A Binary Programming Solution to the Min-Max Multiple-Depots, Multiple Traveling Salesman Problem

We formulate the Min-Max Multiple Depots, Multiple Traveling Salesmen Problem (MMMDMTSP) as a Binary Programming Problem. The MMMDMTSP is an extension of the classical Traveling Salesman Problem (TSP), in the sense that there are several salesmen, whose routes may originate at several depot locations, and where the goal is to minimize the longest tour by any single salesman. This problem is of particular interest in cases where the time required to complete a set of tasks is of the greatest importance, e.g., military missions or civilian relief efforts. Using our formulation, we develop an algorithm that is capable of finding a near optimal solution to the MMMDMTSP, with a bound on the optimal cost. Some sample solutions are shown for randomly generated instances of the problem, and the scalability properties of the solution are discussed.