 days’ written notice of a temporary shutdown period, or any shorter period agreed between the employer and the majority of relevant employees.

(c)           The employer must give written notice of a temporary shutdown period to any employee who is engaged after the notice is given under clause 20.6(b) and who will be affected by that period, as soon as reasonably practicable after the employee is engaged.

(d)          The employer may direct the employee to take a period of paid annual leave to which the employee has accrued an entitlement during a temporary shutdown period.

(e)           A direction by the employer under clause 20.6(d) :

(i)            must be in writing; and

(ii)          must be reasonable.

(f)            The employee must take paid annual leave in accordance with a direction under clause 20.6(d) .

(g)           In respect of any part of a temporary shutdown period which is not the subject of a direction under clause 20.6(d) , an employer and an employee may agree, in writing, for the employee to take leave without pay during that part of the temporary shutdown period.

(h)          An employee may take annual leave in advance during a temporary shutdown period in accordance with an agreement under clause 20.5 .

(i)             In determining the amount of paid annual leave to which an employee has accrued an entitlement, any period of paid annual leave taken in advance by the employee, in accordance with an agreement under clause 20.5 , to which an entitlement has not been accrued, is to be taken into account.

(j)            Clauses 20.7 to 20.9 do not apply to a period of annual leave that an employee is required to take during a temporary shutdown period in accordance with clause 20.6 .

20.7                Excessive leave accruals: general provision

NOTE: Clauses 20.7 to 20.9 contain provisions, additional to the NES , about the taking of paid annual leave as a way of dealing with the accrual of excessive paid annual leave. See Part 2.2, Division 6 of the Act .

(a)           An employee has an excessive leave accrual if the employee has accrued more than 8 weeks’ paid annual leave.

(b)          If an employee has an excessive leave accrual, the employer or the employee may seek to confer with the other and genuinely try to reach agreement on how to reduce or eliminate the excessive leave accrual.

(c)           Clause 20.8 sets out how an employer may direct an employee who has an excessive leave accrual to take paid annual leave.

(d)          Clause 20.9 sets out how an employee who has an excessive leave accrual may require an employer to grant paid annual leave requested by the employee.

20.8                Excessive leave accruals: direction by employer that leave be taken

(a)           If an employer has genuinely tried to reach agreement with an employee under clause 20.7(b) but agreement is not reached (including because the employee refuses to confer), the employer may direct the employee in writing to take one or more periods of paid annual leave.

(b)          However, a direction by the employer under clause 20.8(a) :

(i)            is of no effect if it would result at any time in the employee’s remaining accrued entitlement to paid annual leave being less than 6 weeks when any other paid annual leave arrangements (whether made under clause 20.7 , 20.8 or 20.9 or otherwise agreed by the employer and employee) are taken into account; and

(ii)          must not require the employee to take any period of paid annual leave of less than one week; and

(iii)        must not require the employee to take a period of paid annual leave beginning less than 8 weeks, or more than 12 months, after the direction is given; and

(iv)        must not be inconsistent with any leave arrangement agreed by the employer and employee.

(c)           The employee must take paid annual leave in accordance with a direction under clause 20.8(a) that is in effect.

(d)          An employee to whom a direction has been given under clause 20.8(a) may request to take a period of paid annual leave as if the direction had not been given.

NOTE 1: Paid annual leave arising from a request mentioned in clause 20.8(d) may result in the direction ceasing to have effect. See clause 20.8(b)(i) .

NOTE 2: Under section 88(2) of the Act , the employer must not unreasonably refuse to agree to a request by the employee to take paid annual leave.

20.9                Excessive leave accruals: request by employee for leave

(a)           If an employee has genuinely tried to reach agreement with an employer under clause 20.7(b) but agreement is not reached (including because the employer refuses to confer), the employee may give a written notice to the employer requesting to take one or more periods of paid annual leave.

(b)          However, an employee may only give a notice to the employer under clause 20.9(a) if:

(i)            the employee has had an excessive leave accrual for more than 6 months at the time of giving the notice; and

(ii)          the employee has not been given a direction under clause 20.8(a) that, when any other paid annual leave arrangements (whether made under clause 20.7 , 20.8 or 20.9 or otherwise agreed by the employer and employee) are taken into account, would eliminate the employee’s excessive leave accrual.

(c)           A notice given by an employee under clause 20.9(a) must not:

(i)            if granted, result in the employee’s remaining accrued entitlement to paid annual leave being at any time less than 6 weeks when any other paid annual leave arrangements (whether made under clause 20.7 , 20.8 or 20.9 or otherwise agreed by the employer and employee) are taken into account; or

(ii)          provide for the employee to take any period of paid annual leave of less than one week; or

(iii)        provide for the employee to take a period of paid annual leave beginning less than 8 weeks, or more than 12 months, after the notice is given; or

(iv)        be inconsistent with any leave arrangement agreed by the employer and employee.

(d)          An employee is not entitled to request by a notice under clause 20.9(a) more than 4 weeks’ paid annual leave in any period of 12 months.

(e)           The employer must grant paid annual leave requested by a notice under clause 20.9(a) .

20.10            Cashing out of annual leave

(a)           Paid annual leave must not be cashed out except in accordance with an agreement under clause 20.10 .

(b)          Each cashing out of a particular amount of paid annual leave must be the subject of a separate agreement under clause 20.10 .

(c)           An employer and an employee may agree in writing to the cashing out of a particular amount of accrued paid annual leave by the employee.

(d)          An agreement under clause 20.10 must state:

(i)            the amount of leave to be cashed out and the payment to be made to the employee for it; and

(ii)          the date on which the payment is to be made.

(e)           An agreement under clause 20.10 must be signed by the employer and employee and, if the employee is under 18 years of age, by the employee’s parent or guardian.

(f)            The payment must not be less than the amount that would have been payable had the employee taken the leave at the time the payment is made.

(g)           An agreement must not result in the employee’s remaining accrued entitlement to paid annual leave being less than 4 weeks.

(h)          The maximum amount of accrued paid annual leave that may be cashed out in any period of 12 months is 2 weeks.

(i)             The employer must keep a copy of any agreement under clause 20.10 as an employee record.

NOTE 1: Under section 344 of the Act , an employer must not exert undue influence or undue pressure on an employee to make, or not make, an agreement under clause  20.10 .

NOTE 2: Under section 345(1) of the Act , a person must not knowingly or recklessly make a false or misleading representation about the workplace rights of another person under clause 20.10 .

NOTE 3: An example of the type of agreement required by clause 20.10 is set out at Schedule F —Agreement to Cash Out Annual Leave . There is no requirement to use the form of agreement set out at Schedule F —Agreement to Cash Out Annual Leave .

21.                  Personal/carer’s leave and compassionate leave

Personal/carer’s leave and compassionate leave are provided for in the NES .

22.                  Parental leave and related entitlements

[22 varied by PR763288 ppc 01Aug23]

Parental leave and related entitlements are provided for in the NES .

NOTE: Disputes about requests for extensions to unpaid parental leave may be dealt with under clause  28 — Dispute resolution and/or under section 76B of the Act .

23.                  Community service leave

Community service leave is provided for in the NES .

24.                  Family and domestic violence leave

[24—Unpaid family and domestic violence leave renamed and substituted by PR750453 ppc 15Mar23]

Family and domestic violence leave is provided for in the NES .

NOTE 1: Information provided to employers concerning an employee’s experience of family and domestic violence is sensitive and if mishandled can have adverse consequences for the employee. Employers are subject to confidentiality requirements regarding the handling of this information under section 106C of the Act and requirements as to what can be reported on payslips pursuant to regulations 3.47 and 3.48 of the Fair Work Regulations 2009 .

NOTE 2: Depending upon the circumstances, evidence that would satisfy a reasonable person of the employee’s need to take family and domestic violence leave may include a document issued by the police service, a court or family violence support service, or a statutory declaration.

25.                  Public holidays

[Varied by PR747569 ]

25.1                Public holiday entitlements are provided for in the NES .

25.2                Substitution of public holidays by agreement at the enterprise

(a)           An employer and employee may agree to substitute another day for a day that would otherwise be a public holiday under the NES .

(b)          An employer and employee may agree to substitute another part-day for a part-day that would otherwise be a part-day public holiday under the NES .

[25.3 varied by PR747569 ppc 14Nov22]

25.3                All work done by an employee, other than travelling, at the request of the employer on a public holiday or a substitute day or part-day will be paid at the rate of 250% of the minimum hourly rate with a minimum payment of 3 hours. Provided that instead of such payment, 2 and a half days’ leave with pay may be granted in respect of each such holiday, at a time mutually agreed between the employer and the employee.

[25.4 varied by PR747569 ppc 14Nov22]

25.4                All travelling in connection with work by an employee at the request of the employer on a public holiday or a substitute day or part-day will be paid for at the rate of 150% of the minimum hourly rate with a minimum payment as for 3 hours’ travelling. Provided that instead of such payment, one and a half days’ leave with pay may be granted in respect of each holiday, at a time mutually agreed between the employer and the employee.

25.5                Part-day public holidays

[25.5 substituted by PR747569 ppc 14Nov22]

(a)           If a public holiday is a part-day public holiday, then in relation to leave with pay, clauses 25.3 and 25.4 apply on a pro-rata basis for the number of ordinary hours on the part-day public holiday.

(b)          Hours of work performed immediately before or after a part-day public holiday, that form part of one continuous shift, are counted as part of the minimum payment/engagement period in clauses 25.3 and 25.4 .

Part 7— Consultation and Dispute Resolution

26.                  Consultation about major workplace change

26.1                If an employer makes a definite decision to make major changes in production, program, organisation, structure or technology that are likely to have significant effects on employees, the employer must:

(a)           give notice of the changes to all employees who may be affected by them and their representatives (if any); and

(b)          discuss with affected employees and their representatives (if any):

(i)            the introduction of the changes; and

(ii)          their likely effect on employees; and

(iii)        measures to avoid or reduce the adverse effects of the changes on employees; and

(c)           commence discussions as soon as practicable after a definite decision has been made.

26.2                For the purposes of the discussion under clause 26.1(b) , the employer must give in writing to the affected employees and their representatives (if any) all relevant information about the changes including:

(a)           their nature; and

(b)          their expected effect on employees; and

(c)           any other matters likely to affect employees.

26.3                Clause 26.2 does not require an employer to disclose any confidential information if its disclosure would be contrary to the employer’s interests.

26.4                The employer must promptly consider any matters raised by the employees or their representatives about the changes in the course of the discussion under clause 26.1(b) .

26.5                In clause 26 significant effects , on employees, includes any of the following:

(a)           termination of employment; or

(b)          major changes in the composition, operation or size of the employer’s workforce or in the skills required; or

(c)           loss of, or reduction in, job or promotion opportunities; or

(d)          loss of, or reduction in, job tenure; or

(e)           alteration of hours of work; or

(f)            the need for employees to be retrained or transferred to other work or locations; or

(g)           job restructuring.

26.6                Where this award makes provision for alteration of any of the matters defined at clause 26.5 , such alteration is taken not to have significant effect.

27.                  Consultation about changes to rosters or hours of work

27.1                Clause 27 applies if an employer proposes to change the regular roster or ordinary hours of work of an employee, other than an employee whose working hours are irregular, sporadic or unpredictable.

27.2                The employer must consult with any employees affected by the proposed change and their representatives (if any).

27.3                For the purpose of the consultation, the employer must:

(a)           provide to the employees and representatives mentioned in clause 27.2 information about the proposed change (for example, information about the nature of the change and when it is to begin); and

(b)          invite the employees to give their views about the impact of the proposed change on them (including any impact on their family or caring responsibilities) and also invite their representative (if any) to give their views about that impact.

27.4                The employer must consider any views given under clause 27.3(b) .

27.5                Clause 27 is to be read in conjunction with any other provisions of this award concerning the scheduling of work or the giving of notice.

28.         Dispute resolution

[Varied by PR763288 ]

28.1                Clause 28 sets out the procedures to be followed if a dispute arises about a matter under this award or in relation to the NES .

28.2                The parties to the dispute must first try to resolve the dispute at the workplace through discussion between the employee or employees concerned and the relevant supervisor.

28.3                If the dispute is not resolved through discussion as mentioned in clause 28.2 , the parties to the dispute must then try to resolve it in a timely manner at the workplace through discussion between the employee or employees concerned and more senior levels of management, as appropriate.

28.4                If the dispute is unable to be resolved at the workplace and all appropriate steps have been taken under clauses 28.2 and 28.3 , a party to the dispute may refer it to the Fair Work Commission.

28.5                The parties may agree on the process to be followed by the Fair Work Commission in dealing with the dispute, including mediation, conciliation and consent arbitration.

28.6                If the dispute remains unresolved, the Fair Work Commission may use any method of dispute resolution that it is permitted by the Act to use and that it considers appropriate for resolving the dispute.

28.7                A party to the dispute may appoint a person, organisation or association to support and/or represent them in any discussion or process under clause 28 .

28.8                While procedures are being followed under clause 28 in relation to a dispute:

(a)           work must continue in accordance with this award and the Act ; and

(b)          an employee must not unreasonably fail to comply with any direction given by the employer about performing work, whether at the same or another workplace, that is safe and appropriate for the employee to perform.

28.9                Clause 28.8 is subject to any applicable work health and safety legislation.

[Note 1 varied by PR763288 ppc 01Aug23]

NOTE 1: In addition to clause  28 , a dispute resolution procedure for disputes regarding the NES entitlement to request flexible working arrangements is contained in section 65B of the Act .

[Note 2 varied by PR763288 ppc 01Aug23]

NOTE 2: In addition to clause  28 , a dispute resolution procedure for disputes regarding the NES entitlement to request an extension to unpaid parental leave is contained in section 76B of the Act .

Part 8— Termination of Employment and Redundancy

29.                  Termination of employment

NOTE: The NES sets out requirements for notice of termination by an employer. See sections 117 and 123 of the Act .

29.1                Notice of termination by an employee

(a)           Clause 29.1 applies to all employees except those identified in sections 123(1) and 123(3) of the Act .

(b)          An employee must give the employer notice of termination in accordance with Table 1—Period of notice of at least the period specified in column 2 according to the period of continuous service of the employee specified in column 1.

Table 1—Period of notice

NOTE: The notice of termination required to be given by an employee is the same as that required of an employer except that the employee does not have to give additional notice based on the age of the employee.

(c)           In clause 29.1(b) continuous service has the same meaning as in section 117 of the Act .

(d)          If an employee who is at least 18 years old does not give the period of notice required under clause 29.1(b) , then the employer may deduct from wages due to the employee under this award an amount that is no more than one week’s wages for the employee.

(e)           If the employer has agreed to a shorter period of notice than that required under clause 29.1(b) , then no deduction can be made under clause 29.1(d) .

(f)            Any deduction made under clause 29.1(d) must not be unreasonable in the circumstances.

29.2                Job search entitlement

(a)           Where an employer has given notice of termination to an employee, the employee must be allowed time off without loss of pay of up to one day for the purpose of seeking other employment.

(b)          The time off under clause 29.2 is to be taken at times that are convenient to the employee after consultation with the employer.

30.                  Redundancy

NOTE: Redundancy pay is provided for in the NES . See sections 119 to 123 of the Act .

30.1                Transfer to lower paid duties on redundancy

(a)           Clause 30.1 applies if, because of redundancy, an employee is transferred to new duties to which a lower ordinary rate of pay applies.

(b)          The employer may:

(i)            give the employee notice of the transfer of at least the same length as the employee would be entitled to under section 117 of the Act as if it were a notice of termination given by the employer; or

(ii)          transfer the employee to the new duties without giving notice of transfer or before the expiry of a notice of transfer, provided that the employer pays the employee as set out in clause 30.1(c) .

(c)           If the employer acts as mentioned in clause 30.1(b)(ii) , the employee is entitled to a payment of an amount equal to the difference between the ordinary rate of pay of the employee (inclusive of all-purpose allowances, shift rates and penalty rates applicable to ordinary hours) for the hours of work the employee would have worked in the first role, and the ordinary rate of pay (also inclusive of all-purpose allowances, shift rates and penalty rates applicable to ordinary hours) of the employee in the second role for the period for which notice was not given.

30.2                Employee leaving during redundancy notice period

(a)           An employee given notice of termination in circumstances of redundancy may terminate their employment during the minimum period of notice prescribed by section 117(3) of the Act .

