IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v217y2012i3p580-588.html
   My bibliography  Save this article

Optimal dynamic pricing of inventories with stochastic demand and discounted criterion

Author

Listed:
  • Cao, Ping
  • Li, Jianbin
  • Yan, Hong

Abstract

We consider a continuous time dynamic pricing problem for selling a given number of items over a finite or infinite time horizon. The demand is price sensitive and follows a non-homogeneous Poisson process. We formulate this problem as to maximize the expected discounted revenue and obtain the structural properties of the optimal revenue function and optimal price policy by the Hamilton–Jacobi–Bellman (HJB) equation. Moreover, we study the impact of the discount rate on the optimal revenue function and the optimal price. Further, we extend the problem to the case with discounting and time-varying demand, the infinite time horizon problem. Numerical examples are used to illustrate our analytical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:217:y:2012:i:3:p:580-588
    DOI: 10.1016/j.ejor.2011.09.048
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711009015
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2011.09.048?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Youyi Feng & Baichun Xiao, 2000. "Optimal Policies of Yield Management with Multiple Predetermined Prices," Operations Research, INFORMS, vol. 48(2), pages 332-343, April.
    3. Youyi Feng & Guillermo Gallego, 1995. "Optimal Starting Times for End-of-Season Sales and Optimal Stopping Times for Promotional Fares," Management Science, INFORMS, vol. 41(8), pages 1371-1391, August.
    4. Gabriel R. Bitran & Stephen M. Gilbert, 1996. "Managing Hotel Reservations with Uncertain Arrivals," Operations Research, INFORMS, vol. 44(1), pages 35-49, February.
    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. Tak C. Lee & Marvin Hersh, 1993. "A Model for Dynamic Airline Seat Inventory Control with Multiple Seat Bookings," Transportation Science, INFORMS, vol. 27(3), pages 252-265, August.
    7. 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.
    8. 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.
    9. Varda Liberman & Uri Yechiali, 1978. "On the Hotel Overbooking Problem--An Inventory System with Stochastic Cancellations," Management Science, INFORMS, vol. 24(11), pages 1117-1126, July.
    10. 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.
    11. 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.
    12. Bulut, Zümbül & Gürler, Ülkü & Sen, Alper, 2009. "Bundle pricing of inventories with stochastic demand," European Journal of Operational Research, Elsevier, vol. 197(3), pages 897-911, September.
    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. Gaïgi, M’hamed & Ly Vath, Vathana & Scotti, Simone, 2022. "Optimal harvesting under marine reserves and uncertain environment," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1181-1194.
    2. Wei, Jie & Zhao, Jing & Li, Yongjian, 2013. "Pricing decisions for complementary products with firms’ different market powers," European Journal of Operational Research, Elsevier, vol. 224(3), pages 507-519.
    3. Sobhani, A. & Wahab, M.I.M. & Neumann, W.P., 2015. "Investigating work-related ill health effects in optimizing the performance of manufacturing systems," European Journal of Operational Research, Elsevier, vol. 241(3), pages 708-718.
    4. Huanan Zhang & Cong Shi & Chao Qin & Cheng Hua, 2016. "Stochastic regret minimization for revenue management problems with nonstationary demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(6), pages 433-448, September.
    5. Omar Besbes & Denis Sauré, 2014. "Dynamic Pricing Strategies in the Presence of Demand Shifts," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 513-528, October.
    6. Schlosser, Rainer, 2016. "Joint stochastic dynamic pricing and advertising with time-dependent demand," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 439-452.
    7. Tomohiro Ando, 2018. "Merchant selection and pricing strategy for a platform firm in the online group buying market," Annals of Operations Research, Springer, vol. 263(1), pages 209-230, April.
    8. Cao, Ping & Yang, Ke & Liu, Ke, 2020. "Optimal selection and release problem in software testing process: A continuous time stochastic control approach," European Journal of Operational Research, Elsevier, vol. 285(1), pages 211-222.
    9. Alavi Fard, Farzad & Sy, Malick & Ivanov, Dmitry, 2019. "Optimal overbooking strategies in the airlines using dynamic programming approach in continuous time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 384-399.

    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. 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.
    2. 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.
    3. Kyle Y. Lin, 2004. "A sequential dynamic pricing model and its applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 501-521, June.
    4. 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.
    5. 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.
    6. Marcus, Benjamin & Anderson, Chris K., 2008. "Revenue management for low-cost providers," European Journal of Operational Research, Elsevier, vol. 188(1), pages 258-272, July.
    7. 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.
    8. 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.
    9. 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.
    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. Yongbo Xiao & Sean X. Zhou, 2020. "Trade‐in for Cash or for Upgrade? Dynamic Pricing with Customer Choice," Production and Operations Management, Production and Operations Management Society, vol. 29(4), pages 856-881, April.
    12. Youyi Feng & Baichun Xiao, 2001. "A Dynamic Airline Seat Inventory Control Model and Its Optimal Policy," Operations Research, INFORMS, vol. 49(6), pages 938-949, December.
    13. 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.
    14. 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.
    15. Yongbo Xiao & Jian Chen, 2014. "Evaluating the potential effects from probabilistic selling of similar products," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(8), pages 604-620, December.
    16. Yongbo Xiao, 2018. "Dynamic pricing and replenishment: Optimality, bounds, and asymptotics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 3-25, February.
    17. Xuanming Su, 2007. "Intertemporal Pricing with Strategic Customer Behavior," Management Science, INFORMS, vol. 53(5), pages 726-741, May.
    18. Feng, Youyi & Xiao, Baichun, 2006. "Integration of pricing and capacity allocation for perishable products," European Journal of Operational Research, Elsevier, vol. 168(1), pages 17-34, January.
    19. C S M Currie & R C H Cheng & H K Smith, 2008. "Dynamic pricing of airline tickets with competition," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(8), pages 1026-1037, August.
    20. Netessine, Serguei, 2006. "Dynamic pricing of inventory/capacity with infrequent price changes," European Journal of Operational Research, Elsevier, vol. 174(1), pages 553-580, 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:217:y:2012:i:3:p:580-588. 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.