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Note: Generalized Notions of Concavity with an Application to Capacity Management

Author

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  • John Semple

    (Cox School of Business, Southern Methodist University, Fincher Building, P.O. Box 750333, Dallas, Texas 75275)

Abstract

We introduce a generalization of K -concavity termed weak ( K 1 , K 2 )- concavity and show how it can be used to analyze certain dynamic systems arising in capacity management. We show that weak ( K 1 , K 2 )-concavity has two fundamental properties that are relevant for the analysis of such systems: First, it is preserved for linear interpolations; second, it is preserved for certain types of linear extensions. In capacity management problems where both buying and selling capacity involve a fixed cost plus a proportional cost/revenue term, interpolations and extensions are fundamental building blocks of the optimality analysis. In the context of the capacity management problem studied by Ye and Duenyas (2007), we show that weak ( K 1 , K 2 )-concavity is sufficient to prove the general structure of the optimal policy established in that paper.

Suggested Citation

  • John Semple, 2007. "Note: Generalized Notions of Concavity with an Application to Capacity Management," Operations Research, INFORMS, vol. 55(2), pages 284-291, April.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:2:p:284-291
    DOI: 10.1287/opre.1060.0357
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    Citations

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    Cited by:

    1. Lijian Lu & Xiaoming Yan, 2016. "Capacity investment decisions under risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(3), pages 218-235, April.
    2. Yuan, Quan & Hua, Zhongsheng & Shen, Bin, 2021. "An automated system of emissions permit trading for transportation firms," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    3. Awi Federgruen & Zhe Liu & Lijian Lu, 2020. "Synthesis and Generalization of Structural Results in Inventory Management: A Generalized Convexity Property," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 547-575, May.
    4. 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.
    5. Ozgun Caliskan-Demirag & Youhua (Frank) Chen & Yi Yang, 2012. "Ordering Policies for Periodic-Review Inventory Systems with Quantity-Dependent Fixed Costs," Operations Research, INFORMS, vol. 60(4), pages 785-796, August.

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