(b)          The employee is entitled to receive the benefits and payments they would have received under clause 30 or under sections 119 to 123 of the Act had they remained in employment until the expiry of the notice.

(c)           However, the employee is not entitled to be paid for any part of the period of notice remaining after the employee ceased to be employed.

30.3                Job search entitlement

(a)           Where an employer has given notice of termination to an employee in circumstances of redundancy, the employee must be allowed time off without loss of pay of up to one day each week of the minimum period of notice prescribed by section 117(3) of the Act for the purpose of seeking other employment.

(b)          If an employee is allowed time off without loss of pay of more than one day under clause 30.3(a) , the employee must, at the request of the employer, produce proof of attendance at an interview.

(c)           A statutory declaration is sufficient for the purpose of clause 30.3(b) .

(d)          An employee who fails to produce proof when required under clause 30.3(b) is not entitled to be paid for the time off.

(e)           This entitlement applies instead of clause 29.2 .

Schedule A — Summary of Hourly Rates of Pay

[Varied by PR718901 , PR729342 , PR740768 , PR762192 ]

A.1                Full-time and part-time adult employees

A.1.1            Full-time and part-time employees—ordinary and penalty rates

[A.1.1 varied by PR718901 , PR729342 , PR740768 , PR762192 ppc 01Jul23]

A.1.2            Full-time and part-time employees—overtime rates

[A.1.2 varied by PR718901 , PR729342 , PR740768 , PR762192 ppc 01Jul23]

1 After 6.00 pm or in excess of ordinary hours.

A.2                Casual adult employees

A.2.1            Casual employees—ordinary and penalty rates

[A.2.1 varied by PR718901 , PR729342 , PR740768 , PR762192 ppc 01Jul23]

A.3                Junior employees

The junior hourly rate is based on a percentage of the adult Commercial Traveller/Advertising Sales Representative rate in accordance with clause 15.3 as specified. Adult rates apply from 21 years of age in accordance with clause 15.3 .

A.3.1            Full-time and part-time junior employees (Commercial Traveller/Advertising Sales Representative)—ordinary and penalty rates

[A.3.1 varied by PR718901 , PR729342 , PR740768 , PR762192 ppc 01Jul23]

A.3.2            Junior employees (Commercial Traveller/Advertising Sales Representative)—overtime

[A.3.2 varied by PR718901 , PR729342 , PR740768 , PR762192 ppc 01Jul23]

A.3.3            Junior employees (Commercial Traveller/Advertising Sales Representative)—casual employees—ordinary and penalty rates

[A.3.3 varied by PR718901 , PR729342 , PR740768 , PR762192 ppc 01Jul23]

Schedule B — Summary of Monetary Allowances

See clause 17 — Allowances for full details of allowances payable under this award.

B.1                 Expense-related allowances

[B.1.1 varied by PR719053 , PR729526 , PR740932 , PR762358 ppc 01Jul23]

B.1.1            The following expense-related allowances will be payable to employees in accordance with clause 17.2 :

B.1.2            Adjustment of expense-related allowances

(a)           At the time of any adjustment to the standard rate , each expense-related al l owance will be increase d by the relevant adjustment factor. The relevant adjustment factor for this purpose is the percentage movement in the applicable index figure most recently published by the Australian Bureau of Statistics since the allowance was last adjusted.

(b)          The applicable index figure is the index figure published by the Australian Bureau of Statistics for the Eight Capitals Consumer Price Index (Cat No. 6401.0), as follows:

Schedule C — Supported Wage System

[Varied by PR719661 , PR729672 , PR742256 , PR762969 ]

C.1                  This schedule defines the conditions which will apply to employees who because of the effects of a disability are eligible for a supported wage under the terms of this award.

C.2                  In this schedule:

approved assessor means a person accredited by the management unit established by the Commonwealth under the supported wage system to perform assessments of an individual’s productive capacity within the supported wage system.

assessment instrument means the tool provided for under the supported wage system that records the assessment of the productive capacity of the person to be employed under the supported wage system.

disability support pension means the Commonwealth pension scheme to provide income security for persons with a disability as provided under the Social Security Act 1991 (Cth), as amended from time to time, or any successor to that scheme.

relevant minimum wage means the minimum wage prescribed in this award for the class of work for which an employee is engaged.

supported wage system (SWS) means the Commonwealth Government system to promote employment for people who cannot work at full award wages because of a disability, as documented in the Supported Wage System Handbook. The Handbook is available from the following website: www.jobaccess.gov.au .

SWS wage assessment agreement means the document in the form required by the Department of Social Services that records the employee’s productive capacity and agreed wage rate.

C.3                Eligibility criteria

C.3.1            Employees covered by this schedule will be those who are unable to perform the range of duties to the competence level required within the class of work for which the employee is engaged under this award, because of the effects of a disability on their productive capacity and who meet the impairment criteria for receipt of a disability support pension.

C.3.2            This schedule does not apply to any existing employee who has a claim against the employer which is subject to the provisions of workers compensation legislation or any provision of this award relating to the rehabilitation of employees who are injured in the course of their employment.

C.4                Supported wage rates

C.4.1            Employees to whom this schedule applies will be paid the applicable percentage of the relevant minimum wage according to the following schedule:

[C.4.2 varied by PR719661 , PR729672 , PR742256 , PR762969 ppc 01Jul23]

C.4.2            Provided that the minimum amount payable must be not less than $102 per week.

C.4.3            Where an employee’s assessed capacity is 10%, they must receive a high degree of assistance and support.

C.5                Assessment of capacity

C.5.1            For the purpose of establishing the percentage of the relevant minimum wage, the productive capacity of the employee will be assessed in accordance with the SWS by an approved assessor, having consulted the employer and employee and, if the employee so desires, a union which the employee is eligible to join.

C.5.2            All assessments made under this schedule must be documented in an SWS wage assessment agreement, and retained by the employer as a time and wages record in accordance with the Act .

C.6                Lodgement of SWS wage assessment agreement

C.6.1            All SWS wage assessment agreements under the conditions of this schedule, including the appropriate percentage of the relevant minimum wage to be paid to the employee, must be lodged by the employer with the Fair Work Commission.

C.6.2            All SWS wage assessment agreements must be agreed and signed by the employee and employer parties to the assessment. Where a union which has an interest in the award is not a party to the assessment, the assessment will be referred by the Fair Work Commission to the union by certified mail and the agreement will take effect unless an objection is notified to the Fair Work Commission within 10 working days.

C.7                Review of assessment

The assessment of the applicable percentage should be subject to annual or more frequent review on the basis of a reasonable request for such a review. The process of review must be in accordance with the procedures for assessing capacity under the SWS.

C.8                Other terms and conditions of employment

Where an assessment has been made, the applicable percentage will apply to the relevant minimum wage only. Employees covered by the provisions of this schedule will be entitled to the same terms and conditions of employment as other workers covered by this award on a pro rata basis.

C.9                Workplace adjustment

An employer wishing to employ a person under the provisions of this schedule must take reasonable steps to make changes in the workplace to enhance the employee’s capacity to do the job. Changes may involve re-design of job duties, working time arrangements and work organisation in consultation with other workers in the area.

C.10           Trial period

C.10.1        In order for an adequate assessment of the employee’s capacity to be made, an employer may employ a person under the provisions of this schedule for a trial period not exceeding 12 weeks, except that in some cases additional work adjustment time (not exceeding 4 weeks) may be needed.

C.10.2        During that trial period the assessment of capacity will be undertaken and the percentage of the relevant minimum wage for a continuing employment relationship will be determined.

[C.10.3 varied by PR719661 , PR729672 , PR742256 , PR762969 ppc 01Jul23]

C.10.3        The minimum amount payable to the employee during the trial period must be no less than $102 per week.

C.10.4        Work trials should include induction or training as appropriate to the job being trialled.

C.10.5        Where the employer and employee wish to establish a continuing employment relationship following the completion of the trial period, a further contract of employment will be entered into based on the outcome of assessment under clause  C.5 .

Schedule D — Agreement for Time Off Instead of Payment for Overtime

Link to PDF copy of Agreement for Time Off Instead of Payment for Overtime .

Name of employee: _____________________________________________

Name of employer: _____________________________________________

The employer and employee agree that the employee may take time off instead of being paid for the following amount of overtime that has been worked by the employee:

Date and time overtime started: ___/___/20___ ____ am/pm

Date and time overtime ended: ___/___/20___ ____ am/pm

Amount of overtime worked: _______ hours and ______ minutes

The employer and employee further agree that, if requested by the employee at any time, the employer must pay the employee for overtime covered by this agreement but not taken as time off. Payment must be made at the overtime rate applying to the overtime when worked and must be made in the next pay period following the request.

Signature of employee: ________________________________________

Date signed: ___/___/20___

Name of employer representative: ________________________________________

Signature of employer representative: ________________________________________

Schedule E — Agreement to Take Annual Leave in Advance

Link to PDF copy of Agreement to Take Annual Leave in Advance .

The employer and employee agree that the employee will take a period of paid annual leave before the employee has accrued an entitlement to the leave:

The amount of leave to be taken in advance is: ____ hours/days

The leave in advance will commence on: ___/___/20___

Schedule F — Agreement to Cash Out Annual Leave

Link to PDF copy of Agreement to Cash Out Annual Leave .

The employer and employee agree to the employee cashing out a particular amount of the employee’s accrued paid annual leave:

The amount of leave to be cashed out is: ____ hours/days

The payment to be made to the employee for the leave is: $_______ subject to deduction of income tax/after deduction of income tax (strike out where not applicable)

The payment will be made to the employee on: ___/___/20___

[Schedule G—Part-day Public Holidays deleted by PR747569 ppc 14Nov22]

[ Schedule X—Additional Measures During the COVID-19 Pandemic varied by PR720705 , PR723048 ; deleted by PR742720 ppc 17Jun22]

Modern award and related determinations on the Find My Award tool or otherwise on the Fair Work Ombudsman’s website display content taken from the Fair Work Commission’s website. The Fair Work Commission and Fair Work Ombudsman take care to ensure that modern award and related determination copies are accurate at the time of publication but do not guarantee, and accept no legal liability whatsoever arising from or connected to, the accuracy, reliability, currency or completeness of the information displayed by the Find My Award tool or otherwise on the Fair Work Ombudsman’s website or resources.

Any data extracts must be read in conjunction with the provisions in the modern award. These copies and extracts are not a substitute for independent professional advice and users should obtain any appropriate professional advice relevant to their particular circumstances.

cultures

The Fair Work Ombudsman acknowledges the Traditional Custodians of Country throughout Australia and their continuing connection to land, waters, skies and communities. We pay our respects to them, their Cultures, and Elders past, present and future.

June 1, 2012

Traveling Salesman: A Seemingly Unsolvable Problem Offers a Glimpse of the Limits of Computation

By William J. Cook

Is it hopeless to try to compute the shortest route to visit a large number of cities? Not just a good route but the guaranteed shortest. The task is the long-standing challenge known as the traveling salesman problem, or TSP for short.

Finding a method that can quickly solve every example of the TSP would be a stunning breakthrough in mathematics. Using complexity theory, such a method would allow us to solve efficiently any computational problem for which answers can be easily verified. Most mathematicians expect this to be impossible.

But suppose that you are handed the locations of 100,000 cities. Is it really impossible to find the shortest route? We are not asking for a solution to every instance of the TSP, just the quickest way around these specific locations.

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

To take up the challenge, your best bet is to follow Yogi Berra’s advice: “When you come to a fork in the road, take it.” A tool called linear programming allows us to do just that by assigning fractions to roads that join pairs of cities rather than deciding immediately whether to use a road or not. In this model, it is perfectly fine to send half a salesman along both branches of the fork. The process begins with the requirement that, for every city, the fractions assigned to the arriving and departing roads each sum to 1. Then, step by step, further restrictions are added, each involving sums of fractions assigned to roads. Linear programming eventually points us to the best decision for each road and thus the shortest possible route.

I should add that 100,000 cities is not a hypothetical challenge. Current computations are zeroing in on the solution to a pretty set of 100,000 points created by Robert Bosch of Oberlin College, where the tour traces out a drawing of the Mona Lisa. We may not be able to knock off every example of the TSP, but new ideas can push the frontiers of solvability.

Here is the big picture: complexity theory suggests there are limits to the power of general computational techniques in science and elsewhere. What are these limits and how widely do they constrain our quest for knowledge? That is what research into the TSP is all about. �

This article was published in print as "The Case of the Traveling Salesman."

Forgot password? New user? Sign up

Existing user? Log in

Traveling Salesperson Problem

Already have an account? Log in here.

A salesperson needs to visit a set of cities to sell their goods. They know how many cities they need to go to and the distances between each city. In what order should the salesperson visit each city exactly once so that they minimize their travel time and so that they end their journey in their city of origin?

The traveling salesperson problem is an extremely old problem in computer science that is an extension of the Hamiltonian Circuit Problem . It has important implications in complexity theory and the P versus NP problem because it is an NP-Complete problem . This means that a solution to this problem cannot be found in polynomial time (it takes superpolynomial time to compute an answer). In other words, as the number of vertices increases linearly, the computation time to solve the problem increases exponentially.

The following image is a simple example of a network of cities connected by edges of a specific distance. The origin city is also marked.

Network of cities

Here is the solution for that network, it has a distance traveled of only 14. Any other path that the salesman can takes will result in a path length that is more than 14.

Relationship to Graphs

Special kinds of tsp, importance for p vs np, applications.

The traveling salesperson problem can be modeled as a graph . Specifically, it is typical a directed, weighted graph. Each city acts as a vertex and each path between cities is an edge. Instead of distances, each edge has a weight associated with it. In this model, the goal of the traveling salesperson problem can be defined as finding a path that visits every vertex, returns to the original vertex, and minimizes total weight.

To that end, many graph algorithms can be used on this model. Search algorithms like breadth-first search (BFS) , depth-first search (DFS) , and Dijkstra's shortest path algorithm can certainly be used, however, they do not take into consideration that fact that every vertex must be visited.

The Traveling Salesperson Problem (TSP), an NP-Complete problem, is notoriously complicated to solve. That is because the greedy approach is so computational intensive. The greedy approach to solving this problem would be to try every single possible path and see which one is the fastest. Try this conceptual question to see if you have a grasp for how hard it is to solve.

For a fully connected map with \(n\) cities, how many total paths are possible for the traveling salesperson? Show Answer There are (n-1)! total paths the salesperson can take. The computation needed to solve this problem in this way grows far too quickly to be a reasonable solution. If this map has only 5 cities, there are \(4!\), or 24, paths. However, if the size of this map is increased to 20 cities, there will be \(1.22 \cdot 10^{17}\) paths!

The greedy approach to TSP would go like this:

  • Find all possible paths.
  • Find the cost of every paths.
  • Choose the path with the lowest cost.

Another version of a greedy approach might be: At every step in the algorithm, choose the best possible path. This version might go a little quicker, but it's not guaranteed to find the best answer, or an answer at all since it might hit a dead end.

For NP-Hard problems (a subset of NP-Complete problems) like TSP, exact solutions can only be implemented in a reasonable amount of time for small input sizes (maps with few cities). Otherwise, the best approach we can do is provide a heuristic to help the problem move forward in an optimal way. However, these approaches cannot be proven to be optimal because they always have some sort of downside.

Small input sizes

As described, in a previous section , the greedy approach to this problem has a complexity of \(O(n!)\). However, there are some approaches that decrease this computation time.

The Held-Karp Algorithm is one of the earliest applications of dynamic programming . Its complexity is much lower than the greedy approach at \(O(n^2 2^n)\). Basically what this algorithm says is that every sub path along an optimal path is itself an optimal path. So, computing an optimal path is the same as computing many smaller subpaths and adding them together.

Heuristics are a way of ranking possible next steps in an algorithm in the hopes of cutting down computation time for the entire algorithm. They are often a tradeoff of some attribute - such as completeness, accuracy, or precision - in favor of speed. Heuristics exist for the traveling salesperson problem as well.

The most simple heuristic for this problem is the greedy heuristic. This heuristic simply says, at each step of the network traversal, choose the best next step. In other words, always choose the closest city that you have not yet visited. This heuristic seems like a good one because it is simple and intuitive, and it is even used in practice sometimes, however there are heuristics that are proven to be more effective.

