Consistency in multi-vehicle inventory-routing

Inventory-routing problems (IRPs) arise in vendor-managed inventory systems. They require jointly solving a vehicle routing problem and an inventory management problem. Whereas the solutions they yield tend to benefit the vendor and customers, solving IRPs solely based on cost considerations may lead to inconveniences to both parties. These are related to the fleet size and vehicle load, to the frequency of the deliveries, and to the quantities delivered. In order to alleviate these problems, we introduce the concept of consistency in IRP solutions, thus increasing quality of service. We formulate the multi-vehicle IRP, with and without consistency requirements, as mixed integer linear programs, and we propose a matheuristic for their solution. This heuristic applies an adaptive large neighborhood search scheme in which some subproblems are solved exactly. The proposed algorithm generates solutions offering a good compromise between cost and quality. We analyze the effect of different inventory policies, routing decisions and delivery sizes.