IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v55y2007i2p284-291.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1060.0357
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1060.0357?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:55:y:2007:i:2:p:284-291. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.