Optimal lateral transshipment policy for a two location inventory problem

We consider an inventory model for spare parts with two stockpoints, providing repairable parts for a critical component of advanced technical systems. As downtime costs for these systems are huge, ready-for-use spare parts are kept on stock, to be able to quickly respond to a breakdown of a system. We allow for lateral transshipments of parts between the stockpoints upon a demand arrival for a spare part. We are interested in the optimal lateral transshipment policy. We consider a continuous review setting, where the initial number of spare parts at each location is given. We assume Poisson demand processes, and allow for asymmetric demand rates and asymmetric costs structures at the two locations. Defective parts are replaced, and returned to the stockpoint for repair. Each location has ample repair capacity, and repair times are exponentially distributed, with the same mean repair time for both locations. Demands are satisfied from own stock, via a lateral transshipment, or via an emergency procedure. Using dynamic programming, we completely characterize and prove the structure of the optimal lateral transshipment policy, that is, the policy for satisfying demands, minimizing the long-run average costs of the system. This optimal policy is a threshold type policy. In addition, we derive conditions under which the so-called hold back and complete pooling policies are optimal, which are both policies that are often assumed in the literature