IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v49y2002i3p303-325.html
   My bibliography  Save this article

Dynamic pricing and inventory control with learning

Author

Listed:
  • Nicholas C. Petruzzi
  • Maqbool Dada

Abstract

Optimal operating policies and corresponding managerial insight are developed for the decision problem of coordinating supply and demand when (i) both supply and demand can be influenced by the decision maker and (ii) learning is pursued. In particular, we determine optimal stocking and pricing policies over time when a given market parameter of the demand process, though fixed, initially is unknown. Because of the initially unknown market parameter, the decision maker begins the problem horizon with a subjective probability distribution associated with demand. Learning occurs as the firm monitors the market's response to its decisions and then updates its characterization of the demand function. Of primary interest is the effect of censored data since a firm's observations often are restricted to sales. We find that the first‐period optimal selling price increases with the length of the problem horizon. However, for a given problem horizon, prices can rise or fall over time, depending on how the scale parameter influences demand. Further results include the characterization of the optimal stocking quantity decision and a computationally viable algorithm. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 303–325, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10013

Suggested Citation

  • Nicholas C. Petruzzi & Maqbool Dada, 2002. "Dynamic pricing and inventory control with learning," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 303-325, April.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:3:p:303-325
    DOI: 10.1002/nav.10013
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.10013
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.10013?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
    ---><---

