An Effective Matheuristic for the Multivehicle Inventory Routing Problem

This study considers the multivehicle inventory routing problem in which a supplier has to build a distribution plan over a discrete time horizon to replenish a set of customers that faces a given demand. Transportation costs as well as inventory costs at the supplier and at the customers are to be minimized. A matheuristic algorithm is proposed that is based on sequentially solving different mixed integer linear programs. The algorithm merges the advantage of being easy to design and implement, as it is mainly based on the problem formulation, with the benefit of providing high-quality solutions. A computational study is performed on benchmark test instances by comparing the results with the ones obtained from previous algorithms proposed in the literature. The results show that the matheuristic algorithm outperforms the existing heuristic algorithms and finds a significant number of new best solutions in both small and large instances.