Christofides algorithm is another heuristic. It produces at most 1.5 times the optimal weight for TSP. This algorithm involves finding a minimum spanning tree for the network. Next, it creates matchings for the cities of an odd degree (meaning they have an odd number of edges coming out of them), calculates an eulerian path , and converts back to a TSP path.

Even though it is typically impossible to optimally solve TSP problems, there are cases of TSP problems that can be solved if certain conditions hold.

The metric-TSP is an instance of TSP that satisfies this condition: The distance from city A to city B is less than or equal to the distance from city A to city C plus the distance from city C to city B. Or,

\[distance_{AB} \leq distance_{AC} + distance_{CB}\]

This is a condition that holds in the real world, but it can't always be expected to hold for every TSP problem. But, with this inequality in place, the approximated path will be no more than twice the optimal path. Even better, we can bound the solution to a \(3/2\) approximation by using Christofide's Algorithm .

The euclidean-TSP has an even stricter constraint on the TSP input. It states that all cities' edges in the network must obey euclidean distances . Recent advances have shown that approximation algorithms using euclidean minimum spanning trees have reduced the runtime of euclidean-TSP, even though they are also NP-hard. In practice, though, simpler heuristics are still used.

The P versus NP problem is one of the leading questions in modern computer science. It asks whether or not every problem whose solution can be verified in polynomial time by a computer can also be solved in polynomial time by a computer. TSP, for example, cannot be solved in polynomial time (at least that's what is currently theorized). However, TSP can be solved in polynomial time when it is phrased like this: Given a graph and an integer, x, decide if there is a path of length x or less than x . It's easy to see that given a proposed answer to this question, it is simple to check if it is less than or equal to x.

The traveling salesperson problem, like other problems that are NP-Complete, are very important to this debate. That is because if a polynomial time solution can be found to this problems, then \(P = NP\). As it stands, most scientists believe that \(P \ne NP\).

The traveling salesperson problem has many applications. The obvious ones are in the transportation space. Planning delivery routes or flight patterns, for example, would benefit immensly from breakthroughs is this problem or in the P versus NP problem .

However, this same logic can be applied to many facets of planning as well. In robotics, for instance, planning the order in which to drill holes in a circuit board is a complex task due to the sheer number of holes that must be drawn.

The best and most important application of TSP, however, comes from the fact that it is an NP-Complete problem. That means that its practical applications amount to the applications of any problem that is NP-Complete. So, if there are significant breakthroughs for TSP, that means that those exact same breakthrough can be applied to any problem in the NP-Complete class.

Problem Loading...

Note Loading...

Set Loading...

travelling salesperson award

7 Reasons To Use a Sales Incentive Travel Program

by Laura Broman | Feb 21, 2022 | Blog

Download Our eBook on B2B Customer Loyalty!

We love travel. When HMI was first created over 40 years ago, it was initially only an incentive travel and meetings company. As time has passed and we’ve expanded into other areas of incentives, incentive travel has always remained close to our hearts.

And for good reason: for many companies seeking a competitive advantage, an incentive trip that’s part of a sales incentive program can tip the odds in their favor by boosting motivation and, ultimately, performance.

Today, we’d like to tell you one reason why this type of program is so effective. Heck, why stop at just one? Below are 7 reasons you should start implementing a sales incentive travel program for your sales team right now:

1. It builds loyalty.

The world of business is always evolving, growing, and shifting, but some things will never change. We all know it’s generally better and far more cost-effective to hold on to seasoned, committed employees than to go out looking for new ones. In fact, Gallup estimates that replacing individual employees can cost as much as twice the employee’s annual salary.

What’s more, having to onboard an inexperienced employee could be disruptive to your existing business operations, and introducing a new player to a team might run the risk of upsetting your office’s highly important company culture . So if you agree that bringing in outside hires can be expensive and onerous, what can you do if your current team is unmotivated? What if they’re considering other options, but are looking for a reason to stay?

We talk a lot about how effective incentive travel is for building customer loyalty—but it can be just as powerful internally for an organization. Employee retention is important, and a sales incentive travel program may be your perfect solution to some of these issues.

By offering your most hardworking employees something they can’t buy in stores, something that they’ll look back on fondly years later, you’ll end up with a dedicated, team-oriented, and loyal sales force. They won’t see themselves merely as employees, but as members of a team with a real stake in the success of their company.

2. “Non-monetary” is good. “Experiential” is great.

For some people, working a job is about one thing and one thing only: the paycheck. They’re not invested in their job or their workplace, and the only rewards that will motivate these people are monetary. However, particularly in the last two years , work for many of us has become about more than just money: it’s where you’re spending half of your waking hours, after all, so ideally it should be enjoyable and fulfilling in its own right.

Increasingly, businesses are turning to non-monetary rewards to motivate their top employees, from golf clubs to kitchen appliances to electronics. But recent years have taken this a step further with the rise of “intangible” or  “experiential” rewards , non-monetary rewards that come in the form of experiences. Things like backstage passes to a Broadway show, tickets to a baseball game with seats just behind home plate, and—of course— travel opportunities.

Experiential rewards like a trip to the Caribbean don’t just create lasting memories—they create a positive association with your brand and your company. This is especially true when you can add soft benefits or a rewarding CSR initiative —two experiences we’ve found to be highly motivating when included in an incentive trip. These types of events, and the associations they create with your brand, are invaluable to have in markets that are becoming commoditized and featuring less and less differentiation.

The unquantifiable, but very positive, results that are generated from giving your employees a well-earned reward like this are what we in the incentives game call  ROE: return on experience . Creating a positive brand presence, even internally, will lead to ripple effects elsewhere: your team won’t just perform better, they’ll also become stronger advocates for your brand and leading them to sell better, too.

Want a deep dive into sales incentives and how you can make them achieve your goals? Check out our ebook,  Sales Incentives: How, Why, and ROI

3. sales incentives give you a competitive edge in the labor market..

Here’s an issue we’ve been noticing recently across certain industries: labor shortages. Distributors in areas such as  HVAC  or  electrical supply  are seeing a wave of vacant positions as the former largest generation in history, the Baby Boomers, head into retirement without a sufficient supply of Millennials or Gen Z-ers interested in filling the gaps.

This is where creating that positive brand presence comes in again. Younger generations aren’t simply looking for a paycheck: they’re looking for a company that aligns with their values and fosters positive, mutually beneficial relationships. They actively seek out companies that focus on the ROE.

An easy example we can point to is Google, whose famously laid-back and youthful  workplace culture  has drawn millions of young applicants over the years.

But you don’t have to be a tech giant to take advantage of their strategies:  millennials also love to travel  more than previous generations and are  more likely to prioritize travel  or other bucket-list experiences in their time off. A sales incentive travel program is a built-in opportunity for them to achieve some of their dreams. Offering something they really value and will work hard to achieve will give you a competitive boost in a saturated labor market. You won’t just get more applicants—you’ll get better ones too.

4. Competition drives performance.

We can all admit it: competition is fun. That’s why we play games. By now you should be pretty familiar with the term “ gamification ”—but we can’t emphasize enough how effective it is as a motivational strategy.

Not all sales incentive travel programs need to be competitions, but it’s a strategy many go for: fostering a sense of friendly competition drives engagement in a program, and engagement drives performance. Everybody wants to win, whether the game is for an all-expenses-paid trip to somewhere amazing or for something as simple as bragging rights.

But you can make your incentive travel program about more than just the winner at the end: the process can be fun too. With leaderboards, sweepstakes, and short-term promotions along the way, a program with an incentive trip as the pot of gold at the end of the rainbow can still keep everyone engaged until the very end.

5. Have we mentioned enablement yet?

We love all things  eLearning and enablement . Usually we discuss these topics in the context of  channels , i.e., how to turn your channel partners into experts and advocates for your product. For example, an enablement program could offer online modules to its participants that trains them how to operate a complicated aspect of one of your products.

You can just as easily apply these strategies to members of your own employees. With a sales incentive travel program, the end goal is inevitably to get your participants—in this case, members of your sales team—to bring in more money to your company by selling more product. But along the way you can encourage practices that will help them improve as salespeople and, in doing so, get that much closer to earning a trip.

Again, this could include training modules designed to build up their knowledge base about your clients, your sales methodology, or your products and services. Now, you might be wondering, “Well, why don’t my salespeople already know all these things? Didn’t we already train them when they got here?” But the truth is, nearly 87% of sales training is forgotten within one month , so intermittent refresher courses can actually be quite valuable. Add to this the fact that almost half of sales reps feel they don’t have the right information prior to making a call, while 65% believe that the quality of their training strongly correlates with their engagement, and the picture becomes much clearer.

So how does all of this connect with incentive travel? One great thing about enablement is that you can do it anywhere. For example, you can use the incentive trip itself as an opportunity for enablement. While your trip earners will be spending most of their time exploring tourist attractions or relaxing on the beach, you can also include team-building activities or mini-courses on skill improvement. Your winners will return from their trip relaxed, refreshed, and even better salespeople.

6. ROI, always and forever.

ROE is good and all, but let’s be real here—we’re here for the ROI. Running a business is a constant gamble on investment and capital allocation, whether you’re into taking big risks or you’d rather take baby steps. So, don’t worry—although incentive travel might seem like a big investment, put the work in and you’ll find yourself raking in the returns. At  HMI , for example, our incentive travel programs generate 527% ROI on average.

7. Conclusion: We can site our sources

Don’t take our word for it: ask the research experts. Whether it’s the Incentive Research Foundation , the Society for Incentive Travel Excellence, or any other group dedicated to incentive studies, the numbers all show the same thing: incentive travel works. Case in point: 80% of respondents to a recent IRF survey suggested that incentive travel was either “very” or “extremely” motivating. ROI, brand culture, performance improvement, loyalty—whatever the reason, year by year more companies are using sales incentive travel programs to motivate their internal sales teams, and they’re finding better results than ever before.

Photo by  Ricardo Gomez Angel  on  Unsplash

in-line cta (7)

Free eBook Download: B2B Customer Loyalty

Customer Retention: B2B Customer Loyalty and the Share of Why eBook Cover

Subscribe to Email!

Book a Call!

Need more incentive insights? Check out these related articles.

Experiential Rewards

The Timeless Value of Experiential Rewards

Modernized Incentives

Incentives Program

Incentive Programs: A Recession Proof Tool for HVAC Distributors

Loyalty & Retention | Modernized Incentives

change management header image

How to Change an Incentive Program Structure Without Losing Buy-In

Change management in an incentive program is not without its challenges. But it can also be an opportunity to revitalize engagement, inspire growth, and align your strategy with evolving goals.

Group Incentive Travel | Loyalty & Retention

Start the Conversation Now

Ready to start planning your incentive strategy get in contact with us.

More From Forbes

Seven tips for the traveling salesperson.

Forbes Business Development Council

  • Share to Facebook
  • Share to Twitter
  • Share to Linkedin

Shutterstock

Another Monday rolls around and for most people that means heading back into the office starting the new week working a 9-to-5 job. However, for the traveling salesperson, there are no daily commutes or 9-to-5 hours. Days can start in the wee hours to catch that early flight and take you deep into the night with only the cleaning crew still around at the airport when your delayed flight finally lands. Over my tenure of 12 years as National Sales Director at Trans American Trucking, I have been on both ends of the this and everything in between. In this article, I’d like to give some pointers that my fellow travelers can use making the process a little bit easier to manage.

Create a routine.

Parking in the same level of the parking deck or same area of the lot assures you that you won’t have a hard time finding your vehicle upon your return. After a cross-country flight, the last thing you want to do is search the property looking for your vehicle.

Take advantage of expediting services at the airport.

This should go without saying for any seasoned business traveler, but I still see business travelers standing in the regular security lines at the airport. Take advantage of services such as TSA Pre, Global Entry and Clear. It will save your hours upon hours of time over the course of the year and well worth the cost of enrollment fees.

Don’t rely on airport power and Wi-Fi.

Although it has been getting a little better recently, internet can still be spotty or difficult to log into in many of the nation’s airports. To make matters worse, power sources can be even more scarce, especially in metro airports, with large crowds fighting over a few sockets to keep your device charged in the first place. Invest in a portable phone charger and internet jetpack to alleviate this headache. Not only will be self-sufficient with everything in your bag, it’s a great way to make friends with fellow travelers who may be low on battery or need an internet connection to send off that important email.

Download apps.

In today’s age, the paper airline ticket has gone by the wayside. With airline apps, you can download electronic tickets, have up to the minute updates on your flight and access to the wireless network and even movies while airborne. Apps are essential for any business traveler.

Invest in hard shell luggage.

A few years back, a bottle of cologne in another traveler’s luggage broke soaking all nearby bags in the cargo hold. Unfortunately, my bag was one the victims, resulting in my clothes for the week reeking like the scent. A hard shell suitcase not only lets you avoid this situation but also protects valuables from being broken in transit as well.

Sign up for rewards programs.

Make business traveling work for you and reap the rewards by joining your airline's loyalty program. Over time your enrollment will result in lounge access, free upgrades and dedicated phone lines to assist with your travel plans. Hotel reward programs will include lounge access, free upgrades and rooms on executive level floors which are generally nicer. You’ll see how much more bearable business travel is while enjoying these perks.

Use delays to your advantage.

Death, taxes and flight delays are three things that, without fail, will always happen in life. Rather than joining in the herd of other travelers complaining about the situation, take a walk to a less crowded gate and use this time to send follow up emails to the customers you have seen that week. It makes for a great flight home and the following day knowing that you're all caught up and can focus your attention on other tasks.

In conclusion, following these steps will make the entire travel experience much easier to deal with, saving you time and effort that can be put forth to other areas of your position.

Craig McGraw

  • Editorial Standards
  • Reprints & Permissions

Try RoadWarrior free for 7 days

Solving the Traveling Salesman Problem

red route sign arrow

Get home early with RoadWarrior.

Enter your stops, optimize your routes, manage your team – quickly and efficiently.

Imagine a salesman who needs to visit multiple cities, but he wants to minimize the distance traveled and return to the starting point. This classic problem, known as the Traveling Salesman Problem (TSP), has been a subject of study for over a century. The applications of TSP are widespread, from logistics and agriculture to astronomy and computer-generated art. In this blog post, we will delve into the world of the Traveling Salesman Problem, exploring its history, algorithms, and real-world applications.

Short Summary

  • The Traveling Salesman Problem is a complex problem of finding an optimal route for a round trip.
  • Solutions to the TSP include NP-hard classification, brute force approach, dynamic programming and Christofides’ Algorithm.
  • Route planning software such as OptimoRoute provide businesses with efficient tools for tackling the TSP, thereby improving their operations and saving resources.

Understanding the Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is a problem of determining the most efficient route for a round trip, with the objective of maintaining the minimum cost and distance traveled. It serves as a foundational problem to test the limits of efficient computation in theoretical computer science.

The salesman’s objective in the TSP is to find a minimum weight Hamiltonian cycle, which maintains both the travel costs and the distance traveled at a minimum.

Theoretical Background

The TSP is classified as an NP-hard problem. This shows that the number of solution sequences grows rapidly with the number of cities. The brute force approach to resolving the TSP involves examining each round-trip route to ascertain the shortest one. However, as the number of cities increases, the number of round-trips to check can quickly surpass the capability of the most powerful computers. This limitation has led to the development of more sophisticated algorithms to tackle the TSP, such as dynamic programming and approximation algorithms.

The Hamiltonian Cycle Problem, also known as the Hamiltonian cycle problem, inquires whether there exists a closed walk in a graph that visits each vertex precisely once and is closely related to the TSP. Both problems have been studied extensively by computer scientists due to their implications in complexity theory and the P versus NP problem.

Optimal vs. Approximate Solutions

In solving the TSP, there is a distinction between optimal solutions and approximate solutions. Optimal solutions are the most advantageous route, while approximate solutions are round-trip routes whose lengths approach that of the most advantageous route. The brute force approach involves determining every potential solution and subsequently selecting the most advantageous one. However, this method is computationally intractable for large TSP instances.

One notable approximate solution is Christofides’ algorithm, which begins by determining the shortest spanning tree and subsequently converting it into a round-trip route. This algorithm guarantees a response that is, at most, 1.5 times the optimal solution. While not always yielding the optimal solution, approximate algorithms like Christofides’ algorithm provide a more feasible approach to solving the TSP.

