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Inventory Management Under Market Size Dynamics


  • Tava Lennon Olsen

    () (Olin Business School, Washington University in St. Louis, St. Louis, Missouri 63130)

  • Rodney P. Parker

    () (The University of Chicago Graduate School of Business, Chicago, Illinois 60637)


We investigate the situation where a customer experiencing an inventory stockout at a retailer potentially leaves the firm's market. In classical inventory theory, a unit stockout penalty cost has been used as a surrogate to mimic the economic effect of such a departure; in this study, we explicitly represent this aspect of consumer behavior, incorporating the diminishing effect of the consumers leaving the market upon the stochastic demand distribution in a time-dynamic context. The initial model considers a single firm. We allow for consumer forgiveness where customers may flow back to the committed purchasing market from a nonpurchasing "latent" market. The per-period decisions include a marketing mix to attract latent and new consumers to the committed market and the setting of inventory levels. We establish conditions under which the firm optimally operates a base-stock inventory policy. The subsequent two models consider a duopoly where the potential market for a firm is now the committed market of the other firm; each firm decides its own inventory level. In the first model, the only decisions are the stocking decisions and in the second model, a firm may also advertise to attract dissatisfied customers from its competitor's market. In both cases, we establish conditions for a base-stock equilibrium policy. We demonstrate comparative statics in all models.

Suggested Citation

  • Tava Lennon Olsen & Rodney P. Parker, 2008. "Inventory Management Under Market Size Dynamics," Management Science, INFORMS, vol. 54(10), pages 1805-1821, October.
  • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:10:p:1805-1821
    DOI: 10.1287/mnsc.1080.0889

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    References listed on IDEAS

    1. Vishal Gaur & Young-Hoon Park, 2007. "Asymmetric Consumer Learning and Inventory Competition," Management Science, INFORMS, vol. 53(2), pages 227-240, February.
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    Cited by:

    1. Peng Hu & Stephen Shum & Man Yu, 2016. "Joint Inventory and Markdown Management for Perishable Goods with Strategic Consumer Behavior," Operations Research, INFORMS, vol. 64(1), pages 118-134, February.
    2. Haans, A.J. & Gijsbrechts, E., 2011. "One-deal-fits-all? : On category sales promotion effectiveness in smaller versus larger supermarkets," Other publications TiSEM 2c1a69db-bdfa-4988-a84c-4, Tilburg University, School of Economics and Management.
    3. Shi, Ye & Yu, Yugang & Wang, Lizhi, 2015. "Operational impact on the environment: Managing service systems with environmental deterioration," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 310-320.
    4. Hou, Ruiqi & de Koster, René & Yu, Yugang, 2018. "Service investment for online retailers with social media—Does it pay off?," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 606-628.
    5. Sam Aflaki & Ioana Popescu, 2014. "Managing Retention in Service Relationships," Management Science, INFORMS, vol. 60(2), pages 415-433, February.
    6. Haans, Hans & Gijsbrechts, Els, 2011. "“One-deal-fits-all?” On Category Sales Promotion Effectiveness in Smaller versus Larger Supermarkets," Journal of Retailing, Elsevier, vol. 87(4), pages 427-443.
    7. Shining Wu & Qian Liu & Rachel Q. Zhang, 2015. "The Reference Effects on a Retailer’s Dynamic Pricing and Inventory Strategies with Strategic Consumers," Operations Research, INFORMS, vol. 63(6), pages 1320-1335, December.
    8. Tianhu Deng & Zuo-Jun Max Shen & J. George Shanthikumar, 2014. "Statistical Learning of Service-Dependent Demand in a Multiperiod Newsvendor Setting," Operations Research, INFORMS, vol. 62(5), pages 1064-1076, October.
    9. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    10. Liberopoulos, George & Tsikis, Isidoros & Delikouras, Stefanos, 2010. "Backorder penalty cost coefficient "b": What could it be?," International Journal of Production Economics, Elsevier, vol. 123(1), pages 166-178, January.
    11. Hill, Alex & Doran, Des & Stratton, Roy, 2012. "How should you stabilise your supply chains?," International Journal of Production Economics, Elsevier, vol. 135(2), pages 870-881.
    12. Tava Lennon Olsen & Rodney P. Parker, 2014. "On Markov Equilibria in Dynamic Inventory Competition," Operations Research, INFORMS, vol. 62(2), pages 332-344, April.
    13. Rodney P. Parker & Roman Kapuściński, 2011. "Managing a Noncooperative Supply Chain with Limited Capacity," Operations Research, INFORMS, vol. 59(4), pages 866-881, August.
    14. Daniel Adelman & Adam J. Mersereau, 2013. "Dynamic Capacity Allocation to Customers Who Remember Past Service," Management Science, INFORMS, vol. 59(3), pages 592-612, January.
    15. Felipe Caro & Victor Martínez-de-Albéniz, 2010. "The Impact of Quick Response in Inventory-Based Competition," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 409-429, January.


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