Economic Order Quantity with Stochastic Demand, Imperfect Quality, and Inspection Errors

Abstract

In this paper, EOQ models with stochastic demand for items with imperfect quality are developed for two cases; with and without replacement of nonconforming items, considering 100% inspection policy with the assumption that an imperfect inspection is performed. An order is considered to be placed from a supplier when the inventory level reaches the reorder point. When the order is received, an inspector will inspect the whole lot with the consideration that Type I or Type II inspection errors could be committed by the inspector during the inspection process. The probability of misclassification errors is assumed to be known. The fraction nonconforming is assumed to be a random variable following a known distribution. The objective of this research is to determine the optimal order quantity and reorder point such that the total cost is minimized. A solution for determining the order quantity and reorder point is proposed. Numerical examples with some sensitivity analysis for important model parameters are provided for the proposed model. Possible future extensions to the presented model are presented in the conclusion.