Evolution of TSP Algorithms

TSP algorithms have been in existence since the 1950s, when the initial brute force approach was formulated. Subsequently, more sophisticated techniques such as dynamic programming and Christofides’ algorithm have been developed. These advanced algorithms have enabled researchers and practitioners to find near-optimal solutions to the TSP more quickly and efficiently.

By leveraging these algorithms, it is possible to solve the TSP in a fraction of the time.

Brute Force Approach

The brute force approach to TSP involves attempting all potential solutions, making it the most time-consuming and expensive method. As the number of destinations increases, the number of roundtrips likewise increases exponentially, rendering it computationally intractable even for the most powerful computers. Therefore, the brute force approach is not considered to be a viable solution for large TSP instances.

Despite its limitations, the brute force approach serves an important role in the history of TSP algorithms. It represents the initial attempt to solve the TSP and laid the groundwork for the development of more advanced and efficient algorithms.

Dynamic Programming

Dynamic programming is a technique employed to address intricate issues by segmenting them into more manageable subproblems and resolving them one at a time. It is regularly utilized to resolve the Traveling Salesman Problem due to its ability to avoid redundant calculations and identify the shortest route that visits all cities exactly once. The dynamic programming approach is more scalable than the brute force approach, as it can be employed to solve problems of any size.

However, dynamic programming is not without its limitations. It can be computationally expensive and time-consuming, as it necessitates solving a substantial number of subproblems. Despite these drawbacks, dynamic programming remains a popular and effective method for solving the TSP.

Christofides’ Algorithm

Christofides’ algorithm is an algorithm for obtaining approximate solutions to the Traveling Salesman Problem. It involves constructing a minimum spanning tree and then discovering a minimum-weight perfect matching on the odd-degree vertices of the tree. This algorithm, developed in the 1970s, utilizes a combination of graph theory and heuristics to address the TSP.

The significance of Christofides’ algorithm lies in its ability to yield routes that are guaranteed to be no more than 50 percent longer than the shortest route. While it may not always provide the optimal solution, its development marked a substantial improvement in the pursuit of efficient TSP algorithms.

Recent Advances in TSP Algorithms

In recent years, computer scientists have made significant advancements in TSP algorithms. These breakthroughs include:

  • Approximation algorithms
  • Metaheuristic approaches
  • Local search operators
  • Anytime Automatic Algorithm Selection

These cutting-edge algorithms have enabled researchers to find even more efficient solutions to the TSP, further demonstrating the importance of continued research and development in this area.

Geometry of Polynomials

Oveis Gharan and Nathan Klein used the geometry of polynomials approach to solve the TSP by representing the problem as a polynomial with variables corresponding to the edges between all the cities. This approach permits the utilization of geometric techniques and algorithms to discover an optimal or approximate solution to the problem, including determining the starting and ending point of the route.

This innovative method showcases the potential for leveraging mathematical techniques and geometrical properties in solving the TSP. As research progresses, it is expected that even more efficient algorithms and approaches will be developed, further pushing the boundaries of our understanding of the TSP.

Fractional Solutions and Rounding Techniques

Amin Saberi and Arash Asadpour developed a general rounding technique that employs randomness in an attempt to select a whole-number solution that preserves as many characteristics of the fractional solution as possible. The use of fractional solutions and rounding techniques can be utilized to construct effective approximation algorithms for the TSP.

Saberi, Gharan, and Singh implemented this general rounding technique to formulate a new approximation algorithm for the TSP. As computer scientists continue to explore new approaches and techniques, it is likely that even more powerful and efficient algorithms will be developed to tackle the complex TSP.

Practical Applications of TSP Solutions

TSP solutions are employed in a variety of industries, including logistics, astronomy, agriculture, and vehicle routing. Its applications range from planning efficient delivery routes and optimizing telescope trajectories to designing microchips and creating computer-generated art.

The widespread use of TSP solutions underscores the importance of continued research and development in this area, as advancements in TSP algorithms have the potential to positively impact numerous sectors.

Route Optimization

Route optimization is the process of determining the most efficient routes for various applications. In logistics, for example, TSP solutions can assist in enhancing efficiency in the last mile. By employing optimization techniques, businesses can reduce the number of stops, minimize total distance traveled, and ultimately save on fuel and labor costs.

The Vehicle Routing Problem (VRP), a generalized form of the TSP, focuses on discovering the most efficient set of routes or paths for multiple vehicles and hundreds of delivery locations. By utilizing TSP solutions and optimization techniques, companies can greatly improve their overall efficiency and productivity, leading to significant cost savings and improved customer service.

Last-Mile Delivery Challenges

The last-mile delivery problem refers to the final stage of a supply chain. It involves transporting goods from a transportation hub, such as a depot or warehouse, to the ultimate recipient. TSP solutions play a crucial role in addressing this challenge by optimizing delivery routes, reducing the number of stops, and minimizing total distance traveled.

For example, the Traveling Salesman Problem with Time Windows (TSPTW) approach considers specific time constraints for each delivery location, ensuring that deliveries are made within a specified time frame. By employing TSP algorithms and optimization techniques, businesses can:

  • Overcome last-mile delivery challenges
  • Improve overall efficiency
  • Achieve cost savings
  • Enhance customer satisfaction

TSP Solvers for Real-World Problems

Modern TSP solvers use advanced algorithms to provide near-optimal solutions quickly. These solvers include the routingpy library, real-life TSP and VRP solvers, and state-of-the-art TSP solvers based on local search.

By leveraging these powerful algorithms, businesses and researchers can tackle real-world TSP problems with greater efficiency and accuracy.

Branch and Bound Method

The branch and bound method is an algorithm utilized to address optimization problems, such as the TSP. It functions by exhaustively examining all potential solutions and identifying the most advantageous one. By dividing the problem into smaller subproblems and determining the optimal solution for each subproblem, the branch and bound method permits a more efficient and precise resolution to the problem.

Although the branch and bound method is computationally expensive, it has several advantages, such as being relatively straightforward to implement and capable of addressing large-scale problems. Its application in solving real-life TSP instances showcases its potential in effectively optimizing routes and minimizing costs.

Nearest Neighbor Method

The Nearest Neighbor algorithm is a greedy algorithm that finds the closest unvisited node and adds it to the sequencing until all nodes are included in the tour. While it rarely yields the optimal solution, particularly for large and intricate instances, it can be utilized effectively as a means to generate an initial feasible solution quickly.

This initial solution can then be supplied into a more sophisticated local search algorithm for further optimization. The Nearest Neighbor algorithm demonstrates that even relatively simple algorithms can play a valuable role in providing quick and feasible solutions to real-world TSP problems.

Route Planning Software for TSP

Utilizing route planning software to solve TSP problems in various industries offers numerous benefits. These software solutions, such as Route4Me, leverage advanced algorithms like Dijkstra’s Algorithm to quickly identify the most efficient route for a team.

By implementing route planning software, businesses can improve efficiency, reduce costs, and enhance customer satisfaction.

Advantages of Route Planning Software

Route planning software can help businesses in the following ways:

  • Optimize routes
  • Decrease the number of stops
  • Minimize the total distance traveled
  • Increase efficiency and productivity
  • Reduce fuel and labor costs by optimizing routes and minimizing the time spent on route planning and decision-making.

Improved customer service is another benefit of route planning software. By optimizing routes and ensuring timely deliveries, businesses can enhance their reputation and build customer loyalty. In an increasingly competitive market, utilizing route planning software can give businesses a critical edge in delivering exceptional service and maintaining customer satisfaction.

Examples of Route Planning Solutions

There are numerous route planning solutions available for addressing the TSP, including vehicle routing software, optimization algorithms, and Excel sheets with order details and addresses. These solutions offer businesses a variety of options to choose from, depending on their specific needs and requirements.

Some examples of popular route planning software include OptimoRoute and Straightaway. These software solutions can help businesses tackle TSP problems efficiently, saving time and resources while improving overall operations. By leveraging advanced algorithms and powerful tools, route planning software provides a valuable solution for businesses looking to optimize their logistics and delivery processes.

Throughout this blog post, we have explored the fascinating world of the Traveling Salesman Problem, delving into its history, algorithms, and practical applications. From the early brute force approach to modern approximation algorithms and route planning software, the TSP continues to challenge and inspire researchers, computer scientists, and businesses alike. As we continue to push the boundaries of our understanding of the TSP, the potential for new and innovative solutions to real-world problems remains vast and exciting.

Frequently Asked Questions

Has anyone solved the traveling salesman problem.

No one has successfully come up with an algorithm to efficiently solve every traveling salesman problem, despite notable progress being made over the years.

What is the Traveling Salesman Problem (TSP)?

The Traveling Salesman Problem is an optimization problem that seeks to determine the most efficient route for a round trip, with the aim of minimizing cost and distance traveled.

What are some examples of industries that benefit from TSP solutions?

TSP solutions are widely used in industries such as logistics, astronomy, agriculture, and vehicle routing, providing a range of benefits.

What is the difference between optimal and approximate solutions in TSP?

Optimal solutions in TSP provide the most advantageous route, while approximate solutions offer a similar route whose length is close to that of the optimal solution.

These solutions can be used to solve a variety of problems, such as finding the shortest route between two cities or the most efficient way to deliver goods. They can also be used to optimize the use of resources, such as time and money.

What is an example of a modern TSP solver?

Routingpy is an example of a modern TSP solver, providing comprehensive tools to address the Traveling Salesman Problem and Vehicle Routing Problem.

It offers a range of features, including an intuitive user interface, fast computation times, and a wide range of optimization algorithms. It also provides a comprehensive set of tools for analyzing and visualizing the results of the optimization process.

Related Articles

Android route planning simplified: the best apps on the market.

Android Route Planning Simplified: The Best Apps on the Market

7 minute read

Best Route Planners for iPhone: Navigating the App Choices

Best Route Planners for iPhone: Navigating the App Choices

Route4Me: A Detailed Look at Features and Pricing

Route4Me: A Detailed Look at Features and Pricing

  • Data Structures
  • Linked List
  • Binary Tree
  • Binary Search Tree
  • Segment Tree
  • Disjoint Set Union
  • Fenwick Tree
  • Red-Black Tree
  • Advanced Data Structures
  • Graph Data Structure And Algorithms
  • Introduction to Graphs - Data Structure and Algorithm Tutorials
  • Graph and its representations
  • Types of Graphs with Examples
  • Basic Properties of a Graph
  • Applications, Advantages and Disadvantages of Graph
  • Transpose graph
  • Difference Between Graph and Tree

BFS and DFS on Graph

  • Breadth First Search or BFS for a Graph
  • Depth First Search or DFS for a Graph
  • Applications, Advantages and Disadvantages of Depth First Search (DFS)
  • Applications, Advantages and Disadvantages of Breadth First Search (BFS)
  • Iterative Depth First Traversal of Graph
  • BFS for Disconnected Graph
  • Transitive Closure of a Graph using DFS
  • Difference between BFS and DFS

Cycle in a Graph

  • Detect Cycle in a Directed Graph
  • Detect cycle in an undirected graph
  • Detect Cycle in a directed graph using colors
  • Detect a negative cycle in a Graph | (Bellman Ford)
  • Cycles of length n in an undirected and connected graph
  • Detecting negative cycle using Floyd Warshall
  • Clone a Directed Acyclic Graph

Shortest Paths in Graph

  • How to find Shortest Paths from Source to all Vertices using Dijkstra's Algorithm
  • Bellman–Ford Algorithm
  • Floyd Warshall Algorithm
  • Johnson's algorithm for All-pairs shortest paths
  • Shortest Path in Directed Acyclic Graph
  • Multistage Graph (Shortest Path)
  • Shortest path in an unweighted graph
  • Karp's minimum mean (or average) weight cycle algorithm
  • 0-1 BFS (Shortest Path in a Binary Weight Graph)
  • Find minimum weight cycle in an undirected graph

Minimum Spanning Tree in Graph

  • Kruskal’s Minimum Spanning Tree (MST) Algorithm
  • Difference between Prim's and Kruskal's algorithm for MST
  • Applications of Minimum Spanning Tree
  • Total number of Spanning Trees in a Graph
  • Minimum Product Spanning Tree
  • Reverse Delete Algorithm for Minimum Spanning Tree

Topological Sorting in Graph

  • Topological Sorting
  • All Topological Sorts of a Directed Acyclic Graph
  • Kahn's algorithm for Topological Sorting
  • Maximum edges that can be added to DAG so that it remains DAG
  • Longest Path in a Directed Acyclic Graph
  • Topological Sort of a graph using departure time of vertex

Connectivity of Graph

  • Articulation Points (or Cut Vertices) in a Graph
  • Biconnected Components
  • Bridges in a graph
  • Eulerian path and circuit for undirected graph
  • Fleury's Algorithm for printing Eulerian Path or Circuit
  • Strongly Connected Components
  • Count all possible walks from a source to a destination with exactly k edges
  • Euler Circuit in a Directed Graph
  • Word Ladder (Length of shortest chain to reach a target word)
  • Find if an array of strings can be chained to form a circle | Set 1
  • Tarjan's Algorithm to find Strongly Connected Components
  • Paths to travel each nodes using each edge (Seven Bridges of Königsberg)
  • Dynamic Connectivity | Set 1 (Incremental)

Maximum flow in a Graph

  • Max Flow Problem Introduction
  • Ford-Fulkerson Algorithm for Maximum Flow Problem
  • Find maximum number of edge disjoint paths between two vertices
  • Find minimum s-t cut in a flow network
  • Maximum Bipartite Matching
  • Channel Assignment Problem
  • Introduction to Push Relabel Algorithm
  • Introduction and implementation of Karger's algorithm for Minimum Cut
  • Dinic's algorithm for Maximum Flow

Some must do problems on Graph

  • Find size of the largest region in Boolean Matrix
  • Count number of trees in a forest
  • A Peterson Graph Problem
  • Clone an Undirected Graph
  • Introduction to Graph Coloring

Traveling Salesman Problem (TSP) Implementation

  • Introduction and Approximate Solution for Vertex Cover Problem
  • Erdos Renyl Model (for generating Random Graphs)
  • Chinese Postman or Route Inspection | Set 1 (introduction)
  • Hierholzer's Algorithm for directed graph
  • Boggle (Find all possible words in a board of characters) | Set 1
  • Hopcroft–Karp Algorithm for Maximum Matching | Set 1 (Introduction)
  • Construct a graph from given degrees of all vertices
  • Determine whether a universal sink exists in a directed graph
  • Number of sink nodes in a graph
  • Two Clique Problem (Check if Graph can be divided in two Cliques)

Travelling Salesman Problem (TSP) : Given a set of cities and distances between every pair of cities, the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point.  Note the difference between Hamiltonian Cycle and TSP. The Hamiltonian cycle problem is to find if there exists a tour that visits every city exactly once. Here we know that Hamiltonian Tour exists (because the graph is complete) and in fact, many such tours exist, the problem is to find a minimum weight Hamiltonian Cycle.  For example, consider the graph shown in the figure on the right side. A TSP tour in the graph is 1-2-4-3-1. The cost of the tour is 10+25+30+15 which is 80. The problem is a famous NP-hard problem. There is no polynomial-time known solution for this problem.   

Examples: 

In this post, the implementation of a simple solution is discussed.

  • Consider city 1 as the starting and ending point. Since the route is cyclic, we can consider any point as a starting point.
  • Generate all (n-1)! permutations of cities.
  • Calculate the cost of every permutation and keep track of the minimum cost permutation.
  • Return the permutation with minimum cost.

Below is the implementation of the above idea 

Time complexity:  O(n!) where n is the number of vertices in the graph. This is because the algorithm uses the next_permutation function which generates all the possible permutations of the vertex set.  Auxiliary Space: O(n) as we are using a vector to store all the vertices.

Please Login to comment...

Similar reads.

  • NP Complete
  • Google Releases ‘Prompting Guide’ With Tips For Gemini In Workspace
  • Google Cloud Next 24 | Gmail Voice Input, Gemini for Google Chat, Meet ‘Translate for me,’ & More
  • 10 Best Viber Alternatives for Better Communication
  • 12 Best Database Management Software in 2024
  • 30 OOPs Interview Questions and Answers (2024)

Improve your Coding Skills with Practice

 alt=

What kind of Experience do you want to share?

