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A Primal Method for the Assignment and Transportation Problems

Author

Listed:
  • M. L. Balinski

    (University of Pennsylvania)

  • R. E. Gomory

    (Thomas J. Watson Research Center, IBM Corporation)

Abstract

This paper describes a simple calculation for the assignment and transportation problems which is "dual to" the well-known Hungarian Method. While the Hungarian is a dual method, this method is primal and so gives a feasible assignment at each stage of the calculation. Bounds on the number of steps required for the assignment and transportation problems are given. They are the same as the best bounds known for the Hungarian Method.

Suggested Citation

  • M. L. Balinski & R. E. Gomory, 1964. "A Primal Method for the Assignment and Transportation Problems," Management Science, INFORMS, vol. 10(3), pages 578-593, April.
    • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:3:p:578-593
    DOI: 10.1287/mnsc.10.3.578
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    Cited by:

    1. Behdad Beheshti & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2016. "Exact solution approaches for bilevel assignment problems," Computational Optimization and Applications, Springer, vol. 64(1), pages 215-242, May.
    2. Volgenant, A., 2006. "An addendum on sensitivity analysis of the optimal assignment," European Journal of Operational Research, Elsevier, vol. 169(1), pages 338-339, February.
    3. Chang, Gerard J. & Ho, Pei-Hsin, 1998. "The [beta]-assignment problems," European Journal of Operational Research, Elsevier, vol. 104(3), pages 593-600, February.
    4. Michael Z. Spivey & Warren B. Powell, 2004. "The Dynamic Assignment Problem," Transportation Science, INFORMS, vol. 38(4), pages 399-419, November.
    5. Lin, Chi-Jen & Wen, Ue-Pyng, 2003. "Sensitivity analysis of the optimal assignment," European Journal of Operational Research, Elsevier, vol. 149(1), pages 35-46, August.
    6. Cano-Berlanga, Sebastián & Giménez-Gómez, José-Manuel & Vilella, Cori, 2017. "Enjoying cooperative games: The R package GameTheory," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 381-393.
    7. Ivan Belik & Kurt Jornsten, 2018. "Critical objective function values in linear sum assignment problems," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 842-852, April.

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