Integer Programming Model for Two-Centered Double Traveling Salesman Problem

Abstract

Traveling Salesman Problem (TSP) is among the most popular combinatorial problems and has been widely studied with many extensions in the literature. There have been integer programming formulations and solution approaches for TSP and its variations. One of the most popular topics is the multiple TSP (m-TSP). It has been started to work on the last decades. Generally, m-TSP has a single depot and more than one tour. However, some types have more than one depot. Besides, if seeking, many encounter with double traveling salesman problem (d-TSP). As inferred from the literature, d-TSP is a variation of m-TSP in which two salespersons operate in parallel. They start and end either in a single or two depots. Apart from the literature, a new TSP model has been constructed in this study. The model analyzes the behaviors of traveling salesmen both in the main and secondary tour. Tours have been aggregated via single node existing in the secondary tour. In the application part, Simulated Annealing (SA) was used to optimize the traveling paths of salesmen. The objective parameters of both tours have been explored within a numerical example. According to them, several cost values have been found. The optimum parameters and costs of both tours are to be determined and some practical issues relevant to the behaviors of traveling salesmen have been given. Results suggest that alternative travel plans of traveling salesmen could be possible. Also, findings give hints about both tours and their characteristics.