On the Optimal Policy Structure in Serial Inventory Systems with Lost Sales

We study a periodically reviewed, serial inventory system in which excess demand from external customers is lost. We derive elementary properties of the vector of optimal order quantities in this system. In particular, we derive bounds on the sensitivity (or, more mathematically, the derivative) of the optimal order quantity at each stage to the vector of the current inventory levels. Our analysis uses the concept of L-naturalconvexity, which was studied in discrete convex analysis (Murota (2003)) and recently used by Zipkin (2008) for studying single-stage inventory systems with lost sales. We also remark on how our analysis extends to models with capacity constraints and/or backordering. ∗Industrial Engineering and Operations Research Department, Columbia University, 500 West 120th Street, New York, NY 10027, USA. Email: [email protected]. Research supported partially by NSF grant DMS-0732169. †Stern School of Business, New York University, 44 West 4th Street, New York, NY 10012, USA. Email: [email protected].