A Constraint Programming Model For Serial Batch Scheduling With Minimum Batch Size

Abstract: In serial batch (s-batch) scheduling, jobs are grouped in batches and processed sequentially within their batch. This paper considers multiple parallel machines, nonidentical job weights and release times, and sequence-dependent setup times between batches of different families. Although s-batch has been widely studied in the literature, very few papers have taken into account a minimum batch size, typical in practical settings such as semiconductor manufacturing and the metal industry. The problem with this minimum batch size requirement has been mostly tackled with dynamic programming and meta-heuristics, and no article has ever used constraint programming (CP) to do so. This paper fills this gap by proposing, for the first time, a CP model for s-batching with minimum batch size. The computational experiments on standard cases compare the CP model with two existing mixed-integer programming (MIP) models from the literature. The results demonstrate the versatility of the proposed CP model to handle multiple variations of s-batching; and its ability to produce, in large instances, better solutions than the MIP models faster.