Lot sizing with rework and different inspection costs

This paper deals with the single machine multi-product lot scheduling problem in which defective items are produced in any production run of each product. we have adopted the common cycle scheduling policyand assumed that the setup times for production of each product can be non-zero. further, we have assumed that defective items will be reworked and the inspection costs during the normal production and rework processing times are different. for this system we obtained the optimal batch sizes for each product such that the total cost per unit time is minimized.