IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

A Dynamic Inventory Model with the Right of Refusal

  • Sreekumar Bhaskaran


    (Information Technology and Operations Management, Cox School of Business, Southern Methodist University, Dallas, Texas 75275)

  • Karthik Ramachandran


    (Information Technology and Operations Management, Cox School of Business, Southern Methodist University, Dallas, Texas 75275)

  • John Semple


    (Information Technology and Operations Management, Cox School of Business, Southern Methodist University, Dallas, Texas 75275)

Registered author(s):

    We consider a dynamic inventory (production) model with general convex order (production) costs and excess demand that can be accepted or refused by the firm. Excess demand that is accepted is backlogged and results in a backlog cost whereas demand that is refused results in a lost sales charge. Endogenizing the sales decision is appropriate in the presence of general convex order costs so that the firm is not forced to backlog a unit whose subsequent satisfaction would reduce total profits. In each period, the firm must determine the optimal order and sales strategy. We show that the optimal policy is characterized by an optimal buy-up-to level that increases with the initial inventory level and an order quantity that decreases with the initial inventory level. More importantly, we show the optimal sales strategy is characterized by a critical threshold, a backlog limit, that dictates when to stop selling. This threshold is independent of the initial inventory level and the amount purchased. We investigate various properties of this new policy. As demand stochastically increases, the amount purchased increases but the amount backlogged decreases, reflecting a shift in the way excess demand is managed. We develop two regularity conditions, one that ensures some backlogs are allowed in each period, and another that ensures the amount backlogged is nondecreasing in the length of the planning horizon. We illustrate the buy-up-to levels in our model are bounded above by buy-up-to levels from the pure lost sales and pure backlogging models. We explore additional extensions using numerical experiments.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: no

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 56 (2010)
    Issue (Month): 12 (December)
    Pages: 2265-2281

    in new window

    Handle: RePEc:inm:ormnsc:v:56:y:2010:i:12:p:2265-2281
    Contact details of provider: Postal: 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA
    Phone: +1-443-757-3500
    Fax: 443-757-3515
    Web page:

    More information through EDIRC

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:56:y:2010:i:12:p:2265-2281. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc)

    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.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 profile, as there may be some citations waiting for confirmation.

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

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.