An EPQ model for imperfect production systems with rework and incorporating a multi-delivery policy

In manufacturing firms, the EPQ model is commonly used for determining the optimal replenishment batch size that minimizes total production-inventory costs for items produced. The classical EPQ model assumes that all items manufactured are of perfect quality. However, real-life production systems, due to various controllable and/or uncontrollable factors, the generation of defective items during a production run seems to be inevitable and they should be reworked or repaired with additional cost. A portion of non-conforming items produced is considered to be scrap, while the rest are assumed to be repairable and are reworked in each cycle when regular production ends. Finished items can only be delivered to customers if the whole lot is quality assured after rework. This paper incorporates a multi-delivery policy into an imperfect EPQ model with scrap and rework and finished items can only be delivered to customers at a fixed interval of time during production down time with the purpose of reducing holding cost. The objective is to derive the optimal production lot size and number of deliveries such that the finished items are delivered by request to customers at a fixed interval of time that minimizes total costs. The relevant model is built, solved and necessary and sufficient conditions for a unique and global optimal solution are derived. An illustrative example is provided and numerically verified. The validation of results in this model was coded in Microsoft™ Visual Basic 6.0.