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Technical Note ---Preservation of Quasi- K -Concavity and Its Applications

Author

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  • Xin Chen

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801)

  • Yuhan Zhang

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801)

  • Sean X. Zhou

    (Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, Hong Kong)

Abstract

In this paper, we establish a new preservation property of quasi- K -concavity under certain optimization operations. One important application of the result is to analyze joint inventory-pricing models for single-product periodic-review inventory systems with concave ordering costs. At each period, an ordering quantity and a selling price of the product are determined simultaneously. Demand is random but sensitive to the price. The objective is to maximize the total expected discounted profit over a finite planning horizon. Assuming that demand is a deterministic function of the selling price plus a random perturbation with a positive Pólya or uniform distribution, we show that a generalized ( s , S , p ) policy is optimal.

Suggested Citation

  • Xin Chen & Yuhan Zhang & Sean X. Zhou, 2010. "Technical Note ---Preservation of Quasi- K -Concavity and Its Applications," Operations Research, INFORMS, vol. 58(4-part-1), pages 1012-1016, August.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:4-part-1:p:1012-1016
    DOI: 10.1287/opre.1090.0802
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    References listed on IDEAS

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    1. Evan L. Porteus, 1971. "On the Optimality of Generalized (s, S) Policies," Management Science, INFORMS, vol. 17(7), pages 411-426, March.
    2. Yuyue Song & Saibal Ray & Tamer Boyaci, 2009. "Technical Note---Optimal Dynamic Joint Inventory-Pricing Control for Multiplicative Demand with Fixed Order Costs and Lost Sales," Operations Research, INFORMS, vol. 57(1), pages 245-250, February.
    3. Woonghee Tim Huh & Ganesh Janakiraman, 2008. "( s, S ) Optimality in Joint Inventory-Pricing Control: An Alternate Approach," Operations Research, INFORMS, vol. 56(3), pages 783-790, June.
    4. Edward J. Fox & Richard Metters & John Semple, 2006. "Optimal Inventory Policy with Two Suppliers," Operations Research, INFORMS, vol. 54(2), pages 389-393, April.
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    Cited by:

    1. Wang, Huihui & Yu, Yimin & Zhang, Wei & Hua, Zhongsheng, 2019. "Procurement strategies for lost-sales inventory systems with all-units discounts," European Journal of Operational Research, Elsevier, vol. 272(2), pages 539-548.
    2. Tomas Havranek & Anna Sokolova, 2016. "Do Consumers Really Follow a Rule of Thumb? Three Thousand Estimates from 130 Studies Say "Probably Not"," Working Papers 2016/08, Czech National Bank.
    3. Yi Yang & Youhua (Frank) Chen & Yun Zhou, 2014. "Coordinating Inventory Control and Pricing Strategies Under Batch Ordering," Operations Research, INFORMS, vol. 62(1), pages 25-37, February.

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