Multi Travelling Salesman Problem Formulation

This paper presents a Mixed Integer Linear Programming for a special case of Multi Depot multiple Travelling Salesman Problem (MmTSP) wherein each salesman starts from a unique city, travels to a set of cities and completes the route by returning to his original city with each city visited once. Our approach consists of solving the problem using MmTSP formulation with dummy nodes as depots and with assigning one salesman to each one of these dummy nodes. Then with the aid of constraints that we developed, we were able to formulate the proposed problem. In this paper, we refer to this type of problem as Multi Travelling Salesman Problem, since it does not include a fixed starting point (usually defined as depot). The model was solved using optimization software to obtain preliminary results and the solution will be extended in future papers.