IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v17y1969i5p848-856.html
   My bibliography  Save this article

The Set-Partitioning Problem: Set Covering with Equality Constraints

Author

Listed:
  • R. S. Garfinkel

    (University of Rochester, Rochester, New York)

  • G. L. Nemhauser

    (The Johns Hopkins University, Baltimore, Maryland)

Abstract

This paper gives an enumerative algorithm for the set-partitioning problem, that is, the set-covering problem with equality constraints, and presents computational results for real and randomly generated problems. The fact that many problems can be solved more rapidly than the corresponding linear programs demonstrates the efficiency of the algorithm; for example, a randomly generated problem with 1,400 variables and 100 constraints was solved in 15 minutes.

Suggested Citation

  • R. S. Garfinkel & G. L. Nemhauser, 1969. "The Set-Partitioning Problem: Set Covering with Equality Constraints," Operations Research, INFORMS, vol. 17(5), pages 848-856, October.
    • Handle: RePEc:inm:oropre:v:17:y:1969:i:5:p:848-856
    DOI: 10.1287/opre.17.5.848
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.17.5.848
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.17.5.848?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Niu, Huimin & Zhou, Xuesong & Tian, Xiaopeng, 2018. "Coordinating assignment and routing decisions in transit vehicle schedules: A variable-splitting Lagrangian decomposition approach for solution symmetry breaking," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 70-101.
    2. Hoogendoorn, Y.N. & Dalmeijer, K., 2021. "Resource-robust valid inequalities for set covering and set partitioning models," Econometric Institute Research Papers EI 2020-08, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Rabinowitz, Gad, 1997. "A shrunken cyclic inspection schedule for deteriorating production stages," European Journal of Operational Research, Elsevier, vol. 96(3), pages 493-503, February.
    4. Boubaker, Khaled & Desaulniers, Guy & Elhallaoui, Issmail, 2010. "Bidline scheduling with equity by heuristic dynamic constraint aggregation," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 50-61, January.
    5. Sarin, Subhash C. & Aggarwal, Sanjay, 2001. "Modeling and algorithmic development of a staff scheduling problem," European Journal of Operational Research, Elsevier, vol. 128(3), pages 558-569, February.
    6. Haider, Zulqarnain & Hu, Yujie & Charkhgard, Hadi & Himmelgreen, David & Kwon, Changhyun, 2022. "Creating grocery delivery hubs for food deserts at local convenience stores via spatial and temporal consolidation," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    7. Mert Edali & Gönenç Yücel, 2020. "Analysis of an individual‐based influenza epidemic model using random forest metamodels and adaptive sequential sampling," Systems Research and Behavioral Science, Wiley Blackwell, vol. 37(6), pages 936-958, November.
    8. Mert Edali, 2022. "Pattern‐oriented analysis of system dynamics models via random forests," System Dynamics Review, System Dynamics Society, vol. 38(2), pages 135-166, April.
    9. Guo, Yufeng & Mellouli, Taieb & Suhl, Leena & Thiel, Markus P., 2006. "A partially integrated airline crew scheduling approach with time-dependent crew capacities and multiple home bases," European Journal of Operational Research, Elsevier, vol. 171(3), pages 1169-1181, June.
    10. Dolgui, A. & Ihnatsenka, I., 2009. "Branch and bound algorithm for a transfer line design problem: Stations with sequentially activated multi-spindle heads," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1119-1132, September.
    11. Daniel Selva & Bruce Cameron & Ed Crawley, 2016. "Patterns in System Architecture Decisions," Systems Engineering, John Wiley & Sons, vol. 19(6), pages 477-497, November.
    12. Timo Gschwind & Stefan Irnich, 2016. "Dual Inequalities for Stabilized Column Generation Revisited," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 175-194, February.
    13. Timo Gschwind & Stefan Irnich, 2014. "Dual Inequalities for Stabilized Column Generation Revisited," Working Papers 1407, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 23 Jul 2014.

    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:inm:oropre:v:17:y:1969:i:5:p:848-856. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.