Probabilistic analyses and algorithms for three-level distribution systems

We consider the problem of integrating inventory control and vehicle routing into a cost-effective strategy for a distribution system consisting of a single outside vendor, a fixed number of warehouses and many geographically dispersed retailers. Each retailer faces a constant, retailer specific, demand rate and inventory holding cost is charged at the retailers and the warehouses. We show that, in an effective strategy which minimizes the asymptotic long run average cost, each warehouse receives fully loaded trucks from the vendor but never holds inventory. That is, each warehouse serves only as a coordinator of the frequency, time and sizes of deliveries to the retailers. This insight is used to construct an inventory control policy and vehicle routing strategy for multi-echelon distribution systems. Computational results are also reported.