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Dynamic Pricing and Inventory Control: Uncertainty and Competition

Author

Listed:
  • Elodie Adida

    (Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, Illinois 60607)

  • Georgia Perakis

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

In this paper, we study a make-to-stock manufacturing system where two firms compete through dynamic pricing and inventory control. Our goal is to address competition (in particular a duopoly setting) together with the presence of demand uncertainty. We consider a dynamic setting where multiple products share production capacity. We introduce a demand-based fluid model where the demand is a linear function of the price of the supplier and of her competitor, the inventory and production costs are quadratic, and all coefficients are time dependent. A key part of the model is that no backorders are allowed and the strategy of a supplier depends on her competitor's strategy. First, we reformulate the robust problem as a fluid model of similar form to the deterministic one and show existence of a Nash equilibrium in continuous time. We then discuss issues of uniqueness and address how to compute a particular Nash equilibrium, i.e., the normalized Nash equilibrium.

Suggested Citation

  • Elodie Adida & Georgia Perakis, 2010. "Dynamic Pricing and Inventory Control: Uncertainty and Competition," Operations Research, INFORMS, vol. 58(2), pages 289-302, April.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:2:p:289-302
    DOI: 10.1287/opre.1090.0718
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    References listed on IDEAS

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    1. Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
    2. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    3. Jorgensen, Steffen & Kort, Peter M. & Zaccour, Georges, 1999. "Production, inventory, and pricing under cost and demand learning effects," European Journal of Operational Research, Elsevier, vol. 117(2), pages 382-395, September.
    4. Dimitris Bertsimas & Aurélie Thiele, 2006. "A Robust Optimization Approach to Inventory Theory," Operations Research, INFORMS, vol. 54(1), pages 150-168, February.
    5. E. Cavazzuti & M. Pappalardo & M. Passacantando, 2002. "Nash Equilibria, Variational Inequalities, and Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 491-506, September.
    6. P. Cubiotti, 1997. "Generalized Quasi-Variational Inequalities in Infinite-Dimensional Normed Spaces," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 457-475, March.
    7. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    8. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
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    Cited by:

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    3. Mengshi Lu & Zuo‐Jun Max Shen, 2021. "A Review of Robust Operations Management under Model Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1927-1943, June.
    4. Liao, Haolan & Wu, Di & Wang, Yuhan & Lyu, Zeyu & Sun, Hongmei & Nie, Yongyou & He, He, 2022. "Impacts of carbon trading mechanism on closed-loop supply chain: A case study of stringer pallet remanufacturing," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    5. Ma, Shouyu & Jemai, Zied & Bai, Qingguo, 2022. "Optimal pricing and ordering decisions for a retailer using multiple discounts," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1177-1192.
    6. Qi Feng & Yuanchen Li & J. George Shanthikumar, 2020. "Competitive Revenue Management with Sequential Bargaining," Production and Operations Management, Production and Operations Management Society, vol. 29(5), pages 1307-1324, May.
    7. Lamas, Alejandro & Chevalier, Philippe, 2018. "Joint dynamic pricing and lot-sizing under competition," European Journal of Operational Research, Elsevier, vol. 266(3), pages 864-876.
    8. Peng, Juan & Zhou, Zhili, 2019. "Working capital optimization in a supply chain perspective," European Journal of Operational Research, Elsevier, vol. 277(3), pages 846-856.
    9. Torsten J. Gerpott & Jan Berends, 2022. "Competitive pricing on online markets: a literature review," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(6), pages 596-622, December.
    10. Qiu, Ruozhen & Sun, Yue & Zhou, Hongcheng & Sun, Minghe, 2023. "Dynamic pricing and quick response of a retailer in the presence of strategic consumers: A distributionally robust optimization approach," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1270-1298.
    11. R. Schlosser & K. Richly, 2019. "Dynamic pricing under competition with data-driven price anticipations and endogenous reference price effects," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 18(6), pages 451-464, December.
    12. 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.
    13. Rainer Schlosser & Martin Boissier, 2018. "Dealing with the Dimensionality Curse in Dynamic Pricing Competition: Using Frequent Repricing to Compensate Imperfect Market Anticipations," Papers 1809.02433, arXiv.org.
    14. Miriam Kie{ss}ling & Sascha Kurz & Jorg Rambau, 2014. "The Integrated Size and Price Optimization Problem," Papers 1401.8142, arXiv.org.
    15. Zhao, Xuan & Atkins, Derek & Hu, Ming & Zhang, Wensi, 2017. "Revenue management under joint pricing and capacity allocation competition," European Journal of Operational Research, Elsevier, vol. 257(3), pages 957-970.
    16. Georgia Perakis & Melvyn Sim & Qinshen Tang & Peng Xiong, 2023. "Robust Pricing and Production with Information Partitioning and Adaptation," Management Science, INFORMS, vol. 69(3), pages 1398-1419, March.
    17. Song, Boqian & Li, Michael Z.F. & Zhuang, Weifen, 2021. "Dynamic channel control and pricing of a single perishable product on multiple distribution channels," European Journal of Operational Research, Elsevier, vol. 288(2), pages 539-551.
    18. Elodie Adida & Georgia Perakis, 2014. "The effect of supplier capacity on the supply chain profit," Annals of Operations Research, Springer, vol. 223(1), pages 1-52, December.
    19. Ayşe Kocabıyıkoğlu & Ioana Popescu & Catalina Stefanescu, 2014. "Pricing and Revenue Management: The Value of Coordination," Management Science, INFORMS, vol. 60(3), pages 730-752, March.
    20. Friesz, Terry L. & Lee, Ilsoo & Lin, Cheng-Chang, 2011. "Competition and disruption in a dynamic urban supply chain," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1212-1231, September.

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