IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v54y2007i7p767-795.html
   My bibliography  Save this article

A nonlinear continuous time optimal control model of dynamic pricing and inventory control with no backorders

Author

Listed:
  • Elodie Adida
  • Georgia Perakis

Abstract

In this paper, we present a continuous time optimal control model for studying a dynamic pricing and inventory control problem for a make‐to‐stock manufacturing system. We consider a multiproduct capacitated, dynamic setting. We introduce a demand‐based model where the demand is a linear function of the price, the inventory cost is linear, the production cost is an increasing strictly convex function of the production rate, and all coefficients are time‐dependent. A key part of the model is that no backorders are allowed. We introduce and study an algorithm that computes the optimal production and pricing policy as a function of the time on a finite time horizon, and discuss some insights. Our results illustrate the role of capacity and the effects of the dynamic nature of demand in the model. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Suggested Citation

  • Elodie Adida & Georgia Perakis, 2007. "A nonlinear continuous time optimal control model of dynamic pricing and inventory control with no backorders," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(7), pages 767-795, October.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:7:p:767-795
    DOI: 10.1002/nav.20250
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.20250
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.20250?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. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    2. Gaimon, Cheryl, 1988. "Simultaneous and dynamic price, production, inventory and capacity decisions," European Journal of Operational Research, Elsevier, vol. 35(3), pages 426-441, June.
    3. Thompson, Gerald L. & Sethi, Suresh P. & Teng, Jinn-Tsair, 1984. "Strong planning and forecast horizons for a model with simultaneous price and production decisions," European Journal of Operational Research, Elsevier, vol. 16(3), pages 378-388, June.
    4. Jehoshua Eliashberg & Richard Steinberg, 1987. "Marketing-Production Decisions in an Industrial Channel of Distribution," Management Science, INFORMS, vol. 33(8), pages 981-1000, August.
    5. 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.
    6. 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.
    7. 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.
    8. Jorgensen, Steffen & Kort, Peter M., 2002. "Optimal pricing and inventory policies: Centralized and decentralized decision making," European Journal of Operational Research, Elsevier, vol. 138(3), pages 578-600, May.
    9. Yakov Amihud & Haim Mendelson, 1983. "Price Smoothing and Inventory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 87-98.
    10. Levent Tunçel & Michael J. Todd, 1996. "Asymptotic Behavior of Interior-Point Methods: A View From Semi-Infinite Programming," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 354-381, May.
    11. Feichtinger, Gustav & Hartl, Richard, 1985. "Optimal pricing and production in an inventory model," European Journal of Operational Research, Elsevier, vol. 19(1), pages 45-56, January.
    12. 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.
    13. Ravi Kumar, K. & Loomba, Arvinder P. S. & Hadjinicola, George C., 2000. "Marketing-production coordination in channels of distribution," European Journal of Operational Research, Elsevier, vol. 126(1), pages 189-217, October.
    14. Hugh Everett, 1963. "Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources," Operations Research, INFORMS, vol. 11(3), pages 399-417, June.
    15. Stephen M. Gilbert, 2000. "Coordination of Pricing and Multiple-Period Production Across Multiple Constant Priced Goods," Management Science, INFORMS, vol. 46(12), pages 1602-1616, December.
    16. Dimitris Bertsimas & Sarah Stock Patterson, 2000. "The Traffic Flow Management Rerouting Problem in Air Traffic Control: A Dynamic Network Flow Approach," Transportation Science, INFORMS, vol. 34(3), pages 239-255, August.
    17. Anderson, W H Locke, 1970. "Production Scheduling, Intermediate Goods, and Labor Productivity," American Economic Review, American Economic Association, vol. 60(1), pages 153-162, March.
    18. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 698-723, August.
    19. Constantinos Maglaras & Joern Meissner, 2003. "Dynamic Pricing Strategies for Multi-Product Revenue Management Problems," Working Papers MRG/0002, Department of Management Science, Lancaster University, revised Nov 2005.
    20. Frank H. Clarke, 1976. "A New Approach to Lagrange Multipliers," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 165-174, May.
    21. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case," Operations Research, INFORMS, vol. 52(6), pages 887-896, December.
    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. Guowei Liu & Jianxiong Zhang & Wansheng Tang, 2015. "Joint dynamic pricing and investment strategy for perishable foods with price-quality dependent demand," Annals of Operations Research, Springer, vol. 226(1), pages 397-416, March.

