An optimal batch size for an imperfect production system with quality assurance and rework

We consider a manufacturing system which receives raw material from a supplier, processes it, and delivers it to the customer periodically. The system considered is imperfect and produces defectives at a constant rate. The finished product can only be delivered if the whole lot is quality-certified. Hence, defectives have to be reworked, and the whole lot quality-checked within the cycle. Three different scenarios are considered, viz. (a) a single lot of raw material for multiple lot of finished product and delivery of the product in multiple instalments, (b) a single lot of raw material for a multiple lot of finished product and delivery of the product in a single instalment, and (c) lot-for-lot and delivery of finished product in single instalment. A total cost equation is developed for each model, and the optimal ordering quantities are evaluated. The results found are encouraging and quite simple to use for practical purposes.