IDEAS home Printed from https://ideas.repec.org/a/bla/popmgt/v28y2019i9p2390-2404.html
   My bibliography  Save this article

Joint Inventory‐Pricing Optimization with General Demands: An Alternative Approach for Concavity Preservation

Author

Listed:
  • Alain Bensoussan
  • Yangyang Xie
  • Houmin Yan

Abstract

In this study, we provide an alternative approach for proving the preservation of concavity together with submodularity, and apply it to finite‐horizon non‐stationary joint inventory‐pricing models with general demands. The approach characterizes the optimal price as a function of the inventory level. Further, it employs the Cauchy–Schwarz and arithmetic‐geometric mean inequalities to establish a relation between the one‐period profit and the profit‐to‐go function in a dynamic programming setting. With this relation, we demonstrate that the one‐dimensional concavity of the price‐optimized profit function is preserved as a whole, instead of separately determining the (two‐dimensional) joint concavities in price (or mean demand/risk level) and inventory level for the one‐period profit and the profit‐to‐go function in conventional approaches. As a result, we derive the optimality condition for a base‐stock, list‐price (BSLP) policy for joint inventory‐pricing optimization models with general form demand and profit functions. With examples, we extend the optimality of a BSLP policy to cases with non‐concave revenue functions in mean demand. We also propose the notion of price elasticity of the slope (PES) and articulate the condition as that in response to a price change of the commodity, the percentage change in the slope of the expected sales is greater than the percentage change in the slope of the expected one‐period profit. The concavity preservation conditions for the additive, generalized additive, and location‐scale demand models in the literature are unified under this framework. We also obtain the conditions under which a BSLP policy is optimal for the logarithmic and exponential form demand models.

Suggested Citation

  • Alain Bensoussan & Yangyang Xie & Houmin Yan, 2019. "Joint Inventory‐Pricing Optimization with General Demands: An Alternative Approach for Concavity Preservation," Production and Operations Management, Production and Operations Management Society, vol. 28(9), pages 2390-2404, September.
  • Handle: RePEc:bla:popmgt:v:28:y:2019:i:9:p:2390-2404
    DOI: 10.1111/poms.13059
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/poms.13059
    Download Restriction: no

    File URL: https://libkey.io/10.1111/poms.13059?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. Xiting Gong & Youhua (Frank) Chen & Quan Yuan, 2022. "Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 511-528, February.
    2. Ba, Luyao & Xie, Yangyang & Ma, Lijun, 2023. "Finite-horizon joint inventory-pricing optimization with non-concave demand and lost sales," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 172(C).
    3. Kazemi, Mohammad Sadegh & Fotopoulos, Stergios B. & Wang, Xinchang, 2023. "Minimizing online retailers’ revenue loss under a time-varying willingness-to-pay distribution," International Journal of Production Economics, Elsevier, vol. 257(C).
    4. Qi Feng & J. George Shanthikumar, 2022. "Applications of Stochastic Orders and Stochastic Functions in Inventory and Pricing Problems," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1433-1453, April.

    More about this item

    Statistics

    Access and download statistics

    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:bla:popmgt:v:28:y:2019:i:9:p:2390-2404. 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: Wiley Content Delivery (email available below). General contact details of provider: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1937-5956 .

    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.