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A Periodic Review Inventory Model with Demand Influenced by Promotion Decisions

Author

Listed:
  • 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)

Abstract

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
    DOI: 10.1287/mnsc.45.11.1510
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    References listed on IDEAS

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    1. Suresh P. Sethi & Feng Cheng, 1997. "Optimality of ( s , S ) Policies in Inventory Models with Markovian Demand," Operations Research, INFORMS, vol. 45(6), pages 931-939, December.
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    7. D. Beyer & S. P. Sethi, 1997. "Average Cost Optimality in Inventory Models with Markovian Demands," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 497-526, March.
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    Cited by:

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    3. 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.
    4. 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.
    5. Tunuguntla, Vaishnavi & Basu, Preetam & Rakshit, Krishanu & Ghosh, Debabrata, 2019. "Sponsored search advertising and dynamic pricing for perishable products under inventory-linked customer willingness to pay," European Journal of Operational Research, Elsevier, vol. 276(1), pages 119-132.
    6. Toker Doganoglu & Daniel Klapper, 2006. "Goodwill and dynamic advertising strategies," Quantitative Marketing and Economics (QME), Springer, vol. 4(1), pages 5-29, March.
    7. Wang, Qiang & Zhao, Nenggui & Wu, Jie & Zhu, Qingyuan, 2021. "Optimal pricing and inventory policies with reference price effect and loss-Averse customers," Omega, Elsevier, vol. 99(C).
    8. Asadi, Amin & Nurre Pinkley, Sarah, 2021. "A stochastic scheduling, allocation, and inventory replenishment problem for battery swap stations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 146(C).
    9. 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.
    10. Yiqiang Su & Joseph Geunes, 2013. "Multi-period price promotions in a single-supplier, multi-retailer supply chain under asymmetric demand information," Annals of Operations Research, Springer, vol. 211(1), pages 447-472, December.
    11. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    12. Tinglong Dai & Kinshuk Jerath, 2016. "Technical Note—Impact of Inventory on Quota-Bonus Contracts with Rent Sharing," Operations Research, INFORMS, vol. 64(1), pages 94-98, February.
    13. 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.
    14. Suresh P. Sethi & Houmin Yan & Hanqin Zhang, 2003. "Inventory Models with Fixed Costs, Forecast Updates, and Two Delivery Modes," Operations Research, INFORMS, vol. 51(2), pages 321-328, April.
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