    References listed on IDEAS

    as
    1. Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
    2. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    3. Hirofumi Matsuo, 1990. "A Stochastic Sequencing Problem for Style Goods with Forecast Revisions and Hierarchical Structure," Management Science, INFORMS, vol. 36(3), pages 332-347, March.
    4. William S. Lovejoy, 1990. "Myopic Policies for Some Inventory Models with Uncertain Demand Distributions," Management Science, INFORMS, vol. 36(6), pages 724-738, June.
    5. Katy S. Azoury, 1985. "Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution," Management Science, INFORMS, vol. 31(9), pages 1150-1160, September.
    6. Alpern, Steve & Snower, Dennis J., 1989. "A search model of optimal pricing and production," Engineering Costs and Production Economics, Elsevier, vol. 15(1), pages 279-284, May.
    7. Edwin S. Mills, 1959. "Uncertainty and Price Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 73(1), pages 116-130.
    8. Sanford J. Grossman & Richard E. Kihlstrom & Leonard J. Mirman, 1977. "A Bayesian Approach to the Production of Information and Learning By Doing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(3), pages 533-547.
    9. Steven Nahmias, 1994. "Demand estimation in lost sales inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 739-757, October.
    10. 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.
    11. Wallace B. Crowston & Warren H. Hausman & William R. Kampe, II, 1973. "Multistage Production for Stochastic Seasonal Demand," Management Science, INFORMS, vol. 19(8), pages 924-935, April.
    12. Warren H. Hausman & Rein Peterson, 1972. "Multiproduct Production Scheduling for Style Goods with Limited Capacity, Forecast Revisions and Terminal Delivery," Management Science, INFORMS, vol. 18(7), pages 370-383, March.
    13. Trefler, Daniel, 1993. "The Ignorant Monopolist: Optimal Learning with Endogenous Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 565-581, August.
    14. Herbert E. Scarf, 1960. "Some remarks on bayes solutions to the inventory problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 7(4), pages 591-596, December.
    15. Lazear, Edward P, 1986. "Retail Pricing and Clearance Sales," American Economic Review, American Economic Association, vol. 76(1), pages 14-32, March.
    16. David J. Braden & Marshall Freimer, 1991. "Informational Dynamics of Censored Observations," Management Science, INFORMS, vol. 37(11), pages 1390-1404, November.
    17. Zabel, Edward, 1972. "Multiperiod monopoly under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 524-536, December.
    18. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
    19. Gunnar T. Thowsen, 1975. "A dynamic, nonstationary inventory problem for a price/quantity setting firm," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(3), pages 461-476, September.
    20. Gabriel R. Bitran & Elizabeth A. Haas & Hirofumi Matsuo, 1986. "Production Planning of Style Goods with High Setup Costs and Forecast Revisions," Operations Research, INFORMS, vol. 34(2), pages 226-236, April.
    21. Martin A. Lariviere & Evan L. Porteus, 1999. "Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales," Management Science, INFORMS, vol. 45(3), pages 346-363, March.
    22. George R. Murray, Jr. & Edward A. Silver, 1966. "A Bayesian Analysis of the Style Goods Inventory Problem," Management Science, INFORMS, vol. 12(11), pages 785-797, July.
    23. Diane Reyniers, 1990. "A High-Low Search Algorithm for a Newsboy Problem with Delayed Information Feedback," Operations Research, INFORMS, vol. 38(5), pages 838-846, October.
    24. Maqbool Dada & K. N. Srikanth, 1990. "Monopolistic Pricing and the Learning Curve: An Algorithmic Approach," Operations Research, INFORMS, vol. 38(4), pages 656-666, August.
    25. Giora Harpaz & Wayne Y. Lee & Robert L. Winkler, 1982. "Learning, Experimentation, and the Optimal Output Decisions of a Competitive Firm," Management Science, INFORMS, vol. 28(6), pages 589-603, June.
    26. Narendra Agrawal & Stephen A. Smith, 1996. "Estimating negative binomial demand for retail inventory management with unobservable lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 839-861, September.
    27. David J. Braden & Shmuel S. Oren, 1994. "Nonlinear Pricing to Produce Information," Marketing Science, INFORMS, vol. 13(3), pages 310-326.
    28. Balvers, Ronald J & Cosimano, Thomas F, 1990. "Actively Learning about Demand and the Dynamics of Price Adjustment," Economic Journal, Royal Economic Society, vol. 100(402), pages 882-898, 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. Arnab Bisi & Maqbool Dada, 2007. "Dynamic learning, pricing, and ordering by a censored newsvendor," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 448-461, June.
    2. Cao, Ping & Zhao, Nenggui & Wu, Jie, 2019. "Dynamic pricing with Bayesian demand learning and reference price effect," European Journal of Operational Research, Elsevier, vol. 279(2), pages 540-556.
    3. Philipp Afèche & Barış Ata, 2013. "Bayesian Dynamic Pricing in Queueing Systems with Unknown Delay Cost Characteristics," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 292-304, May.
    4. Sergii Bogachov & Aleksy Kwilinski & Boris Miethlich & Viera Bartosova & Aleksandr Gurnak, 2020. "Artificial intelligence components and fuzzy regulators in entrepreneurship development," Entrepreneurship and Sustainability Issues, VsI Entrepreneurship and Sustainability Center, vol. 8(2), pages 487-499, December.
    5. Nan Yang & Renyu Zhang, 2022. "Dynamic pricing and inventory management in the presence of online reviews," Production and Operations Management, Production and Operations Management Society, vol. 31(8), pages 3180-3197, August.
    6. Qing Li & Shaohui Zheng, 2006. "Joint Inventory Replenishment and Pricing Control for Systems with Uncertain Yield and Demand," Operations Research, INFORMS, vol. 54(4), pages 696-705, August.
    7. Man Yu & Laurens Debo & Roman Kapuscinski, 2016. "Strategic Waiting for Consumer-Generated Quality Information: Dynamic Pricing of New Experience Goods," Management Science, INFORMS, vol. 62(2), pages 410-435, February.
    8. Yiangos Papanastasiou, 2020. "Newsvendor Decisions with Two-Sided Learning," Management Science, INFORMS, vol. 66(11), pages 5408-5426, November.
    9. 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.
    10. Victor F. Araman & René Caldentey, 2009. "Dynamic Pricing for Nonperishable Products with Demand Learning," Operations Research, INFORMS, vol. 57(5), pages 1169-1188, October.
    11. Tatsiana Levina & Yuri Levin & Jeff McGill & Mikhail Nediak, 2009. "Dynamic Pricing with Online Learning and Strategic Consumers: An Application of the Aggregating Algorithm," Operations Research, INFORMS, vol. 57(2), pages 327-341, April.
    12. Vincent C. Li & Yat-wah Wan & Chi-Leung Chu & Yi-Cheng Lin, 2020. "A Dynamic Programming-Based Heuristic for Markdown Pricing and Inventory Allocation of a Seasonal Product in a Retail Chain," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-30, January.
    13. Lu Xiao & Hang Zhang & Yong Qin, 2020. "Competitive Pricing of Innovative Products with Consumers’ Social Learning," Sustainability, MDPI, vol. 12(9), pages 1-13, May.
    14. Gel, Esma S. & Salman, F. Sibel, 2022. "Dynamic ordering decisions with approximate learning of supply yield uncertainty," International Journal of Production Economics, Elsevier, vol. 243(C).

