An efficient matheuristic for the inventory routing problem

Abstract

We consider the general multi-vehicle and multi-period Inventory Routing Problem (IRP). A challenging aspect of solving IRPs is how to capture the relationship among the periods where the routing takes place. Once the routes are defined, computing the optimal inventory at each customer on each period amounts to solving a network flow problem. We investigate the impact of efficiently solving this recurring network problem on the solutions found by the devised algorithm. A very significant impact is observed when solving 638 instances in a classical benchmark set, improving 113 upper bounds through assembling the network optimization into an ILS-RVND algorithm. In particular, the results suggested this approach performs better for larger instances with more periods, obtaining speed-ups of about ten times. A detailed comparison against nine of the most prominent exact and heuristic methods favors the proposed approach.