Optimal batch quantity models for a lean production system with rework and scrap

In an imperfect manufacturing process, the defective items are produced with finished goods. Rework process is necessary to convert those defectives into finished goods. As the system is not perfect, some scrap is produced during this process of rework. In this research, inventory models for a single-stage production process are developed where defective items are produced and reworked, where scrap is produced, detected and discarded during the rework. Two policies of rework processes are considered (a) First policy: rework is done within the cycle, and (b) Second policy: rework is done after N cycles of normal production. Also, three types of scrap production and detection methods are considered for each policy, such as (i) scrap is detected before rework, (ii) scrap is detected during rework and (iii) scrap is detected after rework. Based on these inventory situations, the total cost functions for a single-stage imperfect manufacturing system are developed to find the optimum operational policy. Some numerical examples are provided to validate the model and a sensitivity analysis is carried out with respect to different parameters used to develop the model.