Optimization-based job shop scheduling with transfer lots

Effective scheduling of lots is critical for the production of mid to high volume products. Compared to traditional lot production, using transfer lots can significantly reduce manufacturing lead times and lower work-in-process (WIP) inventory levels. This paper presents a novel integer programming formulation with separable structure and an optimization-based solution methodology for job shop scheduling with transfer lots. Through explicit modeling of lot dynamics, transfer lots can be handled on machines with setups. The solution methodology is based on Lagrangian relaxation (LR), backward dynamic programming (BDP), and heuristics. The algorithm has been implemented using object-oriented programming language C++, and numerical testing results show that schedules with transfer lots are generated by this algorithm to achieve on-time delivery of products and low WIP inventory.