Application of Multi-Choice Fuzzy Linear Programming Problem to a Garment Manufacture Company

Abstract

In this paper, we consider a fuzzy multi-choice linear programming problem where some of the parameters and decision variables are trapezoidal type fuzzy numbers. In order to defuzzify a general fuzzy quantity the concept of nearest trapezoidal fuzzy number is introduced. By assuming all the decision variables as trapezoidal fuzzy number, the objective function and the left hand side of constraints are approximated to their nearest trapezoidal fuzzy number. Interpolating polynomials are formulated for all multi-choice type parameters. Multi-choice type parameters are replaced by polynomials with integer variables. Then an equivalent multi-objective non linear programming problem is established. First and second objective functions represent left and right modal values of the trapezoidal type fuzzy number, where as the third and fourth objective functions represent the left and right spreads of the trapezoidal type fuzzy number. By applying lexicographic method optimal solution is obtained. In addition, a case study on a garment manufacture company is presented to demonstrate the solution procedure.