Fuzzy Economic Production Quantity Model for a Sustainable System via Geometric programming

Abstract

Businesses strive to be Sustainable because of internal and external pressures .To examine sustainability, firms may use different methods of analysis. This paper develops a procedure to derive the fuzzy objective value of the fuzzy  geometric programming problem when the exponents of decision variables in the objective function, the cost and the constraint coefficients, and the right-hand sides are fuzzy numbers. Geometric programming provides a powerful tool for solving a variety of engineering optimization problems.. The idea is based on Zadeh’s extension principle to transform the fuzzy geometric programming problem into a pair of two-level of mathematical programs. Based on duality algorithm and a simple algorithm, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs. The upper bound and lower bound of the objective value are obtained by solving the pair of geometric programs. Using the new representation, the conventional geometric programming algorithm is modified to take into consideration the effect of the uncertainty (the fuzzy level). This modification is achieved by making the calculations of each step of the modified algorithm in pairs..Examples are used to illustrate that the whole idea proposed in this paper.