A new subtour elimination constraint for the vehicle routing problem

Vehicle Routing Problems (VRP) are concerned with the delivery of a single commodity from a centralized depot to a number of specified customer locations with known demands. In this paper we consider the VRP characterized by: fixed or variable number of vehicles, common vehicle capacity, distance restrictions, and minimization of total distance travelled by all vehicles as the objective. We develop an exact algorithm based on a new subtour elimination constraint. The algorithm is implemented using the CPLEX package for solving the relaxed subproblems. Computational results on 1590 simulated problems and 10 literature problems (without distance restrictions) are reported and a comparative analysis is carried out.