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Inventory control under substitutable demand: A stochastic game application

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  • Zeynep Müge Avsar
  • Melike Baykal‐Gürsoy

Abstract

Substitutable product inventory problem is analyzed using the concepts of stochastic game theory. It is assumed that there are two substitutable products that are sold by different retailers and the demand for each product is random. Game theoretic nature of this problem is the result of substitution between products. Since retailers compete for the substitutable demand, ordering decision of each retailer depends on the ordering decision of the other retailer. Under the discounted payoff criterion, this problem is formulated as a two‐person nonzero‐sum stochastic game. In the case of linear ordering cost, it is shown that there exists a Nash equilibrium characterized by a pair of stationary base stock strategies for the infinite horizon problem. This is the unique Nash equilibrium within the class of stationary base stock strategies. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 359–375, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10018

Suggested Citation

  • Zeynep Müge Avsar & Melike Baykal‐Gürsoy, 2002. "Inventory control under substitutable demand: A stochastic game application," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(4), pages 359-375, June.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:4:p:359-375
    DOI: 10.1002/nav.10018
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    References listed on IDEAS

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    Cited by:

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    2. Andy Wei‐Di Wu & David Ming‐Huang Chiang, 2011. "Fashion products with asymmetric sales horizons," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 490-506, August.
    3. Sharfuddin Lisan, 2018. "Safety stock determination of uncertain demand and mutually dependent variables," International Journal of Business and Social Research, MIR Center for Socio-Economic Research, vol. 8(3), pages 1-11, March.
    4. Jian Zhang & Shuang He & Juliang Zhang & T. C. Edwin Cheng, 2020. "Purchase and retrieval competition for seasonal produce," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(3), pages 161-184, April.
    5. A. Gürhan Kök & Marshall L. Fisher, 2007. "Demand Estimation and Assortment Optimization Under Substitution: Methodology and Application," Operations Research, INFORMS, vol. 55(6), pages 1001-1021, December.
    6. Sharfuddin Lisan, 2018. "Safety stock determination of uncertain demand and mutually dependent variables," International Journal of Business and Social Research, LAR Center Press, vol. 8(3), pages 1-11, March.
    7. Uriel Spiegel & Tchai Tavor, 2011. "Second-Degree Monopoly Wholesaler with Variable Ordering Costs," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 10(1), pages 45-59, April.
    8. He, Shuang & Zhang, Jian & Zhang, Juliang & Cheng, T.C.E., 2022. "Production/inventory competition between firms with fixed-proportions co-production systems," European Journal of Operational Research, Elsevier, vol. 299(2), pages 497-509.
    9. Tava Lennon Olsen & Rodney P. Parker, 2014. "On Markov Equilibria in Dynamic Inventory Competition," Operations Research, INFORMS, vol. 62(2), pages 332-344, April.
    10. Cao, Yiyin & Dang, Chuangyin & Xiao, Zhongdong, 2022. "A differentiable path-following method to compute subgame perfect equilibria in stationary strategies in robust stochastic games and its applications," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1032-1050.

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