Production lot sizing with quality screening and rework

Abstract

Most production systems produce items which are of imperfect quality. Handling of the defective items varies by industry and product types. For example, defective items may be sold at discount in the apparel industry, or reworked in the automobile industry where the final product is very expensive. For simplicity, a common assumption in the literature is that items are lumped into two groups, non-defective and to-be-reworked products, ignoring the inspection time needed to identify the repairable items. Our paper explicitly integrates the inspection time into the economic production model with rework, and demonstrates the significant effect that the inspection time has on the results. We consider a manufacturing process with random supply and a screening process conducted during and at the end of production. We analyze two scenarios for dealing with the defective items produced: selling at a discount, and reworking. For each scenario, the demand during production is met using non-defective items only. The expected profit functions are developed using the renewal reward theory, and closed form expressions for the optimal production lot size are derived. Numerical analysis is performed to study the sensitivity of the expected profit and optimal lot size to various system parameters.