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

Author

Listed:
  • Woonghee Tim Huh

    (Industrial Engineering and Operations Research Department, Columbia University, New York, New York 10027)

  • Ganesh Janakiraman

    (Stern School of Business, New York University, New York, New York 10012)

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.

Suggested Citation

  • Woonghee Tim Huh & Ganesh Janakiraman, 2010. "On the Optimal Policy Structure in Serial Inventory Systems with Lost Sales," Operations Research, INFORMS, vol. 58(2), pages 486-491, April.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:2:p:486-491
    DOI: 10.1287/opre.1090.0716
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    References listed on IDEAS

    as
    1. Ganesh Janakiraman & John A. Muckstadt, 2009. "A Decomposition Approach for a Class of Capacitated Serial Systems," Operations Research, INFORMS, vol. 57(6), pages 1384-1393, December.
    2. Yingdong Lu & Jing-Sheng Song, 2005. "Order-Based Cost Optimization in Assemble-to-Order Systems," Operations Research, INFORMS, vol. 53(1), pages 151-169, February.
    3. Paul Zipkin, 2008. "On the Structure of Lost-Sales Inventory Models," Operations Research, INFORMS, vol. 56(4), pages 937-944, August.
    4. Rodney P. Parker & Roman Kapuscinski, 2004. "Optimal Policies for a Capacitated Two-Echelon Inventory System," Operations Research, INFORMS, vol. 52(5), pages 739-755, October.
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