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

Authors:
Woonghee Tim Huh;Ganesh Janakiraman
Affiliations:
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
Venue:
Operations Research
Year:
2010

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Abstract

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.