Optimization of fuzzy inventory models under k-preference

[[abstract]]Inventory is any stored resource that is used to satisfy a current or a future need. In this paper, two fuzzy inventory models with fuzzy parameters for crisp order quantity, or for fuzzy order quantity under decision maker’s preference are introduced. We propose the fuzzy total annual inventory costs based on the fuzzy arithmetical operations under Function Principle. The final purpose is to find the optimal order quantities of our proposed models under the preference of manager by using Graded k-preference Integration Representation method for defuzzifing the fuzzy total annual inventory cost, and by using Extension of the Lagrangean method for solving inequality constrain problem. Furthermore, we find the optimal order quantity or the optimal fuzzy order quantity of our proposed models are the real numbers. In addition, when the k = 0.5 and all fuzzy parameters are the crisp real numbers, our optimal solutions can be specified to meet classical production inventory models