Mathematical Programming

, Volume 53, Issue 1, pp 199–211

Traveling salesman games

  • Jos A. M. Potters
  • Imma J. Curiel
  • Stef H. Tijs
Article

DOI: 10.1007/BF01585702

Cite this article as:
Potters, J.A.M., Curiel, I.J. & Tijs, S.H. Mathematical Programming (1992) 53: 199. doi:10.1007/BF01585702

Abstract

In this paper we discuss the problem of how to divide the total cost of a round trip along several institutes among the institutes visited. We introduce two types of cooperative games—fixed-route traveling salesman games and traveling salesman games—as a tool to attack this problem. Under very mild conditions we prove that fixed-route traveling salesman games have non-empty cores if the fixed route is a solution of the classical traveling salesman problem. Core elements provide us with fair cost allocations. A traveling salesman game may have an empty core, even if the cost matrix satisfies the triangle inequality. In this paper we introduce a class of matrices defining TS-games with non-empty cores.

AMS 1980 Subject Classifications

Primary 90D12Secondary 90C08

Key words

Traveling salesman problemgame theory

Copyright information

© The Mathematical Programming Society, Inc. 1992

Authors and Affiliations

  • Jos A. M. Potters
    • 1
  • Imma J. Curiel
    • 2
  • Stef H. Tijs
    • 1
  1. 1.Department of MathematicsUniversity of Nijmegen, ToernooiveldNijmegenNetherlands
  2. 2.Department of Mathematics and StatisticsUniversity of MarylandBaltimore County, CatonsvilleUSA