    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. Shiming Deng & Candace A. Yano, 2006. "Joint Production and Pricing Decisions with Setup Costs and Capacity Constraints," Management Science, INFORMS, vol. 52(5), pages 741-756, May.
    2. Ibrahim, Michael Nawar & Atiya, Amir F., 2016. "Analytical solutions to the dynamic pricing problem for time-normalized revenue," European Journal of Operational Research, Elsevier, vol. 254(2), pages 632-643.
    3. Lap Mui Ann Chan & David Simchi-Levi & Julie Swann, 2006. "Pricing, Production, and Inventory Policies for Manufacturing with Stochastic Demand and Discretionary Sales," Manufacturing & Service Operations Management, INFORMS, vol. 8(2), pages 149-168, January.
    4. 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.
    5. Hyun-soo Ahn & Mehmet Gümüş & Philip Kaminsky, 2007. "Pricing and Manufacturing Decisions When Demand Is a Function of Prices in Multiple Periods," Operations Research, INFORMS, vol. 55(6), pages 1039-1057, December.
    6. 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.
    7. Serguei Netessine & Sergei Savin & Wenqiang Xiao, 2006. "Revenue Management Through Dynamic Cross Selling in E-Commerce Retailing," Operations Research, INFORMS, vol. 54(5), pages 893-913, October.
    8. Francis de Véricourt & Miguel Sousa Lobo, 2009. "Resource and Revenue Management in Nonprofit Operations," Operations Research, INFORMS, vol. 57(5), pages 1114-1128, October.
    9. Xuanming Su, 2007. "Intertemporal Pricing with Strategic Customer Behavior," Management Science, INFORMS, vol. 53(5), pages 726-741, May.
    10. Wen Chen & Adam J. Fleischhacker & Michael N. Katehakis, 2015. "Dynamic pricing in a dual‐market environment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 531-549, October.
    11. Ilan Lobel, 2021. "Revenue Management and the Rise of the Algorithmic Economy," Management Science, INFORMS, vol. 67(9), pages 5389-5398, September.
    12. Constantinos Maglaras, 2006. "Revenue Management for a Multiclass Single-Server Queue via a Fluid Model Analysis," Operations Research, INFORMS, vol. 54(5), pages 914-932, October.
    13. Elodie Adida & Georgia Perakis, 2010. "Dynamic pricing and inventory control: robust vs. stochastic uncertainty models—a computational study," Annals of Operations Research, Springer, vol. 181(1), pages 125-157, December.
    14. Kaijie Zhu & Ulrich W. Thonemann, 2009. "Coordination of pricing and inventory control across products," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 175-190, March.
    15. 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.
    16. Saif Benjaafar & Ming Hu, 2020. "Operations Management in the Age of the Sharing Economy: What Is Old and What Is New?," Manufacturing & Service Operations Management, INFORMS, vol. 22(1), pages 93-101, January.
    17. 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.
    18. 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.
    19. Abhijit Upasani & Reha Uzsoy, 2008. "Incorporating manufacturing lead times in joint production-marketing models: A review and some future directions," Annals of Operations Research, Springer, vol. 161(1), pages 171-188, July.
    20. Wen Chen & Ying He, 2022. "Dynamic pricing and inventory control with delivery flexibility," Annals of Operations Research, Springer, vol. 317(2), pages 481-508, October.

    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:54:y:2007:i:7:p:767-795. 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.