Optimal policies for inventory systems with lateral transshipments

Using lateral transshipments can be beneficial in order to improve service levels and to reduce system costs. This paper deals with a single-echelon inventory system with two identical locations. Demands are generated by stationary and independent Poisson processes. In general, if a demand occurs at a location and there is no stock on hand, the demand is assumed to be backordered or lost. However, in this paper, lateral transshipments serve as an emergency supply in case of stock out. In this paper, the rule for lateral transshipments is given, while the ordering policies for normal replenishments are optimized. The transshipment rule is to always transship when there is a shortage at one location and stock on hand at the other. First, we assume that the locations apply (R,Q) policies for normal replenishments, and show that the optimal policies are not necessarily symmetric even though the locations are identical. This means that one cannot in general assume that the optimal policy is symmetric under symmetric assumptions. Second, we relax the assumption of (R,Q) policies and derive the optimal replenishment policy using stochastic dynamic programming.