No abstract

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.

This paper considers the general lot sizing and scheduling problem with rich constraints exemplified by means of rework and lifetime constraints for defective items (GLSP-RP), which finds numerous applications in industrial settings, for example, the food processing industry and the pharmaceutical industry. To address this problem, we propose the Late Acceptance Hill-climbing Matheuristic (LAHCM) as a novel solution framework that exploits and integrates the late acceptance hill climbing algorithm and exact approaches for speeding up the solution process in comparison to solving the problem by means of a general solver. The computational results show the benefits of incorporating exact approaches within the LAHCM template leading to high-quality solutions within short computational times.