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A Periodic Review Inventory Model with Demand Influenced by Promotion Decisions


  • Feng Cheng

    (IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598)

  • Suresh P. Sethi

    (School of Management, University of Texas at Dallas, Box 830688, Richardson, Texas 75083)


In this paper, we use a Markov decision process (MDP) to model the joint inventory-promotion decision problem. The state variable of the MDP represents the demand state brought about by changing environmental factors as well as promotion decisions. The demand state in a period determines the distribution of the random demand in that period. Optimal inventory and promotion decision policies in the finite horizon problem are obtained via dynamic programming. Under certain conditions, we show that there is a threshold inventory level P for each demand state such that if the threshold is exceeded, then it is desirable to promote the product. For the proportional ordering cost case, the optimal inventory replenishment policy is a base-stock type policy with the optimal base-stock level dependent on the promotion decision.

Suggested Citation

  • Feng Cheng & Suresh P. Sethi, 1999. "A Periodic Review Inventory Model with Demand Influenced by Promotion Decisions," Management Science, INFORMS, vol. 45(11), pages 1510-1523, November.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:11:p:1510-1523

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    References listed on IDEAS

    1. E. Zabel, 1970. "Monopoly and Uncertainty," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 205-219.
    2. Aram G. Sogomonian & Christopher S. Tang, 1993. "A Modeling Framework for Coordinating Promotion and Production Decisions within a Firm," Management Science, INFORMS, vol. 39(2), pages 191-203, February.
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    Cited by:

    1. Scheller-Wolf, Alan & Tayur, Sridhar, 2009. "Risk sharing in supply chains using order bands--Analytical results and managerial insights," International Journal of Production Economics, Elsevier, vol. 121(2), pages 715-727, October.
    2. Kurata, Hisashi & Liu, John J., 2007. "Optimal promotion planning--depth and frequency--for a two-stage supply chain under Markov switching demand," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1026-1043, March.
    3. Taskin, Selda & Lodree Jr., Emmett J., 2010. "Inventory decisions for emergency supplies based on hurricane count predictions," International Journal of Production Economics, Elsevier, vol. 126(1), pages 66-75, July.
    4. Toker Doganoglu & Daniel Klapper, 2006. "Goodwill and dynamic advertising strategies," Quantitative Marketing and Economics (QME), Springer, vol. 4(1), pages 5-29, March.
    5. Hyun-Soo Ahn & Mehmet Gümüc{s} & Philip Kaminsky, 2009. "Inventory, Discounts, and the Timing Effect," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 613-629, September.
    6. Wei, Ying & Chen, Youhua (Frank), 2011. "Joint determination of inventory replenishment and sales effort with uncertain market responses," International Journal of Production Economics, Elsevier, vol. 134(2), pages 368-374, December.
    7. repec:pal:jorsoc:v:59:y:2008:i:5:d:10.1057_palgrave.jors.2602377 is not listed on IDEAS


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