IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0708.1146.html
   My bibliography  Save this paper

Stochastic Knapsack Problem Revisited: Switch-Over Policies and Dynamic Pricing

Author

Listed:
  • Grace Lin
  • Yingdong Lu
  • David Yao

Abstract

The stochastic knapsack has been used as a model in wide ranging applications from dynamic resource allocation to admission control in telecommunication. In recent years, a variation of the model has become a basic tool in studying problems that arise in revenue management and dynamic/flexible pricing; and it is in this context that our study is undertaken. Based on a dynamic programming formulation and associated properties of the value function, we study in this paper a class of control that we call switch-over policies -- start from accepting only orders of the highest price, and switch to including lower prices as time goes by, with the switch-over times optimally decided via convex programming. We establish the asymptotic optimality of the switch-over policy, and develop pricing models based on this policy to optimize the price reductions over the decision horizon.

Suggested Citation

  • Grace Lin & Yingdong Lu & David Yao, 2007. "Stochastic Knapsack Problem Revisited: Switch-Over Policies and Dynamic Pricing," Papers 0708.1146, arXiv.org.
    • Handle: RePEc:arx:papers:0708.1146
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0708.1146
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Constantinos Maglaras & Assaf Zeevi, 2005. "Pricing and Design of Differentiated Services: Approximate Analysis and Structural Insights," Operations Research, INFORMS, vol. 53(2), pages 242-262, April.
    3. Jason D. Papastavrou & Srikanth Rajagopalan & Anton J. Kleywegt, 1996. "The Dynamic and Stochastic Knapsack Problem with Deadlines," Management Science, INFORMS, vol. 42(12), pages 1706-1718, December.
    4. Shelby Brumelle & Darius Walczak, 2003. "Dynamic Airline Revenue Management with Multiple Semi-Markov Demand," Operations Research, INFORMS, vol. 51(1), pages 137-148, February.
    5. 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.
    6. Richard Van Slyke & Yi Young, 2000. "Finite Horizon Stochastic Knapsacks with Applications to Yield Management," Operations Research, INFORMS, vol. 48(1), pages 155-172, February.
    7. 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.
    8. 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.
    9. 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.
    10. Kalyan Talluri & Garrett van Ryzin, 1999. "A Randomized Linear Programming Method for Computing Network Bid Prices," Transportation Science, INFORMS, vol. 33(2), pages 207-216, May.
    11. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "The Dynamic and Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 46(1), pages 17-35, February.
    12. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    13. Youyi Feng & Guillermo Gallego, 2000. "Perishable Asset Revenue Management with Markovian Time Dependent Demand Intensities," Management Science, INFORMS, vol. 46(7), pages 941-956, July.
    Full references (including those not matched with items on IDEAS)

    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. Grace Y. Lin & Yingdong Lu & David D. Yao, 2008. "The Stochastic Knapsack Revisited: Switch-Over Policies and Dynamic Pricing," Operations Research, INFORMS, vol. 56(4), pages 945-957, August.
    2. 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.
    3. 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.
    4. Guillermo Gallego & Michael Z. F. Li & Yan Liu, 2020. "Dynamic Nonlinear Pricing of Inventories over Finite Sales Horizons," Operations Research, INFORMS, vol. 68(3), pages 655-670, May.
    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. Jeffrey I. McGill & Garrett J. van Ryzin, 1999. "Revenue Management: Research Overview and Prospects," Transportation Science, INFORMS, vol. 33(2), pages 233-256, May.
    7. Alec Morton, 2006. "Structural properties of network revenue management models: An economic perspective," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 748-760, December.
    8. Feng, Youyi & Xiao, Baichun, 2006. "A continuous-time seat control model for single-leg flights with no-shows and optimal overbooking upper bound," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1298-1316, October.
    9. Kalyan Talluri & Garrett van Ryzin, 2000. "Revenue management under general discrete choice model of consumer behavior," Economics Working Papers 533, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2001.
    10. Shelby Brumelle & Darius Walczak, 2003. "Dynamic Airline Revenue Management with Multiple Semi-Markov Demand," Operations Research, INFORMS, vol. 51(1), pages 137-148, February.
    11. Pak, K. & Dekker, R., 2004. "Cargo Revenue Management: Bid-Prices for a 0-1 Multi Knapsack Problem," ERIM Report Series Research in Management ERS-2004-055-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.
    12. Maclean, K.D.S. & Ødegaard, F., 2020. "Dynamic capacity allocation for group bookings in live entertainment," European Journal of Operational Research, Elsevier, vol. 287(3), pages 975-988.
    13. 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.
    14. 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.
    15. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    16. Alexander G. Nikolaev & Sheldon H. Jacobson, 2010. "Technical Note ---Stochastic Sequential Decision-Making with a Random Number of Jobs," Operations Research, INFORMS, vol. 58(4-part-1), pages 1023-1027, August.
    17. Pak, K. & Dekker, R. & Kindervater, G.A.P., 2003. "Airline Revenue Management with Shifting Capacity," Econometric Institute Research Papers ERS-2003-091-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    18. 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.
    19. 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.
    20. Chiang, David Ming-Huang & Wu, Andy Wei-Di, 2011. "Discrete-order admission ATP model with joint effect of margin and order size in a MTO environment," International Journal of Production Economics, Elsevier, vol. 133(2), pages 761-775, 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:arx:papers:0708.1146. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.