An official website of the United States government

Here's how you know

Official websites use .gov A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS. A lock ( Lock Locked padlock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

design element

  • Search Awards
  • Recent Awards
  • Presidential and Honorary Awards
  • About Awards
  • How to Manage Your Award
  • Grant General Conditions
  • Cooperative Agreement Conditions
  • Special Conditions
  • Federal Demonstration Partnership
  • Policy Office Website

travelling salesperson award

Please report errors in award information by writing to: [email protected] .

travelling salesperson award

Global Vision Awards 2024

T hese are the winners of Travel + Leisure’s 2024 Global Vision Awards, plus how this year’s panel arrived at the final list of 26 honorees.

The  Travel + Leisure  Global Vision Awards recognize the many companies, individuals, destinations, and nonprofit organizations that are leading the way in developing a more sustainable travel industry. This annual celebration, timed to coincide with Earth Month, aims to encourage further creativity and spark change.

This year's 26 award winners — an extraordinarily diverse bunch — are notable in their own right. But they're just a few of the many forward-thinking problem solvers helping to make travel better for the planet and its communities. As always, the hope is that these Global Vision Award winners will inspire the next generation of problem solvers looking to make a positive impact.

Many visitors to Japan are eager to learn more about the country’s traditional arts and crafts, such as ceramics, textiles, handmade paper, and metalwork. But it can be hard to know where to look —and harder still to navigate the language barrier. Enter Dento , a new company that aims to open those doors. It’s supported in part by the Kyoto-based travel agency Windows to Japan, whose founder and CEO Avi Lugasi recognized the need for a more equitable relationship between master craftspeople and the travelers keen to meet them. "One of the big issues has been, if a visitor is there talking with the craftsman, that takes the concentration out of what they're doing," Lugasi explains. The solution? Compensating the professionals for their time — as well as creating an online shop that helps expand the market for these one-of-a-kind goods. Dento also operates a foundation that recruits and pays apprentices. "We're supporting the next generation that will carry on these crafts," Lugasi says. — Elaine Glusac

It’s fair to say that Kris Cody’s backpacking trip through Peru in 2015 changed his life. After seeing firsthand the care and craftsmanship that goes into alpaca-wool garments — many of which are still handmade in the Andes Mountains — Cody decided to give up his neuroscience studies and, instead, create an activewear brand. Today, as founder and CEO of Paka , he makes sure every sweater bears the signature of the woman who made it on an interior hem; there’s also a QR code for those who want to learn more. "From the beginning, Paka was about connecting people to where the things come from, what they’re made of, who made them," Cody explains. "Traceability was the next step in being able to see the coordinates, literally, of where that fiber was shorn in the Andes." — Elaine Glusac

Guided-tour company Trafalgar may be best known for taking travelers to more than 70 countries, but it also has a robust slate closer to home. "People think that, to have a deep cultural experience, you need to travel abroad," says company president Melissa DaSilva. “But you only need to travel as far as your backyard.” Trafalgar has spent the past five years working closely with Indigenous communities across North America to connect travelers with tribes and places that have often been overlooked. Today, more than 60 percent of Trafalgar’s U.S. itineraries include at least one Native business, whether it’s a walking tour in the Canadian Rockies with a Cree guide or a day spent at the Oglala Lakota Living History Village, in South Dakota. "Where we’re including these experiences," DaSilva adds, "a hundred percent of the proceeds go back into those communities." — Elaine Glusac

Luke's Lobster

It started with a humble lobster-roll shop in New York City, back in 2009. Since then, Luke’s Lobster has grown into an international restaurant group, with 22 outposts across the U.S., plus 10 locations in Japan and Singapore. Even so, cofounders Ben Conniff and Luke Holden keep a close eye on their home waters in Maine, where they’re working to safeguard the future of lobstering. The company’s Lift All Boats project offers paid student apprenticeships that introduce teens from diverse backgrounds to lobstering, an industry that’s almost exclusively white. "We’re trying to create a well-rounded experience to teach these students about the industry and open up horizons for them," Conniff says. "We want them to feel like they belong on the waterfront." — Hannah Selinger

Launched in 2014, To’ak is a boutique chocolate company based in Ecuador that has big plans. It has partnered with Third Millennium Alliance, a conservation foundation, to train farmers in sustainable agroforestry practices, including the use of native shade trees and prioritizing soil health. To’ak also pays its growers as much as eight times the typical fair-trade rate for cacao, specifically a variety known as Nacional, which nearly disappeared in a 1916 blight. "The only way that we can increase our impact is by buying more cacao at better prices and by supporting more farmers to do regenerative farming," says James Le Compte, CEO of To’ak. The result of all that effort is a decadent product with a meaningful environmental upside. — Hannah Selinger

When the Swedish airline SAS announced a series of experimental, all-electric flights, set to take off in 2028, every last reservation sold out in just 20 seconds, says Ann-Sofie Hörlin, the airline’s head of sustainability. That’s in spite of the fact that SAS didn’t reveal where the planes would go. Such is the demand for anything that can help the fossil-fuel-guzzling industry transition to something greener. Hörlin is quick to acknowledge that batteries aren’t yet a viable alternative when it comes to long hauls, at least with today’s technology. But electric planes could prove a game changer for quicker hops within Scandinavia. "We have a lot of short routes," Hörlin explains. "All of a sudden, aviation will be the most sustainable way to get there." — Hannah Selinger

Tempo Cooler

The Tempo Cooler may be the last one you’ll ever buy. With vacuum-insulated walls that are a third of the thickness of those in popular plastic models, the aluminum chest can accommodate more stuff in a smaller space. And it does so without any loss of frostiness, says Ian Sandmael, cofounder of Oyster , the Norway-based startup behind the innovative product. Even better, you don’t need to add ice: simply load the Tempo with cold drinks, and they will stay that way for hours. Forged from anodized aluminum, the chest is also meant to last, basically, forever — though Sandmael is quick to add that the product is actually fully recyclable. "If you think of plastic straws as being a problem," he says, "then plastic coolers are a much bigger one." — Elaine Glusac

Journeys With Purpose

There’s no such thing as a typical trip for Journeys with Purpose , an "impact travel company" launched in 2019. Instead, each itinerary is designed to showcase the wonders of a specific ecosystem, such as the caves of Chiquibul National Park, in Belize, or Argentina’s Rincón del Socorro, a 75,000-acre reserve in the wildlife-filled Iberá Wetlands. What’s more, each departure is hosted by the conservationists who are helping to protect these priceless places. As a member of 1% for the Planet , an organization that encourages corporate giving, Journeys with Purpose contributes up to 20 percent of a trip’s cost to local partners. As founder and managing director Duncan Grossart explains, "the more people travel with us, the more our mission will be fulfilled." — Hannah Selinger

Though it has long lagged other sectors, the cruise industry has lately stepped up its investments in sustainability. French expedition line Ponant is perhaps at the forefront: in 2021, it deployed a hybrid-electric icebreaker, Le Commandant Charcot , that’s able to operate for short periods on battery power and that uses renewable onshore energy sources when possible. Ponant has also announced a completely carbon-neutral vessel that could launch as soon as 2030. Plans for the 100-cabin prototype, currently named Swap2Zero , call for sails, solar panels, and liquid-hydrogen fuel cells. "This is much more than a new ship," says CEO Hervé Gastinel. "We want to actively contribute to the decarbonization of the maritime sector." — Paul Brady

Today it’s known for its lineup of chic, reusable bottles and adventure-ready filters. But the original mission of LifeStraw is humanitarian relief. Back in 1994, the company developed a mesh water filter that would protect people from Guinea worm disease, at the time a scourge across Africa. "Since then, we’ve provided more than 41 million straws to the Carter Center ," says Tara Lundy, LifeStraw’s chief brand officer. (The Carter Center, an NGO founded by the former president and first lady, counts the eradication of Guinea worm disease among its goals.) Like many Global Vision Award winners, LifeStraw is certified as a B Corp and continues to distribute its water filters and aid to those in need: the company has recently sent rapid-response teams to sites of natural disasters, such as Morocco’s Atlas Mountains after the 2023 earthquake, as well as to conflict areas across the globe. Travelers who support the brand are also contributing to the effort, as LifeStraw devotes a portion of all proceeds to future clean-water projects. — Hannah Selinger

Albania’s Vjosa River runs roughly 169 miles from the Greek border to the Adriatic, carving gorges and providing critical habitat to more than 1,100 species, including the Egyptian vulture and the Ionian sturgeon. When a series of hydroelectric dams was proposed for the Vjosa in 2014, activists created an NGO, EcoAlbania , to defend the waterway. Their goal was to protect it in perpetuity. (EcoAlbania was eventually joined in the effort by the apparel company Patagonia, as well as other advocacy groups.) Last year, in response to the nine-year campaign, the Albanian government created the Vjosa Wild River National Park, where adventurous visitors can go rafting, climbing, and hiking. "The Vjosa is one of the last free-flowing rivers in Europe," says EcoAlbania spokesperson Besjana Guri. "It’s a jewel, and we’re very lucky to have it." — Elaine Glusac

Diving With a Purpose

Since it was founded in 2005, the nonprofit Diving With a Purpose has trained more than 500 divers, often during weeklong masks-on intensives that prepare explorers to seek out shipwrecks related to the global slave trade. Surprisingly, says Jay V. Haigler, the leading instructor, and a founding board member, these sites are often ignored by maritime archaeologists. "There’s great study of and focus on the Titanic , you know, but not the Guerrero ," he explains, referring to a Spanish slave ship that sank off Key Largo, Florida. The hunt for that wreck sparked the creation of Diving With a Purpose, which has so far documented 18 vessels, including many from the 18th and 19th centuries. (The Guerrero remains lost.) In its ongoing efforts, the group partners with the Slave Wrecks Project, a research initiative backed by the National Museum of African American History & Culture that helps disseminate findings and spur further research. — Hannah Selinger

Discover Aboriginal Experiences

Australia is home to some of the oldest cultures on earth, but until recently, it’s been tricky to suss out high-quality outfitters and guides who come from Aboriginal and Torres Strait Islander communities. That’s where Tourism Australia has stepped in, with a new initiative called Discover Aboriginal Experiences , which aims to connect visitors with those in the know. "This goes way beyond general sightseeing," says Nicole Mitchell, who runs the program in collaboration with around 50 different businesses, all of which are owned or led by descendants of the continent’s original inhabitants. One example is Narlijia Experiences, in Western Australia, which offers visits to the area’s mangrove forests led by owner Bart Pigram, who is part of the Yawuru community. The still-growing collective recently added several new members, including Budj Bim Cultural Landscape, a network of archaeological sites about 200 miles west of Melbourne. — Elaine Glusac 

Polynesian Voyaging Society

The Oahu-based Polynesian Voyaging Society has been working to preserve ancient seafaring practices for more than five decades, in part by organizing extraordinary multiyear voyages aboard Hōkūle‘a , a double-hulled canoe that’s been sailing since 1975. But travelers needn’t be hard-core adventurers to learn more about Polynesian practices, such as navigating without instruments by using the stars and the motion of swells. The society welcomes volunteers for all sorts of tasks, such as helping with boat maintenance and organizing community events, either in Hawaii or in ports of call for Hōkūle‘a . "Getting involved is a wonderful, beautiful, life-changing journey for so many people," says Lehua Kamalu, whose title is voyaging director. "But we definitely put you to work." — Hannah Selinger 

Zambian Carnivore Programme

This group is on a mission to protect some of the country’s most critical wildlife, including cheetahs, leopards, and lions. "Apex predators are rare, by their nature, but they’re hugely important for ecosystem dynamics," says Matt Becker, CEO of Zambian Carnivore Programme . The nonprofit takes a multipronged approach to conservation, partnering with safari operators such as Robin Pope Safaris and the Bushcamp Company to collect data and better manage habitats, as well as training a new generation of conservationists within Zambia. Last year, the organization had 48 students, who ranged from fieldwork newcomers to Ph.D. candidates. "The best way to make conservation sustainable," Becker notes, "is to ensure that the people leading these efforts are from the communities where this work is occurring." — Elaine Glusac

Grootbos Florilegium

One of the world’s most remarkable concentrations of plant life can be found along the Atlantic coast of South Africa. The Cape Floral Region is home to 20 percent of the continent’s vegetation, and the majority of what blossoms there is native to the region. All of which explains the art on view at the new Grootbos Florilegium , a collection at the Grootbos Private Nature Reserve in Gansbaai, South Africa, about two hours southeast of Cape Town. "Our exhibition is about making the plants sexy and beautiful so that people understand what we’re trying to protect," says Michael Lutzeyer, the founder of the reserve. To date, Lutzeyer and his team have commissioned more than 240 original artworks that depict not only the area’s distinctive plants, known collectively as fynbos , but also the insects, birds, and other wildlife that make the ecosystem so special. "It’s making visitors aware of the little critters we ignore." — Elaine Glusac

See Turtles

Since 2008, See Turtles has helped shepherd more than 10 million hatchlings into the sea in 25 countries across the Caribbean and Latin America. At the heart of its mission are volunteer trips to beaches in the region, where travelers work alongside conservationists to defend turtle nests and collaborate with scientists. "Just having a presence on the beach is a deterrent to the people who might want to come and take the eggs," says Brad Nahill, the nonprofit’s president. While the weeklong trips are often no-frills — many include stays at remote research stations — they do afford an unvarnished view of fieldwork, with time spent on both daytime wildlife-watching excursions and nocturnal beach patrols. In 2022, the group launched its See Shell App, which helps shoppers identify and avoid souvenirs made from the shells of the hawksbill turtle, an endangered species. — Elaine Glusac

Destinations

Singapore green plan 2030.

One of the world’s smallest countries has some outsize ambitions. Armed with a sustainability strategy, the Singapore Green Plan 2030 , it is on a mission to reimagine its own cityscape — and show the world that sustainable development is within reach. The plan’s bold targets include planting a million trees by 2030, phasing out all internal-combustion vehicles by 2040, and achieving net-zero emissions by 2050. The government-backed campaign is the latest evolution of formal climate-focused commitments that date back more than three decades. 

In addition to those headline goals, Singapore is making strides on other eco-initiatives. Among them is increasing domestic food production — a challenge in a country that’s less than one-third the size of Rhode Island. One solution can be seen at 1-Arden Food Forest, a 10,000-square-foot urban farm situated 51 floors up in a Central Business District skyscraper. Visitors can stroll through its riot of fruits and flowers, enjoy spectacular views of the waterways that surround the city-state, and sample a freshly harvested bounty at the adjoining restaurant, Kaarla. For a deeper look, Tribe Tours has launched a "food sustainability tour" that combines elements of a traditional markets-and-hawkers itinerary with the chance to learn more about locally grown produce. 

Another element of the plan centers on the expansion of the city’s already enviable collection of parks, with the goal of having every household be within 10 minutes of green space by 2030. Groups like Untamed Paths, a community of nature lovers, organize walks and cleanups to educate visitors about the importance of Singapore’s forest system, where creatures like flying lemurs and frogs can be spotted. 

Not that you need be adventurous to see the city’s greenery: the famously design-forward Changi Airport Terminal 2, which fully reopened in November 2023, now has more than 20,000 plants, including orchids, ferns, and towering columns of vegetation. 

New hotels in the city are also making sustainability a priority. Consider Pan Pacific Orchard, Singapore , which counts among its features solar panels, rainwater harvesting, and “low-emissivity” windows that conserve energy. (It also has an arresting Jenga-like design that is blanketed with nearly 130,000 square feet of foliage.) The Garden Pod , an unusual hotel that opened in 2022, was created from solar-panel-topped shipping containers. It offers views of the Gardens by the Bay and Singapore’s skyline from four glass-fronted duplex suites. Other new hotels, including Artyzen Singapore , Mondrian Singapore Duxton , and the Singapore Edition , put an emphasis on biophilic design, with a profusion of landscaping and indoor-outdoor gardens. 

The plan also calls for a 30 percent reduction in landfill waste by 2030. To help make that happen, Singapore’s restaurants and bars are embracing the challenge in creative ways. The city’s first Michelin Green Star restaurant, Seroja , sources many ingredients from the island and neighboring Malaysia and uses vegetable trimmings to create nonalcoholic drinks, such as a refreshing cocktail of watercress, sansho pepper, and water chestnut. Pangium is also on the vanguard of Straits cuisine, with a menu that spotlights lesser-known Asian herbs and hyperlocal preparations, such as sambal tempoyak, or fermented-durian sambal. The fine-dining restaurant Born models sustainability through its architecture: it’s located in a refurbished turn-of-the-20th-century rickshaw depot. 