    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. Arnab Bisi & Maqbool Dada, 2007. "Dynamic learning, pricing, and ordering by a censored newsvendor," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 448-461, June.
    2. Nicholas C. Petruzzi & Maqbool Dada, 2001. "Information and Inventory Recourse for a Two-Market, Price-Setting Retailer," Manufacturing & Service Operations Management, INFORMS, vol. 3(3), pages 242-263, October.
    3. Xiaomei Ding & Martin L. Puterman & Arnab Bisi, 2002. "The Censored Newsvendor and the Optimal Acquisition of Information," Operations Research, INFORMS, vol. 50(3), pages 517-527, June.
    4. Woonghee Tim Huh & Paat Rusmevichientong, 2009. "A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 103-123, February.
    5. Boutselis, Petros & McNaught, Ken, 2014. "Finite-Time Horizon Logistics Decision Making Problems: Consideration of a Wider Set of Factors," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Blecker, Thorsten & Kersten, Wolfgang & Ringle, Christian M. (ed.), Innovative Methods in Logistics and Supply Chain Management: Current Issues and Emerging Practices. Proceedings of the Hamburg International Conferenc, volume 19, pages 249-274, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    6. Schulte, Benedikt & Sachs, Anna-Lena, 2020. "The price-setting newsvendor with Poisson demand," European Journal of Operational Research, Elsevier, vol. 283(1), pages 125-137.
    7. Bitran, Gabriel R. & Wadhwa, Hitendra K. S. (Hitendra Kumar Singh), 1996. "A methodology for demand learning with an application to the optimal pricing of seasonal products," Working papers 3898-96., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    9. Xiangwen Lu & Jing-Sheng Song & Kaijie Zhu, 2008. "Analysis of Perishable-Inventory Systems with Censored Demand Data," Operations Research, INFORMS, vol. 56(4), pages 1034-1038, August.
    10. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    11. Martin A. Lariviere & Evan L. Porteus, 1999. "Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales," Management Science, INFORMS, vol. 45(3), pages 346-363, March.
    12. Kogan, Konstantin & Herbon, Avi, 2008. "Production under periodic demand update prior to a single selling season: A decomposition approach," European Journal of Operational Research, Elsevier, vol. 184(1), pages 133-146, January.
    13. Alain Bensoussan & Pengfei Guo, 2015. "Technical Note—Managing Nonperishable Inventories with Learning About Demand Arrival Rate Through Stockout Times," Operations Research, INFORMS, vol. 63(3), pages 602-609, June.
    14. Li Chen, 2010. "Bounds and Heuristics for Optimal Bayesian Inventory Control with Unobserved Lost Sales," Operations Research, INFORMS, vol. 58(2), pages 396-413, April.
    15. Sen, Alper & Zhang, Alex X., 2009. "Style goods pricing with demand learning," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1058-1075, August.
    16. Ghate, Archis, 2015. "Optimal minimum bids and inventory scrapping in sequential, single-unit, Vickrey auctions with demand learning," European Journal of Operational Research, Elsevier, vol. 245(2), pages 555-570.
    17. Bharadwaj Kadiyala & Özalp Özer & Alain Bensoussan, 2020. "A Mechanism Design Approach to Vendor Managed Inventory," Management Science, INFORMS, vol. 66(6), pages 2628-2652, June.
    18. Agrawal, Narendra & Smith, Stephen A., 2013. "Optimal inventory management for a retail chain with diverse store demands," European Journal of Operational Research, Elsevier, vol. 225(3), pages 393-403.
    19. Apostolos Burnetas & Stephen Gilbert, 2001. "Future Capacity Procurements Under Unknown Demand and Increasing Costs," Management Science, INFORMS, vol. 47(7), pages 979-992, July.
    20. Youhua (Frank) Chen & Saibal Ray & Yuyue Song, 2006. "Optimal pricing and inventory control policy in periodic‐review systems with fixed ordering cost and lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(2), pages 117-136, March.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:49:y:2002:i:3:p:303-325. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.