A Parametric Non Linear Programming Approach to Fuzzy Decision Problem of a Queuing System with Finite Capacity

Abstract

This paper purposes, a mathematical non linear programming method to construct the membership function of a total cost in a queuing decision problem with cost co-efficient and the arrival rate being fuzzy trapezoidal numbers The basic idea is to transform a fuzzy queuing cost problem with finite capacity to a family of conventional crisp queues cost problem with finite capacity by applying the a cut approach and Zadeh's extension principle A set of parametric non linear programs are developed to calculate the lower and upper bound of the minimal expected total cost per unit time at a, through which the membership function of the total cost is constructed. A numerical example is given by specifying two queuing models with finite capacity and among the models, the total minimal cost is obtained by using the proposed method.