IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v54y2003i9d10.1057_palgrave.jors.2601596.html
   My bibliography  Save this article

Binary knapsack problems with random budgets

Author

Listed:
  • S Das

    (QM&IS Area, Indian Institute of Management)

  • D Ghosh

    (P&QM Area, Indian Institute of Management)

Abstract

The binary knapsack problem is a combinatorial optimization problem in which a subset of a given set of elements needs to be chosen in order to maximize profit, given a budget constraint. In this paper, we study a stochastic version of the problem in which the budget is random. We propose two different formulations of this problem, based on different ways of handling infeasibility, and propose an exact algorithm and a local search-based heuristic to solve the problems represented by these formulations. We also present the results from some computational experiments.

Suggested Citation

  • S Das & D Ghosh, 2003. "Binary knapsack problems with random budgets," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(9), pages 970-983, September.
  • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:9:d:10.1057_palgrave.jors.2601596
    DOI: 10.1057/palgrave.jors.2601596
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2601596
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1057/palgrave.jors.2601596?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. Ghosh, D. & Das, S., 2000. "Discrete optimization problems with random cost elements," Research Report 00A33, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    2. Egon Balas, 1965. "An Additive Algorithm for Solving Linear Programs with Zero-One Variables," Operations Research, INFORMS, vol. 13(4), pages 517-546, August.
    3. Mordechai I. Henig, 1990. "Risk Criteria in a Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 38(5), pages 820-825, October.
    4. Gang Yu, 1996. "On the Max-Min 0-1 Knapsack Problem with Robust Optimization Applications," Operations Research, INFORMS, vol. 44(2), pages 407-415, April.
    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. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    2. João Claro & Jorge Sousa, 2010. "A multiobjective metaheuristic for a mean-risk static stochastic knapsack problem," Computational Optimization and Applications, Springer, vol. 46(3), pages 427-450, July.

    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. Alexandre Belloni & Mitchell J. Lovett & William Boulding & Richard Staelin, 2012. "Optimal Admission and Scholarship Decisions: Choosing Customized Marketing Offers to Attract a Desirable Mix of Customers," Marketing Science, INFORMS, vol. 31(4), pages 621-636, July.
    2. Mazzola, Joseph B. & Neebe, Alan W., 1999. "Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type," European Journal of Operational Research, Elsevier, vol. 115(2), pages 285-299, June.
    3. Robert M. Saltzman & Frederick S. Hillier, 1991. "An exact ceiling point algorithm for general integer linear programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 53-69, February.
    4. Sbihi, Abdelkader, 2010. "A cooperative local search-based algorithm for the Multiple-Scenario Max-Min Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 339-346, April.
    5. Abumoslem Mohammadi & Javad Tayyebi, 2019. "Maximum Capacity Path Interdiction Problem with Fixed Costs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-21, August.
    6. 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.
    7. Joseph B. Mazzola & Robert H. Schantz, 1997. "Multiple‐facility loading under capacity‐based economies of scope," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(3), pages 229-256, April.
    8. Taylan İlhan & Seyed M. R. Iravani & Mark S. Daskin, 2011. "TECHNICAL NOTE---The Adaptive Knapsack Problem with Stochastic Rewards," Operations Research, INFORMS, vol. 59(1), pages 242-248, February.
    9. Murthy, Ishwar & Sarkar, Sumit, 1997. "Exact algorithms for the stochastic shortest path problem with a decreasing deadline utility function," European Journal of Operational Research, Elsevier, vol. 103(1), pages 209-229, November.
    10. Yasemin Merzifonluoglu & Joseph Geunes, 2021. "The Risk-Averse Static Stochastic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 931-948, July.
    11. Alireza Amirteimoori & Simin Masrouri, 2021. "DEA-based competition strategy in the presence of undesirable products: An application to paper mills," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 5-21.
    12. Mohammad Sabbagh & Richard Soland, 2009. "An improved partial enumeration algorithm for integer programming problems," Annals of Operations Research, Springer, vol. 166(1), pages 147-161, February.
    13. Jiang, Bo & Tzavellas, Hector, 2023. "Optimal liquidity allocation in an equity network," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 286-294.
    14. Ghosh, Diptesh & Sumanta Basu, 2011. "Diversified Local Search for the Traveling Salesman Problem," IIMA Working Papers WP2011-01-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    15. Jain, A. S. & Meeran, S., 1999. "Deterministic job-shop scheduling: Past, present and future," European Journal of Operational Research, Elsevier, vol. 113(2), pages 390-434, March.
    16. Lijun Wei & Zhixing Luo, & Roberto Baldacci & Andrew Lim, 2020. "A New Branch-and-Price-and-Cut Algorithm for One-Dimensional Bin-Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 428-443, April.
    17. Paola Cappanera & Marco Trubian, 2005. "A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 82-98, February.
    18. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    19. Manfred Padberg, 2005. "Classical Cuts for Mixed-Integer Programming and Branch-and-Cut," Annals of Operations Research, Springer, vol. 139(1), pages 321-352, October.
    20. Chernonog, Tatyana & Avinadav, Tal, 2014. "Profit criteria involving risk in price setting of virtual products," European Journal of Operational Research, Elsevier, vol. 236(1), pages 351-360.

    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:pal:jorsoc:v:54:y:2003:i:9:d:10.1057_palgrave.jors.2601596. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave-journals.com/ .

    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.