Issue: 2021/Vol.31/No.4, Pages 35-52
SENSITIVITY ANALYSIS OF GREY LINEAR PROGRAMMING FOR OPTIMIZATION PROBLEMS
Davood Darvishi
, Farid Pourofoghi, Jeffrey Yi-Lin Forrest
Cite as: D. Darvishi, F. Pourofoghi, J. Y. Forrest. Sensitivity analysis of grey linear programming for optimization problems. Operations Research and Decisions 2021: 31(4), 35-52. DOI 10.37190/ord210402
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.
Keywords: sensitivity analysis, uncertainty, interval grey number, grey linear programming.
Received: 5 October 2021 Accepted: 20 December 2021