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

Industrial Engineering and Operations Research Department, Columbia University, New York, New York 10027
Stern School of Business, New York University, New York, New York 10012
huh{at}ieor.columbia.edu
gjanakir{at}stern.nyu.edu

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-natural-convexity, which was studied in discrete convex analysis and recently used in the study of single-stage inventory systems with lost sales. We also remark on how our analysis extends to models with capacity constraints and/or backordering.

Subject classifications: inventory/production; lost sales; optimal policies; multiechelon.
History: Received May 2008; revision received December 2008; accepted March 2009.