Travelling Salesman Games and Routing Games
Four universities, one in Ohio, one in Pennsylvania, one in Quebec, and one in Rhode Island are considering to invite a speaker from Paris, France, to give lectures at each of the universities. They are studying how to make the costs of travel as low as possible. It is clear to all of them that it does not make sense for each one of them to pay a two way ticket from Paris and back. Once the speaker is in North America they should let him visit each university and then travel back. They want to find an order for him to visit the universities that minimizes the total travel costs. The costs for a one way ticket between Paris and the universities in either direction are: for Ohio, $350, for Pennsylvania, $300, for Quebec, $200, and for Rhode Island, $250. The costs for a one way ticket between the universities in either directions are: Ohio-Pennsylvania, $100, Ohio-Quebec, $150, Ohio-Rhode Island, $150, Pennsylvania-Quebec, $150, Pennsylvania-Rhode Island, $100, and Quebec-Rhode Island, $100. These costs are summarized in table 5.1. After some analysis the universities realize that they will minimize the travel costs if the let the speaker travel form Paris to Pennsylvania, to Ohio, to Rhode Island, to Quebec, and then back to Paris. With this tour the total travel costs are $850. Now they still need a way to divide these costs among them. Simply assigning the cost pertaining to each leg of the tour to the university at which that leg ends will not work, because the speaker will have to return to Paris and the universities will have to cover those costs too.
KeywordsTravel Salesman Problem Travel Cost Optimal Order Grand Coalition Optimal Tour
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