Lot size-reorder point inventory model with fuzzy demands

This paper discusses the lot size-reorder point inventory problem with fuzzy demands. Different from the existing studies, the shortages are backordered with shortage cost incurred. The α cut of the fuzzy demand is used to construct the fuzzy total inventory cost for each inventory policy (Q, r), where Q is the quantity to be ordered and r is the reorder point. Yager's ranking method for fuzzy numbers is utilized to find the best inventory policy in terms of the fuzzy total cost. Five pairs of simultaneous nonlinear equations for the optimal Q* and r* are derived for r in five different ranges of the fuzzy demand. When the demand is a trapezoidal fuzzy number, each pair of the simultaneous equations reduces to a set of closed-form equations. They are proved to be able to produce the optimal solution. Apparently, the methodology developed in this paper can be applied to other types of inventory problems to find the best inventory policy.