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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
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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. Daniel Selva & Bruce Cameron & Ed Crawley, 2016. "Patterns in System Architecture Decisions," Systems Engineering, John Wiley & Sons, vol. 19(6), pages 477-497, November.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Timo Gschwind & Stefan Irnich, 2016. "Dual Inequalities for Stabilized Column Generation Revisited," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 175-194, February.

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