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Inventory is a common name stands for the items which are in stock points or work-in-process serving to decouple successive operations. Effective inventory management is essential for manufacturing organizations for a number of reasons. A basic economic order quantity model allowing backorders is considered in this paper. All cost parameters and the demand is assumed to be fuzzy numbers with trapezoidal membership function. By the graded mean integration representation method of defuzzification, total cost formula will be derived in the fuzzy sense in order to obtain the optimal order quantity. A numerical example is provided to illustrate the results of the proposed model.