Lower-impact preparations and thoughtful design are also trending at bars such as Analogue , which offers plant-based bites alongside cocktails served on a bar that was 3-D printed from recycled plastic bottles. At Fura , meanwhile, the drinks are shaken up with "ugly" fruits and vegetables that would normally be discarded — and, sometimes, invasive species, including jellyfish. Anything for the cause.

Relais & Châteaux

Decadent food and wine have always been nonnegotiable for Relais & Châteaux , a Paris-based association of nearly 600 hotels and restaurants in 65 countries. So it’s perhaps a surprise that the group has been working for a decade to reduce the environmental impact of its members’ culinary operations. Beginning in 2016, it partnered with the organization Slow Food on an annual campaign known as #FoodforChange , which aims to spotlight small-batch products and to encourage members to buy and serve them. (Last fall, 191 properties from the group participated, with a focus on raw-milk cheeses and biodynamic wines.) "We want to push our members even further when it comes to biodiversity," says Lars Seifert, the brand’s chief communications and sustainability officer. "If they embrace endemic products, they’ll keep them alive." The effort isn’t without its potential pitfalls, he concedes, but it opens a wider conversation with guests. "Maybe you won’t get fresh orange juice in February in the U.K., because we don’t have any oranges over there. But we’ll have something else delicious for you." — Hannah Selinger

It’s been more than 30 years since a moratorium on cod fishing struck a heavy blow to the economy of Fogo Island, off the coast of Newfoundland. In 2004, Fogo Islander Zita Cobb, along with her brothers Alan and Anthony, created Shorefast , a social enterprise designed to strengthen communities by creating new economic opportunities. Out of that work came Fogo Island Inn, a striking 29-room property that debuted in 2013 and consistently ranks among the best in Canada in the T+L World’s Best Awards survey. Drawing visitors to this remote corner of the country sustains not only the inn but the island writ large, says Amy Rowsell, director of special projects and impact for Shorefast. "Our mission is to help the local economy thrive in the global economy," she explains. "We’re harnessing the assets of this place to create a sustainable future for Fogo Island." — Hannah Selinger

Urban Villages

Denver’s forthcoming Populus might be the greenest hotel in America. Designed by the architecture firm Studio Gang , the 265-room property, which is slated to open this year, aims to be carbon positive. "We’ve constantly asked, 'Could we do it better?'" says Jon Buerge, president of Urban Villages , the developer. (The firm’s other sustainability-minded efforts include Denver’s Larimer Square and the Rail Spur district in Seattle.) At Populus, doing better has meant using a specialized concrete that incorporates fly ash, a waste product generated by coal-fired power plants. Rooms feature upcycled-wood furnishings and carpeting made from post-consumer materials. And instead of offering parking — there’s no garage — Populus will encourage the use of public transit. "We all have to start thinking more holistically," Buerge notes. — Elaine Glusac

Iberostar Hotels & Resorts

Iberostar Hotels & Resorts , a brand with more than 100 properties in 16 countries, has an ambitious plan to be carbon neutral by 2030. It’s a monumental task to achieve so quickly, admits Megan Morikawa, global director of sustainability for the Iberostar Group. The company has already slashed its annual carbon budget by half through an array of programs: to take two examples, Iberostar offsets its emissions through mangrove planting and coastal restoration in places such as the Dominican Republic, and it is transitioning away from fossil fuels in favor of renewables across the portfolio. Notably, the company has been a paragon of transparency throughout the process, with a website detailing the group’s progress — and challenges — in an effort to inspire others. "We need to be doing this in a way that can synthesize the best lessons," Morikawa says, "and be a tipping point for the sector at large." — Hannah Selinger

Princess Gauravi Kumari

Launched in 2013, the Princess Diya Kumari Foundation aims to improve the lives of women and girls. The princess, the granddaughter of Man Singh II, the last maharajah of Jaipur, India, now serves as deputy chief minister of Rajasthan. The foundation’s day-to-day rests with her daughter Princess Gauravi Kumari. “We now have seven centers across the state,” the younger Kumari says, each of which offers programs such as job training, digital literacy, health education, self-defense training, and legal aid. In the past decade, the group has helped tens of thousands of women, including those who have learned skills such as beadwork and block printing. Their artistry is available for sale in the foundation’s PDKF Store at the City Palace of Jaipur or online. — Hannah Selinger

Alvaro Silberstein

"In one sentence, we are the Expedia for accessible travel," says Alvaro Silberstein, cofounder and CEO of Wheel the World . Established in 2017, the website lists hotel rooms and tours in hundreds of destinations worldwide, along with comprehensive information about their accessibility, including, in the case of hotels, specifics such as bed height, bathroom turning ratio for those who use wheelchairs, and features like grab bars. The company verifies listings with a team of "mappers," who contribute extensive on-the-scene reports. That way, Silberstein says, "we can guarantee that a stay will exactly meet a user’s accessibility needs." — Hannah Selinger

Luke Bailes

When he opened Ebony Lodge in South Africa’s Sabi Sand Reserve in 1993, Luke Bailes believed that high-end, low-volume tourism could sustain environments and communities by attracting, as he calls them, "individuals who have influence." Since then, Bailes has grown Singita , the company he founded, into a conservation powerhouse with 16 lodges, camps, and villas in Rwanda, South Africa, Tanzania, and Zimbabwe. In the past 30 years, Singita has restored native habitat across nearly 1 million acres, worked to curb poaching, and established schools and vocational institutes in many of the communities where it operates. Still, Bailes says, his work continues. "Eighty percent of my time is dedicated to finding areas that have huge potential — that are pristine — so that we can increase our conservation impact by 2030, to help protect more of these vulnerable landscapes for future generations." Luckily, he has help not only from the team but also from a familiar face: his son, Jo Bailes, is now Singita’s CEO. — Elaine Glusac

Saengduean "Lek" Chailert

In 1991, Lek Chailert spent an agonizing night in a rainforest village in northern Thailand, listening to the screams of an elephant forced to haul logs by handlers using slingshots and knives. The harrowing experience inspired her to learn veterinary science, and, in 2003, she opened Elephant Nature Park , a roughly 300-acre sanctuary in Chiang Mai that today is home to more than 100 rescued and rehabilitating pachyderms. Though the country outlawed commercial logging decades ago, other risks to these animals’ well-being remain, including from unscrupulous tourism operators who continue to offer elephant rides and shows. By contrast, Elephant Nature Park welcomes visitors for full- and half-day tours spent observing elephants roaming the preserve; those interested in staying longer — and getting their hands dirty — can volunteer to assist with the feeding and care of the residents. Guests often also become ambassadors for the cause, Chailert says. "They help us to make a movement." — Elaine Glusac

The 2024 Global Vision Awards Panel

The Global Vision Awards is a year-round project that involves  Travel + Leisure  editors and outside contributors, who report on and interview experts about developments in sustainability and responsible travel. Each fall, a small team of T+L staffers convenes to discuss potential award winners. They are joined by an awards panel: these experts, including some past Global Vision Award winners, assist in the compilation of each year's list. (Panelists are always prohibited from submitting their own projects.)

After extensive discussion and additional reporting, T+L editors make the final determination on the winners, who are recognized in the April 2024 edition of the magazine as well as online.

Susmita Baral , Editor, T+L 

Paul Brady , News Director, T+L

Alison Brooks , Vice President of Destination Experience & Advocacy, Visit Mesa (Arizona)

Elizabeth Cantrell , Senior Editor, T+L

Nina Caplan , Contributor, T+L

Samantha Falewée , Senior Editor, T+L

Jacqueline Gifford , Editor In Chief, T+L

Shawna Huffman Owen , CEO, Huffman Travel

Chris Imbsen , Director of Sustainability, World Travel & Tourism Council

Maya Kachroo-Levine , Senior Editor, T+L

Hemant Kumar Dixit , Senior Manager, Access Development Services

Fryda Lidor , Creative Director, T+L

Anders Lindström , Head of PR & Communications, The Americas, Hurtigruten Group

David Lowy , President, Renshaw Travel 

Jeffrey Miller , Chef, Rosella

Heidi Mitchell , Contributor, T+L

Zandile Ndhlovu , Founder, The Black Mermaid Foundation

Beks Ndlovu , Founder & CEO, African Bush Camps

Thao Phuong , Founder, Textileseekers

Olga Placeres , Owner & President, Preferred Travel & Co.

Jen Salerno Yong , Contributor, T+L

Skye Senterfeit , Deputy Photo Editor, T+L

Jim Strong , President, Strong Travel Services

Flora Stubbs , Executive Editor, T+L

Sam Teicher , Cofounder & Chief Reef Officer, Coral Vita

Peter Terzian , Features Editor, T+L

Paul Tumpowsky , Founder And CEO, New Yonder

For more Travel & Leisure news, make sure to sign up for our newsletter!

Read the original article on Travel & Leisure .

Illsutration by Alyce Jones

U.S. flag

An official website of the United States government

Here’s how you know

Official websites use .gov A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS A lock ( Lock A locked padlock ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

USDA Logo

Animal and Plant Health Inspection Service

Take a Pet From the United States to Another Country (Export)

A cartoon woman shows a woman with a suitcase and a dog on a leash. She is standing in front of a map-like image of the United States with two planes flying away from it, representing travel out of the country

Traveling with a pet in a foreign country can be complex and time-consuming. You need to meet the destination country's specific entry requirements for pets. These may include vaccinations, tests, treatments, and a health certificate (also called an international health certificate, a veterinary health certificate, a veterinary certificate, or an export certificate). Find out what you need before you and your pet travel.

Not all animals qualify for pet travel.

What is considered a pet? A pet is a privately owned companion animal not intended for research or resale and includes only certain animal groups.

Find out if your pet qualifies to travel

Your animal doesn't qualify for pet travel and is subject to different import regulations and export regulations if you:

  • Don't see your pet listed below.
  • Are exporting semen or embryos from any animal.
  • Have a pet that's considered livestock or poultry, like pigs or chickens.

The following animals qualify as pets, meaning they're subject to pet travel requirements:

travelling salesperson award

The following birds DON'T qualify as pets, meaning they're subject to different regulations:

Because they may carry and transmit certain diseases to the U.S. poultry industry, these birds are regulated as poultry.

  • Guinea fowl

View import regulations and export regulations if the type of animal you have does not qualify as a pet.

Before You Start the Process

Traveling with a dog know the latest requirements.

The Centers for Disease Control and Prevention (CDC) has extended the temporary suspension on dogs entering the United States from high-risk countries for dog rabies. If you leave the United States with your pet dog, you'll need to meet specific CDC import requirements to bring your dog back into the United States. This extension is in effect until July 31, 2024.

Visit the CDC for details on these requirements and other related information. If you have questions about CDC requirements, contact CDC-INFO or call them at 404-718-3660 .

Find a USDA-Accredited Veterinarian

With help from a USDA-accredited veterinarian , you can learn more about your destination country's entry requirements for pets, including any needed vaccinations, tests, or treatments. We recommend creating a schedule to make sure you meet all requirements within the specified timeframe.

Gather This Information for Your USDA-Accredited Veterinarian

  • The type of pet traveling
  • The destination country
  • If applicable, countries where your pet will stop (for customs clearance or upon leaving the airport or seaport) on the way to the destination country
  • The date of departure from the United States
  • Whether the pet will be traveling alone, as cargo, or with a person in the cabin of the plane
  • Note: If you're traveling with a pet bird or exotic animal, you may need to work with additional agencies, such as the U.S. Fish and Wildlife Service . Visit the pet travel requirements page for your destination country (see dropdown menu below).

Read These Resources

  • In Spanish (En Español): Guía de viaje para mascotas que viajan a otro país desde Estados Unidos
  • In Chinese (用中文(表達): 宠物出国旅行指南
  • Frequently Asked Questions About Traveling With Your Pet

Where Are You Traveling With Your Pet?

Your destination country sets the entry requirements for pets, which can change at any time. You must verify the country requirements every time you plan to travel with your pet.

Find Your Destination Country Requirements

If your country is not listed in the menu, visit Pet Travel: Unknown Requirements .

  • Book a Flight
  • Manage Reservations
  • Explore Destinations
  • Flight Schedules
  • Track Checked Bags
  • International Travel
  • Flight Offers
  • Low Fare Calendar
  • Upgrade My Flight
  • Add EarlyBird Check-In
  • Check Travel Funds
  • Buy Carbon Offsets
  • Flying with Southwest
  • Book a Hotel
  • Redeem Points for Hotels
  • More Than Hotels
  • Hotel Offers
  • Best Rate Guarantee
  • Rapid Rewards Partners
  • Book a Vacation Package
  • Manage My Vacation
  • Vacation Package Offers
  • Vacation Destinations
  • Why Book With Us?
  • FLIGHT STATUS
  • CHANGE FLIGHT

EarlyBird

Enter code SAVE25NOW in the Promo Code box when booking. Offer is valid only for continental U.S. flights. The 25 percent promotion code savings are valid for one-way or round trip Wanna Get Away® and Wanna Get Away Plus® fares booked with Rapid Rewards points during the Booking Period, flown during the Travel Period, and are applied before taxes and fees. Seats and days are limited. Savings are reflected in the price when entering the multiuse code SAVE25NOW in the Promo Code box on Southwest.com and swabiz.com. This discount is only available through Southwest.com and swabiz.com. Discount is valid on new reservations only. Discount will apply only for flights booked during the Booking Period and flown on the dates within the Travel Period. If one segment of the trip is outside the Travel Period and one is within the Travel Period, only the portion of travel falling within the Travel Period will be discounted. Changes made to the itinerary after purchase will eliminate qualification for this promotion. The discount is only valid with the provided promotion code and is not combinable with other promotion codes or fares. All reward travel is subject to taxes, fees, and other government or airport-imposed charges of at least $5.60 per one-way trip. Applicable taxes, fees, and other government or airport-imposed charges can vary significantly based on your arrival and departure destination. The payment of any taxes, fees, and other government or airport-imposed charges is the responsibility of the Passenger and must be paid at the time reward travel is booked with a credit card, flight credit, or Southwest gift card. When traveling on reward travel, you will receive all fare product features except for earning Rapid Rewards points. Any change in itinerary may result in an increase in points used. Points bookings are subject to change until ticketed. If you cancel your reservation at least ten (10) minutes prior to the scheduled departure of your flight, any remaining unused points will be returned to your Rapid Rewards account. All Rapid Rewards rules and regulations apply and can be found at Southwest.com/rrterms . Offer is not redeemable for cash, and may not be used in conjunction with other special offers, or toward the purchase of a gift card or previously booked flight, or changed to a previously booked flight. Discount is not valid on group travel, Southwest Vacations®, and government fares.

Help Center

  • Terms & Conditions
  • Privacy Policy
  • Do Not Sell/Share My Info

© 2024 Southwest Airlines Co. All Rights Reserved.

Vote for your favorite gas station for food!

USA TODAY 10Best Readers' Choice Awards

Gas stations, convenience stores, and truck stops are more than just a place to grab a quick bite when you're on the go. They're serving up delicious food and snacks that make them destinations in and of themselves, from fried chicken and pizza to organic salads and veggie burritos. USA TODAY 10Best editors have teamed up with a panel of seasoned road warriors to highlight their 20 favorite gas station stops for food across the U.S., and we need your help to crown the best of the best. Which gas station is your go-to when you're hungry? Vote once per day until voting ends on Monday, May 6 at noon ET. We'll announce the 10 winners on Wednesday, May 15.  Read the official Readers' Choice rules .

Gas stations, convenience stores, and truck stops are more than just a place to grab a quick bite when you're on the go. They're serving up delicious food and snacks that make them destinations in and of themselves, from...   Read More

Best Gas Station for Food Nominees

7-Eleven

Photo courtesy of 7-Eleven, Inc.

Known by many for their Big Gulp and Slurpee beverages, 7-Eleven is a classic convenience store with many locations doubling as gas stations. They offer a variety of candy bars and snack foods, in addition to quick dishes like pizza, taquitos, and burgers, including a black bean veggie burger. Repeat visitors also enjoy their popular rewards program.

Buc-ee's

Photo courtesy of Buc-ee's

Buc-ee's is known for their nut confections (like butter toffee pecans), barbecue, jerky, and a large menu of comfort foods. The country stores also serve fudge, banana pudding, and trail mixes.

