Modeling and solving the traveling salesman problem with priority prizes

Abstract

This paper addresses the Traveling Salesman Problem with Priority Prizes (TSPPP), an extension of the classical TSP in which the order of the node visits is taken into account in the objective function. A prize pki is received by the traveling salesman when node i is visited in the k-th order of the route, while a travel cost cij is incurred when the salesman travels from node i to node j. The aim of the TSPPP is to find the maximum profit n-node tour. The problem can be seen as a TSP variant with a more general objective function, aiming at solutions that in some way consider the quality of customer service and the delivery priorities and costs. A natural representation for the TSPPP is here grounded in the point of view of Koopmans and Beckmann approach, according to which the problem is seem as a special case of the quadratic assignment problem (QAP). Given the novelty of this TSP variant, we propose different mixed integer programming models to appropriately represent the TSPPP, some of them based on the QAP.Com-putational experiments are also presented when solving the MIP models with a well-known optimization software, as well as with a tabu search algorithm.