Multiobjective Transportation Model with Fuzzy Parameters: Priority based Fuzzy Goal Programming Approach

This paper presents a priority based fuzzy goal programming approach for solving a multiobjective transportation problem with fuzzy coefficients. In the model formulation of the problem, first the membership functions for the fuzzy goals are defined. Subsequently, the membership functions are transformed into membership goals, by assigning the highest degree (unity) of a membership function as the aspiration level and introducing deviational variables to each of them. In the solution process, negative deviational variables are minimized to obtain the most satisficing solution. Sensitivity analysis of the solution, with a change in priorities of the fuzzy goals is performed. Next the Euclidean distance function is used to identify the appropriate priority structure of the goals, thereby obtaining the most satisficing decision for the decision-making unit, by minimizing their regrets of achieving the ideal point dependent decision in the decision-making context. A numerical example is solved to demonstrate the potential use of the proposed approach.