AI 中文总结
针对带时变峰值功率约束的作业车间调度问题，本文开发首个精确SAT与CP模型，在35个基准实例上验证全局最优性，大幅优于此前方法，还修正了基准结果并建立可靠参考。
AI 中文摘要
带功率需求的作业车间调度问题（JSPPR）在经典作业车间调度问题的基础上，对瞬时功耗施加时变限制。此前研究采用混合整数线性规划（MILP）模型及GRASP x ELS元启发式算法，但尚未有基于SAT的精确方法或约束规划（CP）模型的相关报道。本文开发了首个针对JSPPR的精确SAT与约束规划（CP）模型。在35个已公开的基准实例上，SAT与CP均证明所有实例的全局最优性，且得到的最优完工时间（makespan）完全一致，大幅优于此前报道的最佳结果；二者还较原始研究中GRASP x ELS的结果得到4个改进的完工时间值。CP证明最优性的速度快于SAT，同时两种精确方法均显著提升了MILP模型的最优性覆盖率——MILP模型使用CPLEX和Gurobi分别仅在6个和10个实例上证明了最优性。这些经认证的最优解还揭示了若干此前已报道基准结果中的不一致性，包括完工时间低于已证明的最优值的情况。本文提供了修正后的最优完工时间及JSPPR基准的完整经认证最优结果集，为未来研究建立了可靠参考。
英文摘要
The Job Shop Scheduling Problem with Power Requirements (JSPPR) extends the classical job shop scheduling problem by imposing time-varying limits on instantaneous power consumption. Previous studies have used a mixed-integer linear programming formulation and the GRASP x ELS metaheuristic, but no SAT-based exact approach or constraint programming model has been reported. This paper develops the first exact SAT and constraint programming (CP) formulations for the JSPPR. On the 35 published benchmark instances, both SAT and CP prove global optimality for all instances and obtain identical optimal makespans, substantially improving upon the best previously reported results. They also establish four improved makespan values over the GRASP x ELS results reported in the original study. CP proves optimality faster than SAT, while both exact approaches substantially improve the optimality coverage of the MILP formulations, which prove optimality on only 6 and 10 instances using CPLEX and Gurobi, respectively. The certified optimal solutions also reveal inconsistencies in several previously reported benchmark results, including makespans below the proven optimum. We provide corrected optimal makespans and a complete set of certified optimal results for the JSPPR benchmark, establishing a reliable reference for future studies.
