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Sensitivity analysis for bottleneck assignment problems

Author

Listed:
  • Michael, Elad
  • Wood, Tony A.
  • Manzie, Chris
  • Shames, Iman

Abstract

In assignment problems, decision makers are often interested in not only the optimal assignment, but also the sensitivity of the optimal assignment to perturbations in the assignment weights. Typically, only perturbations to individual assignment weights are considered. We present a novel extension of the traditional sensitivity analysis by allowing for simultaneous variations in all assignment weights. Focusing on the bottleneck assignment problem, we provide two different methods of quantifying the sensitivity of the optimal assignment, and present algorithms for each. Numerical examples as well as a discussion of the complexity for all algorithms are provided.

Suggested Citation

  • Michael, Elad & Wood, Tony A. & Manzie, Chris & Shames, Iman, 2022. "Sensitivity analysis for bottleneck assignment problems," European Journal of Operational Research, Elsevier, vol. 303(1), pages 159-167.
    • Handle: RePEc:eee:ejores:v:303:y:2022:i:1:p:159-167
    DOI: 10.1016/j.ejor.2022.02.037
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    References listed on IDEAS

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    1. Chi-Jen Lin & Ue-Pyng Wen, 2007. "Sensitivity Analysis Of Objective Function Coefficients Of The Assignment Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 203-221.
    2. Jansen, B. & de Jong, J. J. & Roos, C. & Terlaky, T., 1997. "Sensitivity analysis in linear programming: just be careful!," European Journal of Operational Research, Elsevier, vol. 101(1), pages 15-28, August.
    3. Carraresi, P. & Gallo, G., 1984. "A multi-level bottleneck assignment approach to the bus drivers' rostering problem," European Journal of Operational Research, Elsevier, vol. 16(2), pages 163-173, May.
    4. Yelin Fu & Jianshan Sun & K. Lai & John Leung, 2015. "A robust optimization solution to bottleneck generalized assignment problem under uncertainty," Annals of Operations Research, Springer, vol. 233(1), pages 123-133, October.
    5. Koltai, Tamas & Terlaky, Tamas, 2000. "The difference between the managerial and mathematical interpretation of sensitivity analysis results in linear programming," International Journal of Production Economics, Elsevier, vol. 65(3), pages 257-274, May.
    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. 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.
    8. Joseph Adams & Egon Balas & Daniel Zawack, 1988. "The Shifting Bottleneck Procedure for Job Shop Scheduling," Management Science, INFORMS, vol. 34(3), pages 391-401, March.
    9. 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.
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