Solving the multi-depot vehicle routing problem with limited supply capacity at the depots with a multi-phase methodology

We consider an extension of the multi-depot vehicle routing problem (MDVRP), in which the supply capacity of the depots is limited. To solve this problem, we propose a multi-phase methodology, that extends the 'cluster first, route second' approach. It is based on iterative routings to find and reassign misplaced customers with respect to the depots and with the objective of improving the final routing. Several assignment and routing algorithms are considered to evaluate the proposed methodology under different settings. A mathematical model of the problem is given to perform a comparative study of the methodology against an exact solution method. We also evaluate the methodology for the MDVRP in order to provide a comparison with benchmark instances of the literature. The results obtained from the numerical experiments carried out allow to conclude that the methodology can be successfully applied to the MDVRP with capacitated depots.