We examine a parallel machine scheduling problem with a job splitting property, sequence-dependent setup times, and limited setup operators, for minimizing makespan. Jobs are split into arbitrary (job) sections that can be processed on different machines simultaneously. When a job starts to be processed on a machine, a setup that requires an operator is performed, and the setup time is sequence-dependent. The number of setup operators is limited, and hence not all of the machines can be set up at the same time. For this problem, we propose a mathematical programming model and analyze a lower bound. We then develop a simple but efficient heuristic algorithm so that it can be used in practice, and analytically derive a worst-case bound of the algorithm. We finally evaluate the performance of the proposed algorithm numerically with various scenarios.

我们检查了一个并行的机器调度问题，该问题具有作业拆分属性，与序列有关的设置时间和有限的设置运算符，以最大程度地缩短制造时间。作业被分为任意（作业）部分，这些部分可以在不同的计算机上同时处理。当开始在机器上处理作业时，将执行需要操作员的设置，并且设置时间取决于序列。设置操作员的数量是有限的，因此并非所有机器都可以同时设置。针对此问题，我们提出了数学编程模型并分析了下界。然后，我们开发一种简单但有效的启发式算法，以便可以在实践中使用它，并通过分析得出该算法的最坏情况范围。我们最终在各种情况下以数字方式评估了该算法的性能。