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TECHNICAL NOTE---Inventory Systems with a Generalized Cost Model

Author

Listed:
  • Woonghee Tim Huh

    (Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada)

  • Ganesh Janakiraman

    (School of Management, The University of Texas at Dallas, Richardson, Texas 75080)

  • Alp Muharremoglu

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Anshul Sheopuri

    (IBM T. J. Watson Research Center, Yorktown Heights, New York 10598)

Abstract

We study a single-stage inventory system with a generalized shortage penalty cost that includes the following three components: (i) a cost that is an increasing function of the number of backordered units in a period, (ii) a fixed cost incurred for each period in which there is a backorder irrespective of how many units are backordered, and finally (iii) a cost that is an increasing function of the number of periods a customer is backordered. We show the problem can be transformed into one in which the backorder cost depends on the inventory position only. Then we present two sets of conditions; the first one restricts our attention to a special case of the generalized penalty cost model while the second one restricts our attention to stationary demand models with some distributional assumptions. Under the first (resp. second) set of conditions, we show that the expected cost in a period can be expressed as a convex (resp. quasiconvex) function of the after-ordering inventory position. We use this property to prove the optimality of order-up-to policies under both sets of conditions and discuss extensions to the cases where either a fixed ordering cost or a batch ordering constraint is present.

Suggested Citation

  • Woonghee Tim Huh & Ganesh Janakiraman & Alp Muharremoglu & Anshul Sheopuri, 2011. "TECHNICAL NOTE---Inventory Systems with a Generalized Cost Model," Operations Research, INFORMS, vol. 59(4), pages 1040-1047, August.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:4:p:1040-1047
    DOI: 10.1287/opre.1110.0933
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    References listed on IDEAS

    as
    1. Chen, Fangruo & Zheng, Yu-Sheng, 1993. "Inventory models with general backorder costs," European Journal of Operational Research, Elsevier, vol. 65(2), pages 175-186, March.
    2. Kaj Rosling, 2002. "Inventory Cost Rate Functions with Nonlinear Shortage Costs," Operations Research, INFORMS, vol. 50(6), pages 1007-1017, December.
    3. Diwakar Gupta & Lei Wang, 2009. "A Stochastic Inventory Model with Trade Credit," Manufacturing & Service Operations Management, INFORMS, vol. 11(1), pages 4-18, November.
    4. Arthur F. Veinott, 1965. "The Optimal Inventory Policy for Batch Ordering," Operations Research, INFORMS, vol. 13(3), pages 424-432, June.
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    Cited by:

    1. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    2. Jianjun Xu & Mustafa Cagri Gürbüz & Youyi Feng & Shaoxiang Chen, 2020. "Optimal Spot Trading Integrated with Quantity Flexibility Contracts," Production and Operations Management, Production and Operations Management Society, vol. 29(6), pages 1532-1549, June.
    3. F. G. Badía & C. Sangüesa, 2015. "Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(5), pages 345-356, August.

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