Casey's

Photo courtesy of Casey's

Casey’s stores are popular for their pizza, in addition to sandwiches, wings, and breakfast items. They also have pre-packaged foods like ice cream, candy bars, potato chips, and protein bars. 

Cumberland Farms

Photo courtesy of bojanstory // Getty Images

Cumberland Farms

Cumberland Farms is a regional chain with locations primarily in New York, Florida, and the New England area. Nicknamed Cumby’s, the stores serve breakfast foods, pizza, and sandwiches, in addition to offering a selection of packaged snacks. They're also known for their fantastic customizable coffee drinks.

Dodge's Southern Style

Photo courtesy of gilaxia // Getty Images

Dodge's Southern Style

Dodge's Southern Style is a convenience store and restaurant chain that serves Southern-style fast foods like biscuits and fried pies, but they're known for their fried chicken. They also offer beverages like fountain sodas, frozen drinks, and a wide variety of flavored coffees. You can find their locations across nine Southern states.

Kum &amp; Go

Photo courtesy of Kum & Go

Kum & Go

Kum & Go is a Midwestern chain with hundreds of locations across 12 states. The stores provide a wide variety of pizzas, burritos, and grab-and-go items at any time of day, while beverages on offer include coffees, sodas, frozen treats, and energy drinks.

Kwik Trip

Photo courtesy of Kwik Trip

Kwik Trip is known for its bakery which serves bread, muffins, cookies, bagels, and doughnuts. In fact, it bakes approximately 24,000 glazed treats in just one hour. The convenience store also offers burritos, pizza, salads, soups, and fried chicken.

Maverik

Photo courtesy of Maverik — Adventure's First Stop

Maverik is a chain with hundreds of stores in Western states, known for its adventure-themed murals and logo. BonFire Foods, an eatery within the store that makes fresh food every day, offers items like pizzas, wraps, salads, sandwiches, and burritos.

Parker's

Photo courtesy of Parker's

Parker's, also known as Parker's Kitchen, serves a wide variety of freshly made hot and cold foods, including breakfast items, sandwiches, and their popular fried chicken and sides. They also offer snacks, like chips, popcorn, candy bars, packaged cakes, and other sweets. Fountain drinks served with Parker's popular chewy ice are a favorite.

QuickChek

Photo courtesy of QuickChek

With a food counter serving soups, salads, sandwiches, wraps, and seasonal dishes, as well as a bakery that sells a variety of baked goods, such as their signature cookies, QuickChek aims to redefine "fresh convenience." They also have bottled and fountain beverages, and energy drink enthusiasts enjoy their Red Bull Infusions.

QuikTrip

Photo courtesy of QuikTrip

Through their QT Kitchens counters, QuikTrip serves food that’s made fresh to order each day. The vast menu includes frozen treat concoctions, specialty drinks, breakfast biscuits, macaroni and cheese, sandwiches, pizza, and tacos, among other yummy fare.

Royal Farms

Photo courtesy of Royal Farms

Royal Farms

Royal Farms offers a breakfast menu that’s available any time of the day or night. That's in addition to other hot food menu items, including sandwiches, burgers, hot dogs, and their popular fried chicken. The stores also sell a wide variety of packaged snacks along with fountain and bottled beverages. Some locations even feature a Blending Bar, where you can craft a milkshake.

Rutter's

Photo courtesy of Rutter's

Rutter's 24-hour shops have a food service counter that’s also open all hours and serves a variety of items, from seafood and burgers to pizza and subs. They also have a full breakfast menu and a children’s menu that includes grilled cheese sandwiches and a hot macaroni and cheese dish.

Sheetz

Photo courtesy of Sheetz

Sheetz offers a consistent and affordable menu of fresh made-to-order items with plenty of options, including sandwiches, burgers, pizza, salads, and breakfast items. Travelers also enjoy a multitude of beverages like hot coffee drinks, cold brews, and milkshakes.

Spinx

Photo courtesy of Savannah Bockus

With stores across South Carolina, Spinx is known for its cost-saving Spinx Xtras offers. It serves traditional gas station snack foods like packaged snacks, bottled beverages, and fountain sodas, in addition to a menu of fresh breakfast foods, fried chicken, sides, sandwiches, and wraps.

TravelCenters of America

Photo courtesy of TravelCenters of America

TravelCenters of America

TravelCenters of America is a chain of full-service truck stops and travel centers, with stores that serve homestyle food in their full-service restaurants. Additionally, they offer a number of fast food restaurants across their many locations, from Popeyes to Taco Bell, grab-and-go options, packaged snacks, and groceries.

TRIO

Photo courtesy of Tran Van Quyet / iStock / Getty Images Plus

At TRIO, you can start your day with a freshly baked cinnamon roll, breakfast sandwich, or breakfast burrito coupled with your favorite coffee or latte. For lunch or dinner, pick up one of the right-from-the-oven pizzas or grab one to bake at home. 

UDF

Photo courtesy of Brothers91 / E+ Getty Images

At UDF, you'll find quite a selection of eats, from fresh-baked doughnuts to grilled hot dogs to tasty treats like classic chocolate malts and hand-dipped ice cream. You also can stock up on must-have grocery items like milk and bread. 

Wawa

Photo courtesy of SbytovaMN // Getty Images

Wawa offers traditional gas station food and beverages, but it's beloved for its wide variety of hot foods. That includes breakfast items, hoagies, burgers, pizzas, soups, and salads, among many other dishes. Their kids meals are popular for families on road trips. 

Weigel's

Photo courtesy of Weigel's

Weigel's has dozens of locations in the East Tennessee region, each serving up sweets from the bakery such as doughnuts, cookies, and muffins. They also serve hot foods like pizzas, sandwiches, fried chicken, and breakfast foods.

About 10Best Readers' Choice Awards

Nominees are submitted by a panel of experts. 10Best editors narrow the field to select the final set of nominees for the Readers’ Choice Awards. Readers can vote once per category, per day. For any questions or comments, please read the FAQ or email USA TODAY 10Best .

The Experts

Chez chesak.

Chez Chesak

‘Chez’ Chesak is Executive Director of the Outdoor...   Read More

‘Chez’ Chesak is Executive Director of the Outdoor Writers Association of America, an adventure travel writer, board member of the Society of American Travel Writers and 22-year veteran of the outdoor and travel industries. While he’s lived all over the U.S. and traveled to more than 30 countries, he has the most fun when he’s exploring with his wife Sally and two daughters. An avid outdoors person, he’s happiest on a trail, on skis, or nestled into a sleeping bag. Learn more about him and his work at www.chezconnects.com .  

Chez Chesak

Jacky Runice

Jacky Runice

Born in Bucktown when bulletproof was a home...   Read More

Born in Bucktown when bulletproof was a home safety choice and not a coffee order, Jacky Runice has been knocking around Chicago as a professional print, online and broadcast journalist and editor specializing in separating the riff from the raff in culture, entertainment, food, travel and pure unadulterated fun. Jacky is a member of the International Food, Wine & Travel Writers Association (IFWTWA). In her best Chicagoese, Jacky asks, "Who has the time or money to blow on hotels, attractions, restaurants, exhibits and activities that blow?"

Jacky Runice

Jenny Peters

Jenny Peters

Jenny Peters – aka Jet Set Jen – is a Los...   Read More

Jenny Peters – aka Jet Set Jen – is a Los Angeles-based freelance journalist, editor and party columnist specializing in travel, entertainment, film, food, wine, fashion and the other good things in life. She is a founding/voting member of the Critics Choice Association, who present the Critics’ Choice Awards every January. Her favorite places to be are on the beach in Southern California playing volleyball, scuba diving with the sharks in warm tropical waters or strolling the streets and soaking in the atmosphere of one of the world's great cities (New Orleans and Florence are her favorites).

Jenny Peters

Melanie Reffes

Melanie Reffes

Melanie is an island girl at heart . Born in...   Read More

Melanie is an island girl at heart . Born in Manhattan, she now lives on the sunny island of Montreal and covers  the Caribbean for a variety of publications  including  USA TODAY 10Best, CaribbeanTravel.com and MarryCaribbean.com.  A journalist with a boatload of writer awards under her belt, Melanie's affection for the Caribbean started  young when her family vacationed in Puerto Rico.   An avid fan of spicy food,   Melanie enjoys the diversity of Montreal - especially during the warmer months -when she's not en route to the Caribbean. She  holds a Masters Degree in Social Work from the University of Toronto. 

Melanie Reffes

Molly O'Brien

Molly O'Brien

Molly O'Brien is a Los Angeles-based freelance...   Read More

Molly O'Brien is a Los Angeles-based freelance travel journalist, who writes and edits for a variety of international travel and lifestyle outlets including Fodor’s Travel, Travel + Leisure, and Business Insider among others. She's lived on both coasts from Massachusetts to California and has so far made Greater Boston, the San Francisco Bay Area, San Luis Obispo, Barcelona, and Los Angeles her home.  Molly earned her journalism degree at Cal Poly San Luis Obispo on the Central Coast of California and since then has worked professionally in the fields of hospitality and travel PR and most recently, as a freelance travel writer and editor. Molly especially enjoys covering feature profiles about interesting people doing interesting things such as chocolate making, beekeeping, wing-walking, and interesting destinations like under-the-radar wine spots, the best brewery towns, and lesser-known ski destinations.  She also loves to write about a boutique hotel with a good story. When she's not writing, Molly enjoys spending time outdoors, exploring new coffee shops and breweries, and of course, traveling.  Her favorite city in the world (so far) is Barcelona, Spain, but she loves traveling anywhere that offers sunny weather and ample hiking opportunities. She loves spending time in the mountains, enjoys connecting with nature through camping and glamping adventures, and is always up for learning about the world through fun, immersive experiences (and then sharing those stories!).  You can connect with Molly here:  Instagram: @metropolitanmolly Twitter: @Molly_A_OBrien Facebook: @MetropolitanMolly LinkedIn: @mollyannobrien www.metropolitanmolly.com

Molly O'Brien

Olivia Christine Perez

Olivia Christine Perez

Olivia Christine Perez is an outdoor + travel...   Read More

Olivia Christine Perez is an outdoor + travel wellness expert, author, and the creator of  O. Christine : a travel and wellness platform inspiring thousands of people to travel more and get outdoors for their wellness. Living with an autoimmune disease herself, Olivia helps people find wellness through the outdoors, self-care adventures, and mindful travel experiences. You can follow her work at  ochristine.com  and  instagram.com/ochristine.

Olivia Christine Perez

Tamara Gane

Tamara Gane

Tamara Gane is an expert panel member for 10Best...   Read More

Tamara Gane is an expert panel member for 10Best Readers' Choice Awards. She's based in Reno/Lake Tahoe and in addition to USA Today 10Best, her work has been published in Travel & Leisure, Fodor's Travel, The Washington Post, SF Gate, Houston Chronicle, Lonely Planet, and more.

Tamara Gane

10Best Editors

10Best Editors

USA TODAY 10Best provides users with original,...   Read More

USA TODAY 10Best provides users with original, unbiased and experiential travel coverage of top attractions, things to see and do, and restaurants for top destinations in the U.S. and around the world.

10Best Editors

  • Search Please fill out this field.
  • Manage Your Subscription
  • Give a Gift Subscription
  • Sweepstakes
  • Travel Products

REI Is Cleaning House With a Massive Spring Sale — Shop the 50 Best Deals Up to 81% Off

Score Patagonia, New Balance, Cotopaxi, and more from just $4

travelling salesperson award

Best Apparel Deals

Best shoe deals, best camping gear deals, best travel bag deals.

We independently evaluate all recommended products and services. If you click on links we provide, we may receive compensation. Learn more .

Travel + Leisure

Since the arrival of spring, my mind has been consumed with non-stop thoughts of my upcoming outdoor adventures that will make the most out of the longer, warmer days. But as I learned the hard way last year, the trademark of any great trip is being prepared with excellent travel gear. Trust me, the last thing that anyone wants is to let uncomfortable athleisure hinder their enjoyment or have a flimsy tent spoil their camping trip. When it comes to exceptional outdoor gear, REI is my ultimate destination for purchasing high-quality and dependable travel essentials that are built to last.

If you've been searching for the perfect opportunity to upgrade your gear, then you're in luck, because REI also happens to be hosting an incredible (and under-the-radar) spring sale to ring in the season. With hundreds deals on top brands like Patagonia , Vuori , New Balance , Hoka , and Cotopaxi , this sale requires some diligent scrolling, so I’ve taken the time to carefully sift through them alls to curate a list of the  50 best ones, starting at just $4 ahead of all of your upcoming ventures. 

The apparel deals at REI are truly next-level. With mega discounts on the top-rated and extra stylish Outdoor Voices Doing Things Dress and Arc'teryx Men's Cormac Crew SS Shirt in Pytheas Heather , you have the chance to upgrade your wardrobe with high-quality pieces that are perfect for any adventure. And guess what? You can snag a pair of the REI Co-op Women’s Trailsmith Overalls in Washed Blue for just $27 and even get $50 off a pair of the Kuhl Men’s Renegade Rock Pants in Bedrock . We don’t know how long these deals will last, or how much longer they’ll be in stock. So if I were you, I’d get shopping. 

  • Vuori Women's Halo Essential Hoodie , $28 (originally $96)
  • Outdoor Voices Doing Things Dress , $32 (originally $108) 
  • REI Co-op Women's Powderbound Insulated Jacket , $100 (originally $199)
  • Vuori Women's Vintage Ripstop Shorts , $30 (originally $68)
  • Patagonia Women's Wind Shield Pants , $84 (originally $169)
  • REI Co-op Women's Wallace Lake Flannel Shirt , $18 (originally $75)
  • Arc'teryx Men's Cormac Crew SS Shirt in Pytheas Heather , $56 (originally $70) 
  • REI Co-op Men’s Trailsmith Fleece Jacket in Red Cascade , $45 (originally $90)
  • Kuhl Men’s Renegade Rock Pants in Bedrock , $49 (originally $99)
  • Patagonia Women’s Strider Pro Shorts 3.5-inch , $23 (originally $79)
  • REI Co-op Women’s Trailsmith Overalls in Washed Blue , $27 (originally $90) 
  • Topo Designs Men’s Patagonia Women's Wind Shield Pants , $84 (originally $169)
  • REI Co-op Men's Trail Pants , $30 (originally $100)

Vuori Women's Halo Essential Hoodie

Any experienced hiker, runner, or traveler will tell you that the shoes you wear (and pack) play an important role in ensuring a comfortable trip. If your shoe collection is lacking in that department ahead of spring hikes and other outdoor activities, then consider this REI sale as a clear indication that it's time for an upgrade. Whether its with a pair of the New Balance Men’s Fresh Foam X More v4 Sneakers to wear on your next run or the top-rated Merrell Men's Merrell Moab Women's Speed Mid Gore-Tex Hiking Boots for your next trek, be sure to take advantage of significant discounts on both pairs while they’re still in stock. 

  • New Balance Men’s Fresh Foam X More v4 Sneakers in Summer Aqua , $112 (originally $150) 
  • La Sportiva Men’s Jackal GTX Trail-Running Shoes , $117 (originally $195)
  • Black Diamond Women's Fuel Approach Shoes , $93 (originally $170) 
  • Allbirds Women's SuperLight Wool Runner Sneakers , $60 (originally $120)
  • Helly Hansen Women’s Cascade Mid HT Hiking Boots , $88 (originally $160)
  • Keen Women's Targhee III Waterproof Mid Hiking Boots in Atlantic Blue , $82 (originally $165)
  • Keen Women's Astoria West Sandals , $81 (originally $125) 
  • Oboz Bozeman Women's Mid Hiking Boots , $74 (originally $135)
  • Rockfish Women's Chelsea Wellington Ankle Boots , $66 (originally $135)
  • La Sportiva Men's Ultra Raptor II Mid GTX Hiking Boots , $140 (originally $199)
  • Hoka Men's Arahi 6 Road-Running Shoes , $113 (originally $140)
  • Merrell Men's Merrell Moab Women's Speed Mid Gore-Tex Hiking Boots , $102 (originally $170)
  • Columbia Men's Rostra Beachcomber PFG Flip-Flops , $32 (originally $50)

Keen Women's Astoria West Sandals

Complete with stellar deals on spacious tents and campsite must-haves , REI has some of the best discounts on camping gear across the web right now. If you’re looking to turn your next camping experience into a glamping experience, I recommend snagging the REI Co-op Outward Hammock while it's on sale for $99. Or, if your camping accessory department needs a bit more love, you’ll have to check out the TheTentLab The Deuce UL Backcountry Trowel while its on sale for $15, the Princeton Tec Snap Solo Headlamp for just $21, and the cooling and UV-blocking Sunday Afternoons UVShield Cool Face Mask for a mere $4.

