Dynamic lot-sizing with rework of defective items and minimum lot-size constraints

In most production processes, defective items may result from an imperfect production system and the need of reworking them is inevitable in many production environments. Despite the great importance of rework in real-world manufacturing, the body of literature is very limited. This paper deals with the effects of defective items and rework on the Capacitated Lot-Sizing Problem (CLSP). We present a mixed-integer programming formulation of the CLSP with rework of defective items and minimum lot-size constraints on production lots. The formulation describes an imperfect production process that leads to a fraction of defective items that have to be reworked before they can be sold to customers. Detailed numerical experiments show that while the occurrence of defective items significantly increases the computational times, reasonably sized minimum lot-size constraints, besides their practical importance, can be a good strategy to accelerate the solution process.