A transformation for multiple depot multiple traveling salesman problem

Abstract

In this paper, we present a transformation for the Multi Depot Multiple TSP (MmTSP) into Asymmetrical TSP (ATSP). The transformation is done by duplicating the depots, and with the aid of a precedence constraint, the salesman in the transformed graph will visit the original depot and its duplicates before proceeding to the next depots. We proved that solving the transformed problem leads to the same optimal solution. We test the proposed transformation against a Mixed Integer Linear Programming formulation for the MmTSP and compare the computational time between the two.