Optimization of Fuzzy Inventory Models under Fuzzy Demand and Fuzzy Lead Time

Abstract

Inventory model under risk that demand is uncertain is recognized. In this paper, the fuzzy demand per day and fuzzy lead time on a cycle in fuzzy inventory control system are assumed to trapezoidal distribution, trapezoidal fuzzy number by decision maker. A fuzzy inventory model under manager’s preference for order quantity is presented first. This model is given by fuzzy total annual inventory cost summating of total annual holding cost and fuzzy total annual setup cost. We obtain the optimal order quantity by using both Function Principle and Graded Mean Integration Representation method for both computing and representing fuzzy total annual inventory cost. The number of orders in a year, then, is getting by the above optimal order quantity. In addition, we get the reorder point and safety stock under a unit service level by manager. Furthermore, we also introduce a fuzzy inventory model under safety stock based on fuzzy total annual safety stock cost combined by total annual holding cost of safety stock and fuzzy total annual stockout cost. Fuzzy average demand in lead time, mean, thus is calculated by using Graded Mean Integration Representation method. Moreover, we find the optimal reorder point and the optimal safety stock of our second proposed model.