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Inferring linear feasible regions using inverse optimization

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  • Ghobadi, Kimia
  • Mahmoudzadeh, Houra

Abstract

Consider a problem where a set of feasible observations are provided by an expert, and a cost function exists that characterizes which of the observations dominate the others and are hence, preferred. Assume the expert has an implicit optimization model in mind to identify the feasible observations, but the explicit constraints of this underlying model are unknown. Our goal is to infer the feasible region of such an optimization model that would render these observations feasible while making the best ones optimal for the cost (objective) function. Such feasible regions (i) build a baseline for a systematic categorization of future observations, and (ii) allow for using sensitivity analysis to discern changes in optimal solutions if the objective function changes in the future.

Suggested Citation

  • Ghobadi, Kimia & Mahmoudzadeh, Houra, 2021. "Inferring linear feasible regions using inverse optimization," European Journal of Operational Research, Elsevier, vol. 290(3), pages 829-843.
    • Handle: RePEc:eee:ejores:v:290:y:2021:i:3:p:829-843
    DOI: 10.1016/j.ejor.2020.08.048
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    References listed on IDEAS

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    1. Çiğdem Güler & Horst W. Hamacher, 2010. "Capacity inverse minimum cost flow problem," Journal of Combinatorial Optimization, Springer, vol. 19(1), pages 43-59, January.
    2. Dimitris Bertsimas & Vishal Gupta & Ioannis Ch. Paschalidis, 2012. "Inverse Optimization: A New Perspective on the Black-Litterman Model," Operations Research, INFORMS, vol. 60(6), pages 1389-1403, December.
    3. Thierry Petit & Andrew C. Trapp, 2019. "Enriching Solutions to Combinatorial Problems via Solution Engineering," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 429-444, July.
    4. Zeynep Erkin & Matthew D. Bailey & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2010. "Eliciting Patients' Revealed Preferences: An Inverse Markov Decision Process Approach," Decision Analysis, INFORMS, vol. 7(4), pages 358-365, December.
    5. Chan, Timothy C.Y. & Kaw, Neal, 2020. "Inverse optimization for the recovery of constraint parameters," European Journal of Operational Research, Elsevier, vol. 282(2), pages 415-427.
    6. 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.
    7. 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.
    8. Ravindra K. Ahuja & James B. Orlin, 2001. "Inverse Optimization," Operations Research, INFORMS, vol. 49(5), pages 771-783, October.
    9. Stephan Dempe & Sebastian Lohse, 2006. "Inverse Linear Programming," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 19-28, Springer.
    10. 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.
    11. 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.
    12. Chow, Joseph Y.J. & Recker, Will W., 2012. "Inverse optimization with endogenous arrival time constraints to calibrate the household activity pattern problem," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 463-479.
    13. John R. Birge & Ali Hortaçsu & J. Michael Pavlin, 2017. "Inverse Optimization for the Recovery of Market Structure from Market Outcomes: An Application to the MISO Electricity Market," Operations Research, INFORMS, vol. 65(4), pages 837-855, August.
    14. Turgay Ayer, 2015. "Inverse optimization for assessing emerging technologies in breast cancer screening," Annals of Operations Research, Springer, vol. 230(1), pages 57-85, July.
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