  • Sunday Afternoons UVShield Cool Face Mask , $4 (originally $20) 
  • GSI Outdoors Cascadian 1-Person Table Set , $9 (originally $18)
  • Big Agnes Wyoming Trail 2 Tent , $390 (originally $650)
  • Alpine Mountain Gear Weekender Tent 4 , $65 (originally $150) 
  • Alps Mountaineering Dash Chair , $45 (originally $120)
  • Princeton Tec Snap Solo Headlamp , $21 (originally $40)
  • TheTentLab The Deuce UL Backcountry Trowel , $15 (originally $20)
  • Hydro Flask Cooler Cup , $15 (originally $25)
  • Mountain Equipment Starlight I Sleeping Bag , $90 (originally $205)
  • Leki Jannu FX TA Trekking Poles , $110 (originally $150)
  • Trekmates Bomberlite Sleeping Pad , $54 (originally $120) 
  • REI Co-op Outward Hammock , $99 (originally $199)

Big Agnes Wyoming Trail 2 Tent

So you’ve shopped for new camping accessories, clothes, and shoes, but what about something to carry those precious valuables in? You'll need a durable backpack, duffel, or suitcase to withstand the weight of your essentials, so that’s where REI’s deals on spacious and practical bags come in. Shoppers can score the stylish Cotopaxi Luzon Del Dia 18-liter Backpack , a roomy and sleek hiking bag for just $65 off and high-quality Eagle Creek Tarmac XE 2-Wheel 95-liter Wheeled Luggage while it's sporting an enticing $100 discount. That’s not all, as customers can also enjoy steep discounts on daypacks and hip packs for a fraction of their price. But you’ll have to act accordingly because there’s no way these bag deals will be in stock for much longer. 

  • Eagle Creek Tarmac XE 2-Wheel 95-liter Wheeled Luggage , $240 (originally $339)
  • Cotopaxi Luzon Del Dia 18-liter Backpack , $45 (originally $60) 
  • Granite Gear Perimeter 35 Pack , $112 (originally $230) 
  • Patagonia Ultralight Black Hole Mini Hip Pack , $24 (originally $35)
  • Patagonia Fieldsmith Roll-Top Pack , $70 (originally $129)
  • Osprey Heritage Aether 30 Backpack , $98 (originally $180)
  • Topo Designs Mini Shoulder Bag , $27 (originally $39)
  • Gregory Men’s Zulu 30 Pack in Fiery Red , $120 (originally $160)
  • Sherpani Women’s Cabo Convertible Pack , $52 (originally $75)
  • Kavu Wombat Pack , $45 (originally $65)
  • REI Co-op Big Haul 28 Recycled Duffel , $70 (originally $100)
  • Mountain Hardwear Camp 4 Duffel , $91 (originally $130)

Eagle Creek Tarmac XE 2-Wheel 95-liter Wheeled Luggage

Love a great deal? Sign up for our T+L Recommends newsletter and we’ll send you our favorite travel products each week.

See More T+L Shopping Deals

travelling salesperson award

AiSDR Triumphs with 2024 Global Recognition Award: A Milestone in AI-Driven Sales and Marketing

AiSDR, a pioneering entity in the AI B2B Sales sector, has been honored with a 2024 Global Recognition Award. This award highlights organizations and individuals demonstrating remarkable innovation, growth, and leadership. AiSDR's recognition underscores its impactful contributions to sales and marketing through advanced AI-driven solutions.

New York, United States - April 12, 2024 —

travelling salesperson award

AiSDR has distinguished itself as a leading AI sales assistant provider that engages prospects in meaningful dialogues. From being merely an idea at Y Combinator to securing $3 million in seed funding and engaging a Fortune 500 company for a pilot, achieving more than $500,000 in ARR within four months, AiSDR's trajectory showcases its rapid growth and pioneering approach to sales development.

Innovations and Achievements

AiSDR's journey is marked by acceptance into Y Combinator with a prototype, swift product evolution, significant investments from esteemed angels and funds, and successful client integration. These achievements signify the company's adaptability and the effectiveness of its product. Yuriy Zaremba, co-founder of AiSDR, shared, "At AiSDR, our mission is to continue setting the pace in AI engagement; our dedication to prioritizing our customers and providing unparalleled support inspires AI interactions with a distinctly human essence."

The company's distinctive approach to AI-driven sales development, highlighted by personalized email outreach and autonomous query and objection handling, differentiates it from others. AiSDR's technology stands out in the market through its unparalleled depth and flexibility in configuration, ensuring high conversion rates by responding to leads within 10 minutes. This approach demonstrates AI's immense potential to enhance sales strategies and highlights the sophistication and adaptability of AiSDR's solution in catering to diverse business needs.

Client Growth and Market Influence

From the beginning, AiSDR has secured 65 clients, proving the efficacy of its solutions in the B2B SaaS space. The company has received recognition for its innovative contributions, earning accolades from various reputable sources. Forbes has listed it among the top 25 Ukrainian startups with unicorn potential. AiSDR's commitment to scaling personalized email communications and automating sales development tasks significantly benefits its clients.

AiSDR distinguishes itself through comprehensive management of email outreach, from initial setup to lead generation and follow-up messaging. The platform's collaboration with over 50 sales and SDR team leaders to refine its AI-generated content ensures unparalleled precision and human likeness.

Final Words

Alex Sterling from the Global Recognition Awards observed, "AiSDR's recognition marks its leadership in AI-driven sales and marketing solutions. Their pioneering approach improves email outreach efficiency and sets new engagement standards within the sector." This accolade reflects AiSDR's pursuit of excellence and influential role in advancing sales development through artificial intelligence.

About Global Recognition AwardsTM:

Global Recognition Awards TM is an international organization that recognizes exceptional companies and individuals who have significantly contributed to their industry. Their awards are highly regarded and sought after by businesses across the globe.

Contact Info: Name: Alexander Sterling Email: Send Email Organization: Global Recognition Awards Website: https://globalrecognitionawards.org

Source: Baden Bower

Release ID: 89126991

In case of identifying any errors, concerns, or inconsistencies within the content shared in this press release that necessitate action or if you require assistance with a press release takedown, we strongly urge you to notify us promptly by contacting [email protected]. Our expert team is committed to addressing your concerns within 8 hours by taking necessary actions diligently to rectify any identified issues or supporting you with the removal process. Delivering accurate and reliable information remains our top priority.

IMAGES

  1. Travelling Salesperson using Branch and bound by Prof Anamika Joshi

    travelling salesperson award

  2. Travelling Salesperson Algorithm

    travelling salesperson award

  3. 9 Types of Sales Awards, Design Ideas & Names

    travelling salesperson award

  4. Top Award Trophies for Your Sales Team

    travelling salesperson award

  5. Sales Recognition Achievement Award (#062-3)

    travelling salesperson award

  6. Top Salesperson Award Sample Ideas

    travelling salesperson award

VIDEO

  1. Travelling Salesperson By Prof Anamika Joshi

  2. CA Travelling Salesperson Problem Part 2

  3. Travelling Salesperson Problem

  4. Travelling Salesperson Problem

  5. D2 Edexcel Travelling Salesperson Exam Questions

  6. L- 32

COMMENTS

  1. Travelling Salesman

    Travelling Salesman is an award-winning intellectual thriller about four mathematicians hired by the U.S. government to solve the most elusive problem in computer science history -- P vs. NP. ... "Travelling Salesman's mathematicians are all too aware of what their work will do to the world, ...

  2. $1M Prize for Solution of Traveling Salesman Problem

    The Show. Mechaniker March 17, 2012, 8:44am 1. "Meanwhile, the Clay Mathematics Institute is offering a $1 million prize to anyone who can show whether the Traveling Salesman Problem can be fully solved at all, which the mathematician Jordan Ellenberg recently called "the biggest open problem in complexity theory.".

  3. Commercial Sales Award [MA000083]

    Source reference: Commercial Sales Award [MA000083] clauses 2 and 4. Who the Commercial Sales Award doesn't cover. Commercial Travellers, Merchandisers and Advertising Sales Representatives are not covered by this award when they are employed by a business that is covered by a different modern award that has a classification for them.

  4. Travelling Salesman (2012 film)

    Travelling Salesman is a 2012 intellectual thriller film about four mathematicians who solve the P versus NP problem, one of the most challenging mathematical problems in history. The title refers to the travelling salesman problem, an optimization problem that acts like a key to solving other difficult mathematical problems. It has been proven that a quick travelling salesman algorithm, if ...

  5. A brief History of the Travelling Salesman Problem

    Leaping forward to the 1970s R.M. Karp and M. Held published "The travelling-salesman problem and minimum spanning trees", a paper which introduced the 1-tree relaxation of the TSP and the idea of using node weights to improve the bound given by the optimal 1-tree. Part II was published in 1971, and detailed An iterative method for computing a ...

  6. Last-mile routing research challenge awards $175,000 to three winning

    Author: Douglas Gantenbein. This article originally appeared at Amazon Science. Finding the optimal route between multiple destinations — the traveling salesman problem — is a challenge regularly faced by Amazon's Last Mile team. Meeting that challenge has meant developing planning software to allow Amazon's delivery fleet to find the most efficient routes.

  7. Traveling Man

    Traveling Man. Illinois explores the history of the profession shared by L. Frank Baum, Benedict Arnold, and Johnny Appleseed. Corinne Zeman. HUMANITIES, November/December 2011, Volume 32, Number 6. Photo caption. When Arthur Miller's Death of a Salesman appeared on stage in 1949, the traveling salesman became—and, in the minds of many, has ...

  8. Travelling Salesman (2012)

    Travelling Salesman: Directed by Timothy Lanzone. With Danny Barclay, Eric Bloom, David John Cole, Malek Houlihan. Four mathematicians are hired by the US government to solve the most powerful problem in computer science history.

  9. FWO

    Part 1— Application and Operation of this Award 1. Title and commencement. 1.1 This award is the Commercial Sales Award 2020.. 1.2 This modern award commenced operation on 1 January 2010. The terms of the award have been varied since that date.. 1.3 A variation to this award does not affect any right, privilege, obligation or liability that a person acquired, accrued or incurred under the ...

  10. Travelling salesman problem

    The generalized travelling salesman problem, also known as the "travelling politician problem", deals with "states" that have (one or more) "cities" and the salesman has to visit exactly one "city" from each "state". One application is encountered in ordering a solution to the cutting stock problem in order to minimize knife changes.

  11. Traveling Salesman: A Seemingly Unsolvable Problem Offers a Glimpse of

    The task is the long-standing challenge known as the traveling salesman problem, or TSP for short. Finding a method that can quickly solve every example of the TSP would be a stunning breakthrough ...

  12. How to plan and implement a sales award incentive trip

    First, have a number of attendees in mind. You'll need to establish your budget early on in order to make the most of this trip, so knowing how many employees you'll need to provide transportation and lodging for is extremely important. Once you have that number in mind - maybe it's 5% of the sales force or more like 10% if you have a ...

  13. Traveling Salesperson Problem

    The traveling salesperson problem can be modeled as a graph. Specifically, it is typical a directed, weighted graph. Each city acts as a vertex and each path between cities is an edge. Instead of distances, each edge has a weight associated with it. In this model, the goal of the traveling salesperson problem can be defined as finding a path ...

  14. Computer Scientists Break Traveling Salesperson Record

    The traveling salesperson problem is one of a handful of foundational problems that theoretical computer scientists turn to again and again to test the limits of efficient computation. The new result "is the first step towards showing that the frontiers of efficient computation are in fact better than what we thought," Williamson said.

  15. 7 Reasons To Use a Sales Incentive Travel Program

    2. "Non-monetary" is good. "Experiential" is great. For some people, working a job is about one thing and one thing only: the paycheck. They're not invested in their job or their workplace, and the only rewards that will motivate these people are monetary.

  16. Seven Tips For The Traveling Salesperson

    Create a routine. Parking in the same level of the parking deck or same area of the lot assures you that you won't have a hard time finding your vehicle upon your return. After a cross-country ...

  17. Solving the Traveling Salesman Problem

    The Traveling Salesman Problem (TSP) is a problem of determining the most efficient route for a round trip, with the objective of maintaining the minimum cost and distance traveled. It serves as a foundational problem to test the limits of efficient computation in theoretical computer science. The salesman's objective in the TSP is to find a ...

  18. Traveling Salesperson

    Traveling Salesperson is a widely studied graph theory problem that is solved by using a greedy algorithm. The premise is that you have a graph of cities with certain distances (or weights) between them. The objective is to find the shortest path that will allow you to visit each city once, leaving you at the city in which you began your journey.

  19. What does a Travelling Salesman do? Role & Responsibilities

    What does a Travelling Salesman do? Sales representatives are responsible for selling a company's products by identifying leads, educating prospects on products through calls, trainings, and presentations, and providing existing customers with exceptional support. Sales representatives are either inside or outside sales reps.

  20. Traveling Salesman Problem (TSP) Implementation

    Travelling Salesman Problem (TSP) : Given a set of cities and distances between every pair of cities, the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point. Note the difference between Hamiltonian Cycle and TSP. The Hamiltonian cycle problem is to find if there exists a tour that visits every city exactly once.

  21. NSF Award Search: Award # 9528462

    This project's goal is to develop an exposition of a new algorithm for the Traveling Salesman problem. This problem is theoretically intractable, and practical heuristic techniques for large TSP problems have been elusive. ... Please report errors in award information by writing to: [email protected]. Top. 2415 Eisenhower Ave Alexandria, VA ...

  22. Neural Network Estimators for Optimal Tour Lengths of Traveling

    We introduce quick and highly accurate Traveling Salesperson Problem (TSP) tour length estimators based on neural networks (NNs) to facilitate this. Our approach combines the power of NNs and theoretical knowledge in the routing domain, utilizing a novel feature set that includes node-level, instance-level, and solution-level features.

  23. Learning the travelling salesperson problem requires rethinking

    Abstract. End-to-end training of neural network solvers for graph combinatorial optimization problems such as the Travelling Salesperson Problem (TSP) have seen a surge of interest recently, but remain intractable and inefficient beyond graphs with few hundreds of nodes. While state-of-the-art learning-driven approaches for TSP perform closely ...

  24. Global Vision Awards 2024

    These are the winners of Travel + Leisure's 2024 Global Vision Awards, plus how this year's panel arrived at the final list of 26 honorees. The Travel + Leisure Global Vision Awards recognize ...

  25. Pet Travel

    Traveling with a pet in a foreign country can be complex and time-consuming. You need to meet the destination country's specific entry requirements for pets. These may include vaccinations, tests, treatments, and a health certificate (also called an international health certificate, a veterinary health certificate, a veterinary certificate, or ...

  26. Save 25% Now

    Terms and conditions. Book a Southwest ® flight on Southwest.com or swabiz.com using your Rapid Rewards® points from April 12 through April 15, 2024 (the "Booking Period") and receive 25 percent off when you fly between April 12-September 30, 2024 with travel blacked out May 23, May 24, May 27, July 7, July 14, July 21, and July 28, 2024 (the "Travel Period").

  27. What is the Best Gas Station for Food for 2024?

    Olivia Christine Perez is an outdoor + travel wellness expert, author, and the creator of O. Christine: a travel and wellness platform inspiring thousands of people to travel more and get outdoors for their wellness. Living with an autoimmune disease herself, Olivia helps people find wellness through the outdoors, self-care adventures, and ...

  28. The 50 Best REI Spring Sale Outdoor Gear Deals

    REI is having a massive sale on outdoor gear and travel accessories. Right now, shoppers can save up to 81 percent off on hiking boots, camping gear, and travel clothes from brands like Patagonia ...

  29. AiSDR Triumphs with 2024 Global Recognition Award: A Milestone in AI

    AiSDR, a pioneering entity in the AI B2B Sales sector, has been honored with a 2024 Global Recognition Award. This award highlights organizations and individuals demonstrating remarkable ...