IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v239y2014i3p625-635.html
   My bibliography  Save this article

An adaptive stochastic knapsack problem

Author

Listed:
  • Chen, Kai
  • Ross, Sheldon M.

Abstract

We consider a stochastic knapsack problem in which the event of overflow results in the problem ending with zero return. We assume that there are n types of items available where each type has infinite supply. An item has an exponentially distributed random weight with a known mean depending on its type and the item’s value is proportional to its weight with a given factor depending on the item’s type. We have to make a decision on each stage whether to stop, or continue to put an item of a selected type in the knapsack. An item’s weight is learned when placed to the knapsack. The objective of this problem is to find a policy that maximizes the expected total values. Using the framework of dynamic programming, the optimal policy is found when n=2 and a heuristic policy is suggested for n>2.

Suggested Citation

  • Chen, Kai & Ross, Sheldon M., 2014. "An adaptive stochastic knapsack problem," European Journal of Operational Research, Elsevier, vol. 239(3), pages 625-635.
    • Handle: RePEc:eee:ejores:v:239:y:2014:i:3:p:625-635
    DOI: 10.1016/j.ejor.2014.06.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171400530X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.06.027?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. L L Lu & S Y Chiu & L A Cox, 1999. "Optimal project selection: Stochastic knapsack with finite time horizon," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(6), pages 645-650, June.
    2. Donald R. Smith, 1978. "Note--On "A Renewal Decision Problem"," Management Science, INFORMS, vol. 24(5), pages 562-563, January.
    3. 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.
    4. 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.
    5. 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.
    6. Lee, Tae-Eog & Oh, Geun Tae, 1997. "The asymptotic value-to-capacity ratio for the multi-class stochastic knapsack problem," European Journal of Operational Research, Elsevier, vol. 103(3), pages 584-594, December.
    7. C. Derman & G. J. Lieberman & S. M. Ross, 1978. "A Renewal Decision Problem," Management Science, INFORMS, vol. 24(5), pages 554-561, January.
    8. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "The Dynamic and Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 46(1), pages 17-35, February.
    9. Martello, Silvano & Pisinger, David & Toth, Paolo, 2000. "New trends in exact algorithms for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 325-332, June.
    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. Yasemin Merzifonluoglu & Joseph Geunes, 2021. "The Risk-Averse Static Stochastic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 931-948, July.
    2. Diaz, Juan Esteban & Handl, Julia & Xu, Dong-Ling, 2018. "Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system," European Journal of Operational Research, Elsevier, vol. 266(3), pages 976-989.
    3. Clifford Stein & Van-Anh Truong & Xinshang Wang, 2020. "Advance Service Reservations with Heterogeneous Customers," Management Science, INFORMS, vol. 66(7), pages 2929-2950, July.
    4. Asaf Levin & Aleksander Vainer, 2018. "Lower bounds on the adaptivity gaps in variants of the stochastic knapsack problem," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 794-813, April.
    5. Kai Chen & Sheldon M. Ross, 2014. "The burglar problem with multiple options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 359-364, August.

    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. 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.
    2. Kai Chen & Sheldon M. Ross, 2014. "The burglar problem with multiple options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 359-364, August.
    3. 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.
    4. So, Mee Chi & Thomas, Lyn C. & Huang, Bo, 2016. "Lending decisions with limits on capital available: The polygamous marriage problem," European Journal of Operational Research, Elsevier, vol. 249(2), pages 407-416.
    5. 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.
    6. Clifford Stein & Van-Anh Truong & Xinshang Wang, 2020. "Advance Service Reservations with Heterogeneous Customers," Management Science, INFORMS, vol. 66(7), pages 2929-2950, July.
    7. Shelby Brumelle & Darius Walczak, 2003. "Dynamic Airline Revenue Management with Multiple Semi-Markov Demand," Operations Research, INFORMS, vol. 51(1), pages 137-148, February.
    8. 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.
    9. 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.
    10. Grace Lin & Yingdong Lu & David Yao, 2007. "Stochastic Knapsack Problem Revisited: Switch-Over Policies and Dynamic Pricing," Papers 0708.1146, arXiv.org.
    11. 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.
    12. 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.
    13. Tianke Feng & Joseph C. Hartman, 2015. "The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 267-292, June.
    14. Senay Solak & Armagan Bayram & Mehmet Gumus & Yueran Zhuo, 2019. "Technical Note—Optimizing Foreclosed Housing Acquisitions in Societal Response to Foreclosures," Operations Research, INFORMS, vol. 67(4), pages 950-964, July.
    15. Wei Zhang & Sriram Dasu & Reza Ahmadi, 2017. "Higher Prices for Larger Quantities? Nonmonotonic Price–Quantity Relations in B2B Markets," Management Science, INFORMS, vol. 63(7), pages 2108-2126, July.
    16. Brian C. Dean & Michel X. Goemans & Jan Vondrák, 2008. "Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 945-964, November.
    17. Keumseok Kang & J. George Shanthikumar & Kemal Altinkemer, 2016. "Postponable Acceptance and Assignment: A Stochastic Dynamic Programming Approach," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 493-508, October.
    18. Soumia Ichoua & Michel Gendreau & Jean-Yves Potvin, 2006. "Exploiting Knowledge About Future Demands for Real-Time Vehicle Dispatching," Transportation Science, INFORMS, vol. 40(2), pages 211-225, May.
    19. , & , & ,, 2011. "Revenue maximization in the dynamic knapsack problem," Theoretical Economics, Econometric Society, vol. 6(2), May.
    20. Jihyeok Jung & Chan-Oi Song & Deok-Joo Lee & Kiho Yoon, 2024. "Optimal Mechanism in a Dynamic Stochastic Knapsack Environment," Papers 2402.14269, arXiv.org.

    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:239:y:2014:i:3:p:625-635. 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.