The multilocation transshipment problem

We consider a supply chain, which consists of several retailers and one supplier. The retailers, who possibly differ in their cost and demand parameters, may be coordinated through replenishment strategies and transshipments, that is, movement of a product among the locations at the same echelon level. We prove that in order to minimize the expected long-run average cost for this system, an optimal replenishment policy is for each retailer to follow an order-up-to S policy. Furthermore, we demonstrate how the values of the order-up-to quantities can be calculated using a sample-path-based optimization procedure. Given an order-up-to S policy, we show how to determine an optimal transshipment policy, using a linear programming/network flow framework. Such a combined numerical approach allows us to study complex and large systems.