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Behavioral Estimation of Mathematical Programming Objective Function Coefficients

Author

Listed:
  • Marvin D. Troutt

    (Department of Management and Information Systems, Graduate School of Management, Kent State University, P.O. Box 5190, Kent, Ohio 44242-0001)

  • Wan-Kai Pang

    (Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

  • Shui-Hung Hou

    (Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

Abstract

We propose a parameter estimation method based on what we call the minimum decisional regret principle. We focus on mathematical programming models with objective functions that depend linearly on costs or other parameters. The approach is illustrated for cost estimation in production planning using linear programming models. The method uses past planning data to estimate costs that are otherwise difficult to estimate. We define a monetary measure of distance between observed plans and optimal ones, called decisional regret. The proposed estimation algorithm finds parameter values for which the associated optimal plans are as near as possible to the observed ones on average. Such techniques may be called behavioral estimation because they are based on the observed planning or decision-making behavior of managers or firms. Two numerical illustrations are given. A supporting hyperplane algorithm is used to solve the estimation model. A method is proposed for obtaining range estimates of the parameters when multiple alternative estimates exist. We also propose a new validation approach for this estimation principle, which we call the target-mode agreement criterion.

Suggested Citation

  • Marvin D. Troutt & Wan-Kai Pang & Shui-Hung Hou, 2006. "Behavioral Estimation of Mathematical Programming Objective Function Coefficients," Management Science, INFORMS, vol. 52(3), pages 422-434, March.
    • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:3:p:422-434
    DOI: 10.1287/mnsc.1050.0445
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    References listed on IDEAS

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    Cited by:

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    2. Timothy C. Y. Chan & Tim Craig & Taewoo Lee & Michael B. Sharpe, 2014. "Generalized Inverse Multiobjective Optimization with Application to Cancer Therapy," Operations Research, INFORMS, vol. 62(3), pages 680-695, June.
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    5. Rishabh Gupta & Qi Zhang, 2022. "Decomposition and Adaptive Sampling for Data-Driven Inverse Linear Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2720-2735, September.
    6. Timothy C. Y. Chan & Katharina Forster & Steven Habbous & Claire Holloway & Luciano Ieraci & Yusuf Shalaby & Nasrin Yousefi, 2022. "Inverse optimization on hierarchical networks: an application to breast cancer clinical pathways," Health Care Management Science, Springer, vol. 25(4), pages 590-622, December.
    7. Ghobadi, Kimia & Mahmoudzadeh, Houra, 2021. "Inferring linear feasible regions using inverse optimization," European Journal of Operational Research, Elsevier, vol. 290(3), pages 829-843.
    8. Troutt, Marvin D. & Brandyberry, Alan A. & Sohn, Changsoo & Tadisina, Suresh K., 2008. "Linear programming system identification: The general nonnegative parameters case," European Journal of Operational Research, Elsevier, vol. 185(1), pages 63-75, February.
    9. Timothy C. Y. Chan & Taewoo Lee & Daria Terekhov, 2019. "Inverse Optimization: Closed-Form Solutions, Geometry, and Goodness of Fit," Management Science, INFORMS, vol. 65(3), pages 1115-1135, March.

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