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A Shortest Augmenting Path Algorithm for the Semi-Assignment Problem

Author

Listed:
  • J. Kennington

    (Southern Methodist University, Dallas, Texas)

  • Z. Wang

    (Southern Methodist University, Dallas, Texas)

Abstract

The objective of this study is to develop a shortest augmenting path algorithm for solving the semi-assignment problem and conduct an extensive computational comparison with the best alternative approaches. The algorithm maintains dual feasibility and complementary slackness and works toward satisfying primal feasibility. Effective heuristics arc used to achieve an excellent advanced start, and convergence is assured via the use of the shortest augmenting path procedure using reduced costs for arc lengths. Unlike other algorithms, such as the primal simplex or the auction algorithm, each iteration during the final phase of the procedure (also known as the end-game) achieves one additional assignment. The software implementations of our algorithm are fastest for the semi-assignment problems that we tested. Our dense code is also faster than the best software for assignment problems. In addition, the algorithm has the best polynomial worst-case running time bound that we have seen; and the memory requirements are relatively small.

Suggested Citation

  • J. Kennington & Z. Wang, 1992. "A Shortest Augmenting Path Algorithm for the Semi-Assignment Problem," Operations Research, INFORMS, vol. 40(1), pages 178-187, February.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:1:p:178-187
    DOI: 10.1287/opre.40.1.178
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    Citations

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    Cited by:

    1. Andreas Kleine & Andreas Dellnitz, 2017. "Allocation of seminar applicants," Journal of Business Economics, Springer, vol. 87(7), pages 927-941, October.
    2. Andreas Dellnitz & Damian Pozo & Jochen Bauer & Andreas Kleine, 2023. "Practice Summary: Seminar Assignments in a University—MATLAB-Based Decision Support," Interfaces, INFORMS, vol. 53(4), pages 307-311, July.
    3. Ioannis T. Christou & Armand Zakarian & Jun-Min Liu & Helen Carter, 1999. "A Two-Phase Genetic Algorithm for Large-Scale Bidline-Generation Problems at Delta Air Lines," Interfaces, INFORMS, vol. 29(5), pages 51-65, October.
    4. Volgenant, A., 2004. "Solving the k-cardinality assignment problem by transformation," European Journal of Operational Research, Elsevier, vol. 157(2), pages 322-331, September.
    5. Jonker, R. & Volgenant, A., 1999. "Linear assignment procedures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 233-234, July.
    6. Pentico, David W., 2007. "Assignment problems: A golden anniversary survey," European Journal of Operational Research, Elsevier, vol. 176(2), pages 774-793, January.
    7. Yuli Zhang & Zuo-Jun Max Shen & Shiji Song, 2018. "Exact Algorithms for Distributionally β -Robust Machine Scheduling with Uncertain Processing Times," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 662-676, November.
    8. Volgenant, A., 2004. "A note on the assignment problem with seniority and job priority constraints," European Journal of Operational Research, Elsevier, vol. 154(1), pages 330-335, April.

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