IDEAS home Printed from
   My bibliography  Save this paper

Competition under Time-Varying Demands and Dynamic Lot-Sizing Costs


  • Awi Federgruen

    (Graduate School of Business, Columbia University)

  • Joern Meissner

    (Department of Management Science, Lancaster University Management School)


We develop a competitive pricing model which combines the complexity of time-varying demand and cost functions and that of scale economies arising from dynamic lot sizing costs. Each firm can replenish inventory in each of the T periods into which the planing horizon is partitioned. Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carrying costs. Each firm adopts, at the beginning of the planning horizon, a (single) price to be employed throughout the horizon. Based on each period's system of demand equations, these prices determine a time series of demands for each firm, which needs to service them with an optimal corresponding dynamic lot sizing plan. We establish the existence of a price equilibrium and associated optimal dynamic lotsizing plans, under mild conditions and employing a close approximation for the optimal lotsizing costs. We also design efficient procedures to compute the equilibrium prices and dynamic lotsizing plans.

Suggested Citation

  • Awi Federgruen & Joern Meissner, 2004. "Competition under Time-Varying Demands and Dynamic Lot-Sizing Costs," Working Papers MRG/0003, Department of Management Science, Lancaster University, revised May 2008.
  • Handle: RePEc:lms:mansci:mrg-0003

    Download full text from publisher

    File URL:
    File Function: Webpage
    Download Restriction: no

    File URL:
    File Function: Full Paper
    Download Restriction: no

    References listed on IDEAS

    1. Jehoshua Eliashberg & Abel P. Jeuland, 1986. "The Impact of Competitive Entry in a Developing Market Upon Dynamic Pricing Strategies," Marketing Science, INFORMS, vol. 5(1), pages 20-36.
    2. Engelbert Dockner & Steffen Jørgensen, 1988. "Optimal Pricing Strategies for New Products in Dynamic Oligopolies," Marketing Science, INFORMS, vol. 7(4), pages 315-334.
    3. Shlomo Kalish, 1983. "Monopolist Pricing with Dynamic Demand and Production Cost," Marketing Science, INFORMS, vol. 2(2), pages 135-159.
    4. Cecchetti, Stephen G., 1986. "The frequency of price adjustment : A study of the newsstand prices of magazines," Journal of Econometrics, Elsevier, vol. 31(3), pages 255-274, April.
    5. Anil K Kashyap, 1995. "Sticky Prices: New Evidence from Retail Catalogs," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 245-274.
    6. Clarke, Darral G & Dolan, Robert J, 1984. "A Simulation Analysis of Alternative Pricing Strategies for Dynamic Environments," The Journal of Business, University of Chicago Press, vol. 57(1), pages 179-200, January.
    7. Howard Kunreuther & Linus Schrage, 1973. "Joint Pricing and Inventory Decisions for Constant Priced Items," Management Science, INFORMS, vol. 19(7), pages 732-738, March.
    8. van den Heuvel, Wilco & Wagelmans, Albert P.M., 2006. "A polynomial time algorithm for a deterministic joint pricing and inventory model," European Journal of Operational Research, Elsevier, vol. 170(2), pages 463-480, April.
    9. Judith A. Chevalier & Anil K. Kashyap & Peter E. Rossi, 2003. "Why Don't Prices Rise During Periods of Peak Demand? Evidence from Scanner Data," American Economic Review, American Economic Association, vol. 93(1), pages 15-37, March.
    10. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    11. Joseph Thomas, 1970. "Price-Production Decisions with Deterministic Demand," Management Science, INFORMS, vol. 16(11), pages 747-750, July.
    12. Gérard P. Cachon & Patrick T. Harker, 2002. "Competition and Outsourcing with Scale Economies," Management Science, INFORMS, vol. 48(10), pages 1314-1333, October.
    Full references (including those not matched with items on IDEAS)

    More about this item


    equilibrium; price; competition; game theory; inventory models; lot sizing; pricing; supply chain management;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:lms:mansci:mrg-0003. 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: (Joern Meissner). General contact details of provider: .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.