IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

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

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Martin S. Eichenbaum, 1988. "Some Empirical Evidence on the Production Level and Production Cost Smoothing Models of Inventory Investment," NBER Working Papers 2523, National Bureau of Economic Research, Inc.
    2. Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
    3. Jehoshua Eliashberg & Richard Steinberg, 1991. "Competitive Strategies for Two Firms with Asymmetric Production Cost Structures," Management Science, INFORMS, vol. 37(11), pages 1452-1473, November.
    4. Griffin, James M, 1972. "The Process Analysis Alternative to Statistical Cost Functions: An Application to Petroleum Refining," American Economic Review, American Economic Association, vol. 62(1), pages 46-56, March.
    5. Kenneth R. Smith, 1970. "Risk and the Optimal Utilization of Capital," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 253-259.
    6. Donald M. Topkis, 1968. "Optimal Ordering and Rationing Policies in a Nonstationary Dynamic Inventory Model with n Demand Classes," Management Science, INFORMS, vol. 15(3), pages 160-176, November.
    7. Mordechai Henig & Yigal Gerchak & Ricardo Ernst & David F. Pyke, 1997. "An Inventory Model Embedded in Designing a Supply Contract," Management Science, INFORMS, vol. 43(2), pages 184-189, February.
    8. Andrew B. Abel, 1985. "Inventories, Stock-Outs and Production Smoothing," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 283-293.
    9. Alan S. Blinder, 1986. "Can the Production Smoothing Model of Inventory Behavior be Saved?," The Quarterly Journal of Economics, Oxford University Press, vol. 101(3), pages 431-453.
    10. Spulber, Daniel F, 1993. "Monopoly Pricing of Capacity Usage under Asymmetric Information," Journal of Industrial Economics, Wiley Blackwell, vol. 41(3), pages 241-57, September.
    11. Andrew B. Abel, 1985. "Inventories, Stock-Outs, and Production Smoothing," NBER Working Papers 1563, National Bureau of Economic Research, Inc.
    12. Driskill, Robert, 1997. "Durable-Goods Monopoly, Increasing Marginal Cost and Depreciation," Economica, London School of Economics and Political Science, vol. 64(253), pages 137-54, February.
    Full references (including those not matched with items on IDEAS)

    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.