We study an inventory routing problem where the goal is to determine an opti-mal distribution plan to replenish a set of customers, by routing a limited fleet ofcapacitated vehicles over a discrete planning horizon. Each customer consumes aper period quantity of products and have a maximum inventory capacity. Productscan be distributed by a supplier to the customers in advance compared to theirconsumption, provided that their inventory capacity is not violated. The goal is tominimize the total distribution cost, that comprises the routing and the inventorycosts. We develop a novel matheuristic approach to solve this problem. The algo-rithm is based on Kernel Search (KS), a heuristic framework that has been shownto find high-quality solutions for a number of combinatorial optimization problems.The basic idea of KS is to identify subsets of the decision variables and then solving,using a general-purpose solver, a sequence of Mixed-Integer linear Programs (MIPs),each one restricted to a subset of variables. Extensive computational experimentsare conducted on a very large set of benchmark instances. The results show thatKS outperforms state-of-the-art heuristic algorithms. It finds 103 new best-knownsolutions out of 240 large-scale instances.

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