Abstract:Traditionally, most of the publications assume that the annual demand is deterministic. However, there are many uncertain factors in real world. So we use the signed distance, a ranking method for fuzzy numbers to estimate the annual demand. This paper investigates the impact of safety factor on the fuzzy annual demand inventory model with mixture of backorder discount and partial lost sales. The goal of this study is to minimize the expected total annual cost with respect to order quantity, backorder price discount and safety factor. Numerical example is included to illustrate the solution procedure of the proposed algorithm.