An instantaneous replenishment model under the effect of a sampling policy for defective items

We propose to study a EOQ-type inventory model with unreliable supply, with each order containing a random proportion of defective items. Every time an order is received, an acceptance sampling plan is applied to the lot, according to which only a sample is inspected instead of the whole lot. If the sample conforms to the standards, i.e. if the number of imperfect items is below an “acceptance number”, no further screening is performed. Otherwise, the lot is subject to 100% screening. We formulate an integer non-linear mathematical program that integrates inventory and quality decisions into a unified profit model, to jointly determine the optimal lot size and optimal sampling plan, characterized by a sample size, and an acceptance number. The optimal decisions are determined in a way to achieve a certain average outgoing quality limit (AOQL), which is the highest proportion of defective items in the outgoing material sold to customers. We provide a counter-example demonstrating that the expected profit function, objective of the mathematical program, is not jointly concave in the lot and sample size. However, we show that for a given sampling plan, the expected profit function is concave in the lot size. A solution procedure is presented to compute the optimal solution. Numerical analysis is provided to gain managerial insights by analyzing the impact of changing various model parameters on the optimal solution. We also show numerically that the optimal profit determined using this model is significantly higher when compared to the optimal profit obtained using Salameh and Jaber (2000)’s 1] model, indicating much higher profits when acceptance sampling is used.