IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v207y2010i1p330-338.html
   My bibliography  Save this article

A competitive dynamic pricing model when demand is interdependent over time

Author

Listed:
  • Sibdari, Soheil
  • Pyke, David F.

Abstract

In this study, we contribute to the dynamic pricing literature by developing a finite horizon model for two firms offering substitutable and nonperishable products with different quality levels. Customers can purchase and store the products, even if they do not need them at the time, in order to use them in future. The stockpile of the products generated by customers affects the demand in future periods. Therefore, the demand for each product not only is a function of prices and quality levels, but also of the products' stockpile levels. In addition, the stockpile levels change the customers' consumption behavior; more product in a stockpile leads to more consumption. Therefore, we address not only the price and demand relationship but also the stockpiling and consumption relationship in a competitive environment. The decision variable of each firm at the beginning of each period is its unit sale price. We use a deterministic dynamic program to calculate the equilibrium prices at the beginning of each period. By assuming that the market stockpile is public information, we show the existence of a unique Nash equilibrium. We next consider the case when the firms do not know the market stockpile. We then develop appropriate heuristics to calculate the optimal prices in each case. A numerical study is also provided to calculate the price levels in different scenarios and compare their performances.

Suggested Citation

  • Sibdari, Soheil & Pyke, David F., 2010. "A competitive dynamic pricing model when demand is interdependent over time," European Journal of Operational Research, Elsevier, vol. 207(1), pages 330-338, November.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:1:p:330-338
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00227-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chatwin, Richard E., 2000. "Optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices," European Journal of Operational Research, Elsevier, vol. 125(1), pages 149-174, August.
    2. João L. Assunção & Robert J. Meyer, 1993. "The Rational Effect of Price Promotions on Sales and Consumption," Management Science, INFORMS, vol. 39(5), pages 517-535, May.
    3. Guillermo Gallego & Garrett van Ryzin, 1997. "A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management," Operations Research, INFORMS, vol. 45(1), pages 24-41, February.
    4. Marc Dudey, 1992. "Dynamic Edgeworth-Bertrand Competition," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(4), pages 1461-1477.
    5. 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.
    6. Wen Zhao & Yu-Sheng Zheng, 2000. "Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous Demand," Management Science, INFORMS, vol. 46(3), pages 375-388, March.
    7. Youyi Feng & Baichun Xiao, 2000. "A Continuous-Time Yield Management Model with Multiple Prices and Reversible Price Changes," Management Science, INFORMS, vol. 46(5), pages 644-657, May.
    8. Gabriel R. Bitran & Susana V. Mondschein, 1995. "An Application of Yield Management to the Hotel Industry Considering Multiple Day Stays," Operations Research, INFORMS, vol. 43(3), pages 427-443, June.
    9. Shuba Srinivasan & Koen Pauwels & Dominique M. Hanssens & Marnik G. Dekimpe, 2004. "Do Promotions Benefit Manufacturers, Retailers, or Both?," Management Science, INFORMS, vol. 50(5), pages 617-629, May.
    10. Anderson, Simon P & De Palma, Andre, 1992. "The Logit as a Model of Product Differentiation," Oxford Economic Papers, Oxford University Press, vol. 44(1), pages 51-67, January.
    11. Praveen K. Kopalle & Ambar G. Rao & João L. Assunção, 1996. "Asymmetric Reference Price Effects and Dynamic Pricing Policies," Marketing Science, INFORMS, vol. 15(1), pages 60-85.
    12. David R. Bell & Jeongwen Chiang & V. Padmanabhan, 1999. "The Decomposition of Promotional Response: An Empirical Generalization," Marketing Science, INFORMS, vol. 18(4), pages 504-526.
    13. Martin Natter & Thomas Reutterer & Andreas Mild & Alfred Taudes, 2007. "—An Assortmentwide Decision-Support System for Dynamic Pricing and Promotion Planning in DIY Retailing," Marketing Science, INFORMS, vol. 26(4), pages 576-583, 07-08.
    14. Eric A. Greenleaf, 1995. "The Impact of Reference Price Effects on the Profitability of Price Promotions," Marketing Science, INFORMS, vol. 14(1), pages 82-104.
    15. Lin, Kyle Y. & Sibdari, Soheil Y., 2009. "Dynamic price competition with discrete customer choices," European Journal of Operational Research, Elsevier, vol. 197(3), pages 969-980, September.
    16. Franses,Philip Hans & Paap,Richard, 2010. "Quantitative Models in Marketing Research," Cambridge Books, Cambridge University Press, number 9780521143653, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ming Yin & Zheng Wan & Kap Hwan Kim & Shi Yuan Zheng, 2019. "An optimal variable pricing model for container line revenue management systems," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 21(2), pages 173-191, June.
    2. Kuo, Chia-Wei & Huang, Kwei-Long, 2012. "Dynamic pricing of limited inventories for multi-generation products," European Journal of Operational Research, Elsevier, vol. 217(2), pages 394-403.
