Cost parametric analysis of linear programming problems with fuzzy cost coefficients based on ranking functions

Parametric analysis (PA) as a basic tool for studying perturbations in optimisation problems is applied to study the effect of the continuous variations of several parameters in the objective function coefficients on the optimum solution. To the best of our knowledge, till now there is no study in the literature to deal with the PA of the fuzzy linear programming problem in which the cost coefficients are represented by LR flat fuzzy numbers. In this paper, the parametric analysis for the same problem is investigated to determine the optimal solution and the fuzzy optimal objective values as a function of parameters when the fuzzy cost coefficients are perturbed along a new fuzzy cost vector. Then, its main advantages over the existing fuzzy sensitivity analysis problems are discussed. Finally, to show the application of fuzzy PA problem, an existing real-life fuzzy transportation problem is solved and the obtained results are explored.

cost parametric analysis, fuzzy linear programming, fuzzy numbers, ranking function