Economic Production Quantity in Reworkable Production Systems with Inspection Errors, Scraps and Backlogging

The classical economic production quantity (EPQ) model is a well-known and commonly used inventory control technique. Common assumptions in this model are that all units produced are of perfect quality and shortage is not allowed, since in practice shortage, non-conforming product or scrap items are possible, these assumptions will underestimate the actual required quantity. The objective of this paper is to provide a framework to integrate production of imperfect quality items, inspection errors, rework, scrap items and backlogging into a single EPQ model. To achieve this objective a suitable mathematical model is developed and the optimal production lot size which minimizes the total cost is derived. The sensitivity analysis results indicate the model is very sensitive to shortage cost per unit shortage and type-I error of inspection. While findings of this study show that the model is very sensitive to parameters type-I error of inspection, proportion of defectives in production process and shortage cost per unit short, it is much less sensitive to parameters like proportion of scraps in rework process and Type-II error of inspection. If the existence of such error and shortages are ignored, then the obtained results may differ considerably from the optimal outcome. This will impose additional costs to the system.