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An Algorithm for Large Set Partitioning Problems

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  • Roy E. Marsten

    (Northwestern University)

Abstract

An algorithm is presented for the special integer linear program known as the set partitioning problem. This problem has a binary coefficient matrix, binary variables, and unit resources. Furthermore, all of its constraints are equations. In spite of its very special form, the set partitioning problem has many practical interpretations. The algorithm is of the branch and bound type. A special class of finite mappings is enumerated rather than the customary set of binary solution vectors. Linear programming is used to obtain bounds on the minimal costs of the subproblems that arise. Computational results are reported for several large problems.

Suggested Citation

  • Roy E. Marsten, 1974. "An Algorithm for Large Set Partitioning Problems," Management Science, INFORMS, vol. 20(5), pages 774-787, January.
    • Handle: RePEc:inm:ormnsc:v:20:y:1974:i:5:p:774-787
    DOI: 10.1287/mnsc.20.5.774
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    Cited by:

    1. 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.
    2. Sun, Wei & Yu, Yang & Wang, Junwei, 2019. "Heterogeneous vehicle pickup and delivery problems: Formulation and exact solution," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 125(C), pages 181-202.
    3. Hanif D. Sherali & Youngho Lee & Donald D. Boyer, 1995. "Scheduling target illuminators in naval battle‐group anti‐air warfare," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(5), pages 737-755, August.
    4. E. Rod Butchers & Paul R. Day & Andrew P. Goldie & Stephen Miller & Jeff A. Meyer & David M. Ryan & Amanda C. Scott & Chris A. Wallace, 2001. "Optimized Crew Scheduling at Air New Zealand," Interfaces, INFORMS, vol. 31(1), pages 30-56, February.
    5. Mohamed Haouari & Farah Zeghal Mansour & Hanif D. Sherali, 2019. "A New Compact Formulation for the Daily Crew Pairing Problem," Transportation Science, INFORMS, vol. 53(3), pages 811-828, May.
    6. Yuceer, Umit, 1997. "A multi-product loading problem: a model and solution method," European Journal of Operational Research, Elsevier, vol. 101(3), pages 519-531, September.

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