    3. Gisches, Eyran J. & Qi, Hang & Becker, William J. & Rapoport, Amnon, 2021. "Strategic retailers and myopic consumers: Competitive pricing of perishable goods," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 92(C).
    4. Quan, Yuting & Hong, Jiangtao & Song, Jingpu & Leng, Mingming, 2021. "Game-theoretic analysis of trade-in services in closed-loop supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    5. Jalali, Hamed & Carmen, Raïsa & Van Nieuwenhuyse, Inneke & Boute, Robert, 2019. "Quality and pricing decisions in production/inventory systems," European Journal of Operational Research, Elsevier, vol. 272(1), pages 195-206.
    6. Sibdari, Soheil & Pyke, David F., 2014. "Dynamic pricing with uncertain production cost: An alternating-move approach," European Journal of Operational Research, Elsevier, vol. 236(1), pages 218-228.
    7. Dass, Mayukh & Reshadi, Mehrnoosh & Li, Yuewu, 2023. "An exploration of ripple effects of advertising among major suppliers in a supply chain network," Journal of Business Research, Elsevier, vol. 169(C).
    8. Zhang, Jianxiong & Wang, Yu & Lu, Lihao & Tang, Wansheng, 2015. "Optimal dynamic pricing and replenishment cycle for non-instantaneous deterioration items with inventory-level-dependent demand," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 136-145.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lin, Kyle Y. & Sibdari, Soheil Y., 2009. "Dynamic price competition with discrete customer choices," European Journal of Operational Research, Elsevier, vol. 197(3), pages 969-980, September.
    2. 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.
    3. Sibdari, Soheil & Pyke, David F., 2014. "Dynamic pricing with uncertain production cost: An alternating-move approach," European Journal of Operational Research, Elsevier, vol. 236(1), pages 218-228.
    4. 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.
    5. Pak, K. & Piersma, N., 2002. "airline revenue management," ERIM Report Series Research in Management ERS-2002-12-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    6. Fleischmann, M. & Hall, J.M. & Pyke, D.F., 2005. "A Dynamic Pricing Model for Coordinated Sales and Operations," ERIM Report Series Research in Management ERS-2005-074-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Pak, K. & Piersma, N., 2002. "Airline revenue management: an overview of OR techniques 1982-2001," Econometric Institute Research Papers EI 2002-03, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. Yalç{i}n Akçay & Harihara Prasad Natarajan & Susan H. Xu, 2010. "Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice," Management Science, INFORMS, vol. 56(8), pages 1345-1361, August.
    9. Ming Yin & Zheng Wan & Kap Hwan Kim & Shi Yuan Zheng, 2019. "An optimal variable pricing model for container line revenue management systems," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 21(2), pages 173-191, June.
    10. Chew, Ek Peng & Lee, Chulung & Liu, Rujing, 2009. "Joint inventory allocation and pricing decisions for perishable products," International Journal of Production Economics, Elsevier, vol. 120(1), pages 139-150, July.
    11. Constantinos Maglaras & Joern Meissner, 2006. "Dynamic Pricing Strategies for Multiproduct Revenue Management Problems," Manufacturing & Service Operations Management, INFORMS, vol. 8(2), pages 136-148, July.
    12. Syed Asif Raza & Rafi Ashrafi & Ali Akgunduz, 2020. "A bibliometric analysis of revenue management in airline industry," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 19(6), pages 436-465, December.
    13. Cao, Ping & Li, Jianbin & Yan, Hong, 2012. "Optimal dynamic pricing of inventories with stochastic demand and discounted criterion," European Journal of Operational Research, Elsevier, vol. 217(3), pages 580-588.
    14. Doan, Xuan Vinh & Lei, Xiao & Shen, Siqian, 2020. "Pricing of reusable resources under ambiguous distributions of demand and service time with emerging applications," European Journal of Operational Research, Elsevier, vol. 282(1), pages 235-251.
    15. Dan Zhang & Larry Weatherford, 2017. "Dynamic Pricing for Network Revenue Management: A New Approach and Application in the Hotel Industry," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 18-35, February.
    16. Aldric Vives & Marta Jacob & Marga Payeras, 2018. "Revenue management and price optimization techniques in the hotel sector," Tourism Economics, , vol. 24(6), pages 720-752, September.
    17. Zhang Wensi & Li Jinlin & Ran Lun, 2014. "Price Increasing Timing of Competitive Perishable Products," Journal of Systems Science and Information, De Gruyter, vol. 2(1), pages 29-37, February.
    18. Lin, Kyle Y., 2006. "Dynamic pricing with real-time demand learning," European Journal of Operational Research, Elsevier, vol. 174(1), pages 522-538, October.
    19. Yongbo Xiao & Liming Wang & Jian Chen, 2020. "Dynamic pricing in a trade‐in program with replacement and new customers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(5), pages 334-352, August.
    20. Michael N. Katehakis & Yifeng Liu & Jian Yang, 2022. "A revisit to the markup practice of irreversible dynamic pricing," Annals of Operations Research, Springer, vol. 317(1), pages 77-105, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:207:y:2010:i:1:p:330-338. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.