Robustness of inventory replenishment and customer selection policies for the dynamic and stochastic inventory-routing problem

When inventory management, distribution and routing decisions are determined simultaneously, implementing a vendor-managed inventory strategy, a difficult combinatorial optimization problem must be solved to determine which customers to visit, how much to replenish, and how to route the vehicles around them. This is known as the inventory-routing problem. We analyze a distribution system with one depot, one vehicle and many customers under the most commonly used inventory policy, namely the (s,S), for different values of s. In this paper we propose three different customer selection methods: big orders first, lowest storage first, and equal quantity discount. Each of these policies will select a different subset of customers to be replenished in each period. The selected customers must then be visited by a vehicle in order to deliver a commodity to satisfy the customers' demands. The system was analyzed using public benchmark instances of different sizes regarding the number of customers involved. We compare the quality and the robustness of our algorithms and detailed computational experiments show that our methods can significantly improve upon existing solutions from the literature.