Resource-constrained parallel machine scheduling with setups, job release/due time, and resource transition limit
研究了考虑设置时间、资源限制等实际约束的并行机调度问题，提出了混合整数线性规划模型和偏随机密钥遗传算法，在食品加工案例和基准数据集上验证了算法的可扩展性和优越性。
The unrelated parallel machines scheduling problem with setup times and additional resources (UPMSR) is common in the manufacturing and service sectors, requiring the optimal assignment of jobs to machines supervised by limited additional resources. This paper investigates how to efficiently solve the UPMSR considering manufacturing constraints such as job release times, due dates, machine eligibility, and resource transition limits per machine. Previous research has not addressed this combination of real-world industrial constraints, leaving limitations on practical and scalable scheduling algorithms for the UPMSR. To address this gap, we develop a mixed integer linear programming (MILP) model and introduce a novel biased random key genetic algorithm (BRKGA) approach. We demonstrate the scalability of BRKGA compared to the MILP model on synthetic datasets based on a real-world case study of a food processing plant. Furthermore, we demonstrate that BRKGA either outperforms or matches state-of-the-art metaheuristic and exact methods on benchmark datasets from the literature. This research provides a broadly adaptable, scalable, and license-free scheduling software tool, enabling practitioners and researchers to tackle similar resource-constrained parallel machine scheduling problems effectively.