The Variable Lead Time Stochastic Inventory Model with a Fuzzy Backorder Rate

Cost and operation of inventory depends a great deal on what happens to demand when the system is out of stock. In real inventory systems, it is more reasonable to assume that part of the excess demand is backordered and the rest is lost. However, the amount of backorders (or lost sales) often incurs disturbance due to various uncertainties. To incorporate this reality, this article attempts to apply the fuzzy set concepts to deal with the uncertain backorders and lost sales. The purpose of this paper is to modify Moon and Choi's continuous review inventory model with variable lead time and partial backorders by fuzzifying the backorder rate (or equivalently, fuzzifying the lost sales rate). We first consider the case where the lost sales rate is treated as the triangular fuzzy number. Then, through the statistical method for establishing the interval estimation of the lost sales rate, we construct a new fuzzy number, namely statistic-fuzzy number. For each fuzzy case, we investigate a computing schema for the modified continuous review inventory model and develop an algorithm to find the optimal inventory strategy.