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A Monopolistic and Oligopolistic Stochastic Flow Revenue Management Model

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  • Xiaowei Xu

    (Department of Management Science and Information Systems, Rutgers University, The State University of New Jersey, Newark, New Jersey 07102)

  • Wallace J. Hopp

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

This paper studies a one-shot inventory replenishment problem with dynamic pricing. The customer arrival rate is assumed to follow a geometric Brownian motion. Homogeneous customers have an isoelastic demand function and do not behave strategically. We find a closed-form optimal pricing policy, which utilizes current demand information. Under this pricing policy the inventory trajectory is deterministic, and a retailer sells all inventory. We show that dynamic pricing coordinated with the inventory decision achieves significantly higher profits than does static pricing. Furthermore, under oligopolistic competition we establish a weak perfect Bayesian equilibrium for the price and inventory replenishment game. We find the pricing equilibrium to be cooperative even in a noncooperative environment, but that inventory competition results in overstock and damages profits. Finally, we examine the trade-off between dynamic pricing and price precommitment and find that flexible pricing is still beneficial, provided competition is not too intense.

Suggested Citation

  • Xiaowei Xu & Wallace J. Hopp, 2006. "A Monopolistic and Oligopolistic Stochastic Flow Revenue Management Model," Operations Research, INFORMS, vol. 54(6), pages 1098-1109, December.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:6:p:1098-1109
    DOI: 10.1287/opre.1060.0336
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    References listed on IDEAS

    as
    1. Nicholas C. Petruzzi & Maqbool Dada, 1999. "Pricing and the Newsvendor Problem: A Review with Extensions," Operations Research, INFORMS, vol. 47(2), pages 183-194, April.
    2. J. Michael Harrison & Michael I. Taksar, 1983. "Instantaneous Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 439-453, August.
    3. Piccione, Michele & Rubinstein, Ariel, 1997. "On the Interpretation of Decision Problems with Imperfect Recall," Games and Economic Behavior, Elsevier, vol. 20(1), pages 3-24, July.
    4. Carl Davidson & Raymond Deneckere, 1986. "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
    5. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    6. Fernando Bernstein & Awi Federgruen, 2004. "Dynamic inventory and pricing models for competing retailers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(2), pages 258-274, March.
    7. Serguei Netessine & Robert A. Shumsky, 2005. "Revenue Management Games: Horizontal and Vertical Competition," Management Science, INFORMS, vol. 51(5), pages 813-831, May.
    8. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    9. J. Michael Harrison & Thomas M. Sellke & Allison J. Taylor, 1983. "Impulse Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 454-466, August.
    10. Bikhchandani, Sushil & Mamer, John W., 1993. "A duopoly model of pricing for inventory liquidation," European Journal of Operational Research, Elsevier, vol. 69(2), pages 177-186, September.
    11. Fernando Bernstein & Awi Federgruen, 2005. "Decentralized Supply Chains with Competing Retailers Under Demand Uncertainty," Management Science, INFORMS, vol. 51(1), pages 18-29, January.
    12. Serguei Netessine & Nils Rudi, 2003. "Centralized and Competitive Inventory Models with Demand Substitution," Operations Research, INFORMS, vol. 51(2), pages 329-335, April.
    13. René Caldentey & Lawrence M. Wein, 2006. "Revenue Management of a Make-to-Stock Queue," Operations Research, INFORMS, vol. 54(5), pages 859-875, October.
    14. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    15. Kalyan Raman & Rabikar Chatterjee, 1995. "Optimal Monopolist Pricing Under Demand Uncertainty in Dynamic Markets," Management Science, INFORMS, vol. 41(1), pages 144-162, January.
    16. Gabriel Bitran & René Caldentey, 2003. "An Overview of Pricing Models for Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 5(3), pages 203-229, August.
    17. Siddharth Mahajan & Garrett van Ryzin, 2001. "Inventory Competition Under Dynamic Consumer Choice," Operations Research, INFORMS, vol. 49(5), pages 646-657, October.
    18. 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.
    19. Steven A. Lippman & Kevin F. McCardle, 1997. "The Competitive Newsboy," Operations Research, INFORMS, vol. 45(1), pages 54-65, February.
    20. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
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    2. Ouardighi, Fouad El & Sim, Jeong Eun & Kim, Bowon, 2016. "Pollution accumulation and abatement policy in a supply chain," European Journal of Operational Research, Elsevier, vol. 248(3), pages 982-996.
    3. 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.
    4. Jian Yang & Yusen Xia & Xiangtong Qi & Yifeng Liu, 2014. "A nonatomic‐game model for timing clearance sales under competition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 365-385, August.
    5. Sato, Kimitoshi, 2019. "Price Trends and Dynamic Pricing in Perishable Product Market Consisting of Superior and Inferior Firms," European Journal of Operational Research, Elsevier, vol. 274(1), pages 214-226.
    6. Sato, Kimitoshi & Sawaki, Katsushige, 2013. "A continuous-time dynamic pricing model knowing the competitor’s pricing strategy," European Journal of Operational Research, Elsevier, vol. 229(1), pages 223-229.
    7. 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.
    8. Benny Mantin & Daniel Granot & Frieda Granot, 2011. "Dynamic pricing under first order Markovian competition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 608-617, September.
    9. Chua, Geoffrey A. & Mokhlesi, Reza & Sainathan, Arvind, 2017. "Optimal Discounting and Replenishment Policies for Perishable Products," International Journal of Production Economics, Elsevier, vol. 186(C), pages 8-20.
    10. Yuri Levin & Jeff McGill & Mikhail Nediak, 2009. "Dynamic Pricing in the Presence of Strategic Consumers and Oligopolistic Competition," Management Science, INFORMS, vol. 55(1), pages 32-46, January.
    11. Mak, Vincent & Rapoport, Amnon & Gisches, Eyran J., 2012. "Competitive dynamic pricing with alternating offers: Theory and experiment," Games and Economic Behavior, Elsevier, vol. 75(1), pages 250-264.
    12. Dasci, A. & Karakul, M., 2009. "Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly," European Journal of Operational Research, Elsevier, vol. 197(3), pages 945-968, September.
    13. Lingxiu Dong & Panos Kouvelis & Zhongjun Tian, 2009. "Dynamic Pricing and Inventory Control of Substitute Products," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 317-339, December.
    14. Guillermo Gallego & Ming Hu, 2014. "Dynamic Pricing of Perishable Assets Under Competition," Management Science, INFORMS, vol. 60(5), pages 1241-1259, May.
    15. Yi Zheng & Zehao Li & Peng Jiang & Yijie Peng, 2024. "Dual-Agent Deep Reinforcement Learning for Dynamic Pricing and Replenishment," Papers 2410.21109, arXiv.org.
    16. Qian Liu & Dan Zhang, 2013. "Dynamic Pricing Competition with Strategic Customers Under Vertical Product Differentiation," Management Science, INFORMS, vol. 59(1), pages 84-101, August.
    17. Li, Mengmeng & Mizuno, Shinji, 2022. "Comparison of dynamic and static pricing strategies in a dual-channel supply chain with inventory control," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 165(C).
    18. Jian Yang, 2015. "Analysis of Markovian Competitive Situations using Nonatomic Games," Papers 1510.06813, arXiv.org, revised Apr 2017.

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