This paper examines scheduling problem denoted as $P|seq, ser|C_{max}$ in Graham's notation; in other words, scheduling of tasks on parallel identical machines ($P$) with sequence-dependent setups ($seq$) each performed by one of the available servers ($ser$). The goal is to minimize the makespan ($C_{max}$). We propose a Constraint Programming (CP) model for finding the optimal solution and constructive heuristics suitable for large problem instances. These heuristics are also used to provide a feasible starting solution to the proposed CP model, significantly improving its efficiency. This combined approach constructs solutions for benchmark instances of up to 20 machines and 500 tasks in 10 seconds, with makespans 3-11.5% greater than the calculated lower bounds with a 5% average. The extensive experimental comparison also shows that our proposed approaches outperform the existing ones.

翻译：本文研究了Graham符号中表示为 $P|seq, ser|C_{max}$ 的调度问题；即在并行同构机器（$P$）上调度任务，其中任务具有序列相关设置时间（$seq$），每次设置由可用的服务器之一执行（$ser$）。目标是最小化最大完工时间（$C_{max}$）。我们提出一个约束规划（CP）模型用于求解最优解，并针对大规模问题实例设计了构造启发式算法。这些启发式算法也为所提出的CP模型提供了可行的初始解，显著提升了模型效率。该组合方法可在10秒内为包含多达20台机器和500个任务的基准实例构建解，其最大完工时间比计算所得下界高出3-11.5%，平均偏差为5%。广泛的实验比较表明，我们提出的方法优于现有方法。