Lot sizing in a production system with rework and product deterioration

Producing new and recovering defective products often takes place on a common facility, with these activities carried out in lots. Consequently, there is a necessity to coordinate the production and rework activities with respect to the timing of operations and also regarding appropriate lot sizes for both processes while completely satisfying given demand. Thereby, it has to be taken into account whether the state of the defective items may change in the course of time while they wait to be reworked. Such a deterioration of reworkable goods can result in increasing rework time and rework cost per unit. In this paper an EPQ model which addresses all of these aspects is presented. Considering set-up and inventory holding costs as well as set-up times, optimization algorithms are developed covering different planning situations. Closed-form results for optimal lot sizes can be obtained and exploited for new analytical insights into coordinated lot sizing in the case of returns and product deterioration.