Fuzzy Inventory Model with Backorder under Function Principle

Based on the generalized defuzzifying approach derived in this paper, we establish the fuzzy economic order quantity (EOQ) model with backorder. When the order quantity is a crisp number, we use the direct derivation method to obtain the optimal solution. When the order quantity is a fuzzy number, we use the extension of the Lagrangean method to solve the inequality constraints. The results indicate that the optimal decision-making is determinate. In addition, if all fuzzy parameters are crisp numbers or the backorder cost is extremely large, this model will degrade into the classical inventory model with backorder and the simple inventory model without backorder, respectively