Model and algorithms for the Multicommodity Traveling Salesman Problem

We are introducing in this article the Multicommodity Traveling Salesman Problem (MTSP), where the objective is to deliver all the demands of different commodities by a tour that minimizes the sum of the fixed and variable costs for the selected arcs. The MTSP yields then a large scale mixed integer linear programming problem. In this article we devise a Lagrangean based heuristic approach to tackle this more general TSP variant.