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Sensitivity analysis of grey linear programming for optimization problems

Author

Listed:
  • Davood Darvishi
  • Farid Pourofoghi
  • Jeffrey Yi-Lin Forrest

Abstract

Sensitivity analysis of parameters is usually more important than the optimal solution when it comes to linear programming. Nevertheless, in the analysis of traditional sensitivities for a coefficient, a range of changes is found to maintain the optimal solution. These changes can be functional constraints in the coefficients, such as good values or technical coefficients, of the objective function. When real-world problems are highly inaccurate due to limited data and limited information, the method of grey systems is used to perform the needed optimisation. Several algorithms for solving grey linear programming have been developed to entertain involved inaccuracies in the model parameters; these methods are complex and require much computational time. In this paper, the sensitivity of a series of grey linear programming problems is analysed by using the definitions and operators of grey numbers. Also, uncertainties in parameters are preserved in the solutions obtained from the sensitivity analysis. To evaluate the efficiency and importance of the developed method, an applied numerical example is solved.

Suggested Citation

  • Davood Darvishi & Farid Pourofoghi & Jeffrey Yi-Lin Forrest, 2021. "Sensitivity analysis of grey linear programming for optimization problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(4), pages 35-52.
    • Handle: RePEc:wut:journl:v:31:y:2021:i:4:p:35-52:id:1651
    DOI: 10.37190/ord210402
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    References listed on IDEAS

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    1. Abhijit Baidya & Uttam Kumar Bera & Manoranjan Maiti, 2016. "The grey linear programming approach and its application to multi-objective multi-stage solid transportation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 500-522, September.
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