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Sensitivity Analysis Of Objective Function Coefficients Of The Assignment Problem

Author

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  • CHI-JEN LIN

    (Department of Industrial Engineering and Management, Ta Hwa Institute of Technology, Hsinchu, Taiwan, R.O.C.)

  • UE-PYNG WEN

    (Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan, R.O.C.)

Abstract

Information of sensitivity analysis, in a linear programming problem, is usually more important than the optimal solution itself. However, traditional sensitivity analysis, which perturbs exactly one coefficient and then determines the range preserving the optimality of the current optimal base, is impractical for the assignment problem. An optimal basic solution of the assignment problem is inherently degenerate, so it may be that the optimal base has changed but the optimal assignment remains unchanged. Furthermore, elements of a column (or row) in a cost matrix of assignment problem are usually closely related and change simultaneously, not uniquely. This paper focuses on two kinds of sensitivity analyses for the assignment problem. One is to determine the sensitivity range, over which the current optimal assignment or all the optimal assignments remain optimal, while perturbing the elements of one column (or row) in a cost matrix of the assignment problem simultaneously but dependently. The other is to perturb elements of one column (or row) in a cost matrix of the assignment problem simultaneously but independently. Numerical illustrations are presented to demonstrate that the approaches are useful in practice.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:apjorx:v:24:y:2007:i:02:n:s0217595907001115
    DOI: 10.1142/S0217595907001115
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    Cited by:

    1. 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.
    2. Ma, Kang-Ting & Lin, Chi-Jen & Wen, Ue-Pyng, 2013. "Type II sensitivity analysis of cost coefficients in the degenerate transportation problem," European Journal of Operational Research, Elsevier, vol. 227(2), pages 293-300.

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