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Note: Optimality Conditions for an (s, S) Policy with Proportional and Lump-Sum Penalty Costs

Author

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  • Sila Çetinkaya

    (Department of Industrial Engineering, Texas A&M University, College Station, Texas 77843--3131)

  • Mahmut Parlar

    (DeGroote School of Business, McMaster University, Hamilton, Ontario L8S 4M4, Canada)

Abstract

We consider the optimality of the (s, S) policy for a periodic-review stochastic inventory problem with two types of shortage costs. The problem may arise in a rush-order application at a bank branch where the emergency provision costs during a foreign currency stockout are represented by proportional and lump-sum penalties. Aneja and Noori (1987) analyzed this problem and presented a set of conditions for the convexity of a particular function and made a claim about the K-convexity of another function to prove the optimality of the (s, S) policy. We show that because the function that is claimed to be K-convex is actually concave over a subset of its domain, Aneja and Noori's arguments cannot be used to prove the optimality of the (s, S) policy. However, we argue that Aneja and Noori's problem is equivalent to the typical lost-sales problem, and using this equivalence, we .nd a simple convexity condition that assures the optimality of the (s, S) policy.

Suggested Citation

  • Sila Çetinkaya & Mahmut Parlar, 2002. "Note: Optimality Conditions for an (s, S) Policy with Proportional and Lump-Sum Penalty Costs," Management Science, INFORMS, vol. 48(12), pages 1635-1639, December.
    • Handle: RePEc:inm:ormnsc:v:48:y:2002:i:12:p:1635-1639
    DOI: 10.1287/mnsc.48.12.1635.443
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    Cited by:

    1. Koos, Shelby E. & Shaikh, Nazrul I., 2019. "Dynamics of consumers' dissatisfaction due to stock-outs," International Journal of Production Economics, Elsevier, vol. 208(C), pages 461-471.
    2. Youhua (Frank) Chen & Ye Lu & Minghui Xu, 2012. "Optimal inventory control policy for periodic‐review inventory systems with inventory‐level‐dependent demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(6), pages 430-440, September.
    3. Xiaobo, Zhao & Xu, Deju & Zhang, Hanqin & He, Qi-Ming, 2007. "Modeling and analysis of a supply-assembly-store chain," European Journal of Operational Research, Elsevier, vol. 176(1), pages 275-294, January.
    4. Doran Wood & Sıla Çetinkaya, 2024. "A comparative analysis of how to handle stockout scenarios: the impact of newsvendor’s risk attitude," Annals of Operations Research, Springer, vol. 338(2), pages 1187-1218, July.

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    Keywords

    Stochastic Inventory Models; K-Convexity;

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