Generalized multiple depot traveling salesmen problem - polyhedral study and exact algorithm

TL;DR

This paper studies the generalized multiple depot traveling salesmen problem, providing a new integer programming formulation, polyhedral analysis, and an exact branch-and-cut algorithm with computational validation.

Contribution

It introduces a novel polyhedral study and an exact algorithm for the GMDTSP, enhancing solution methods for this NP-hard problem.

Findings

The proposed algorithm efficiently solves benchmark instances.

Valid inequalities improve the linear programming relaxation.

Polyhedral analysis identifies facet-defining inequalities.

Abstract

The generalized multiple depot traveling salesmen problem (GMDTSP) is a variant of the multiple depot traveling salesmen problem (MDTSP), where each salesman starts at a distinct depot, the targets are partitioned into clusters and at least one target in each cluster is visited by some salesman. The GMDTSP is an NP-hard problem as it generalizes the MDTSP and has practical applications in design of ring networks, vehicle routing, flexible manufacturing scheduling and postal routing. We present an integer programming formulation for the GMDTSP and valid inequalities to strengthen the linear programming relaxation. Furthermore, we present a polyhedral analysis of the convex hull of feasible solutions to the GMDTSP and derive facet-defining inequalities that strengthen the linear programming relaxation of the GMDTSP. All these results are then used to develop a branch-and-cut algorithm to obtain optimal solutions to the problem. The performance of the algorithm is evaluated through extensive computational experiments on several benchmark instances.