Solving an Open Path Multiple Depot Multiple Traveling Salesman Problem after transformation

In this paper, we present a transformation of the Open Path Multi Depot Multiple TSP (OP-MmTSP) into Asymmetrical Traveling Salesman Problem (ATSP). The transformation was done by duplicating the depots and then by redefining the cost matrix for both the original and duplicated depots. We were able to prove that the optimal solution on the transformed problem will lead to the same optimal solution on the original graph. Moreover, we tested the proposed transformation against a Mixed Integer Linear Programming (MILP) formulation for the MmTSP and measured the computational time for both problems.