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Solving the Assignment Problem by Relaxation

Author

Listed:
  • Ming S. Hung

    (Kent State University, Kent, Ohio)

  • Walter O. Rom

    (Cleveland State University, Cleveland, Ohio)

Abstract

This paper presents a new algorithm for solving the assignment problem. The algorithm is based on a scheme of relaxing the given problem into a series of simple network flow (transportation) problems for each of which an optimal solution can be easily obtained. The algorithm is thus seen to be able to take advantage of the nice properties in both the primal and the dual approaches for the assignment problem. The computational bound for the algorithm is shown to be 0( n 3 ) and the average computation time is better than most of the specialized assignment algorithms.

Suggested Citation

  • Ming S. Hung & Walter O. Rom, 1980. "Solving the Assignment Problem by Relaxation," Operations Research, INFORMS, vol. 28(4), pages 969-982, August.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:4:p:969-982
    DOI: 10.1287/opre.28.4.969
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    Cited by:

    1. P. Senthil Kumar, 2020. "Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 9(1), pages 1-34, January.
    2. 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.
    3. Arora, Shalini & Puri, M. C., 1998. "A variant of time minimizing assignment problem," European Journal of Operational Research, Elsevier, vol. 110(2), pages 314-325, October.
    4. Prabhjot Kaur & Kalpana Dahiya & Vanita Verma, 2021. "Time-cost trade-off analysis of a priority based assignment problem," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 448-482, June.
    5. Ishwar Murthy, 1993. "Solving the multiperiod assignment problem with start‐up costs using dual ascent," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(3), pages 325-344, April.
    6. Orlin, James B., 1953-. & Ahuja, Ravindra K., 1956-., 1988. "New scaling algorithms for the assignment and minimum cycle mean problems," Working papers 2019-88., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. Sonia & Puri, M.C., 2008. "Two-stage time minimizing assignment problem," Omega, Elsevier, vol. 36(5), pages 730-740, October.
    8. Gallegos, María Teresa & Ritter, Gunter, 2010. "Using combinatorial optimization in model-based trimmed clustering with cardinality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 637-654, March.

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