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 p ki is received by the traveling salesman when node i is visited in the k-th order of the route, while a travel cost c i j 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. Computational experiments are also presented when solving the MIP models with a well-known optimization software, as well as with a tabu search algorithm.

Dye Schedule Optimization: A Case Study in a Textile Industry

“…For large models structured, considering the traveling salesman problem approach becomes necessary for other methodologies [30][31][32].…”

The multicommodity traveling salesman problem with priority prizes: a mathematical model and metaheuristics

“…In this variation, the quality of customer service and delivery priorities are considered because customer preferences in terms of delivery sequence order must be quantified and optimized. Pureza et al (2018) modeled this problem as a special case of a quadratic assignment problem (Koopmans and Beckmann 1957) called the Travelling Salesman Problem with Priority Prizes (TSPPP) and they solved it by a Tabu Search metaheuristic (Glover 1986). Silva (2017); Silva et al (2018) used the TSPPP and the Profitable Tour Problem (PTP) (Archetti et al 2014;Balas 1987) to formulate the problem of elaborating touristic itineraries considering variables such as the profile of the visitors, the planning of the trip, visitors' preferences and touristic attractions.…”