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 consider that only a portion of the excess demand can be 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 sets concept to deal with the uncertain backorders and lost sales. The purpose of this paper is to modify the 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 a case where the lost sales rate is treated as a triangular fuzzy number. Then, we utilize the statistical method to construct a confidence interval for the lost sales rate, and through it to establish the corresponding fuzzy number called the 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.