An application of fuzzy sets theory to the EOQ model with imperfect quality items

This article investigates the inventory problem for items received with imperfect quality, where, upon the arrival of order lot, 100% screening process is performed and the items of imperfect quality are sold as a single batch at a discounted price, prior to receiving the next shipment. The objective is to determine the optimal order lot size to maximize the total profit. We first propose a model with fuzzy defective rate. Then, the model with fuzzy defective rate and fuzzy annual demand is presented. For each case, we employ the signed distance, a ranking method for fuzzy numbers, to find the estimate of total profit per unit time in the fuzzy sense, and then derive the corresponding optimal lot size. Numerical examples are provided to illustrate the results of proposed models.