We consider two versions of two-machine flow shop scheduling problems, where each job requires an additional resource from the start of its first operation till the end of its second operation. We refer to this resource as storage space. The storage requirement of each job is determined by the processing time of its first operation. The two problems differ from each other in the way resources are allocated for each job. In the first case, the job captures all the necessary units of storage space at the beginning of processing its first operation. In the second case, the job takes up storage space gradually as its first operation is performed. In both problems, the goal is to minimize the makespan. In our paper, we establish the exact borderline between the NP-hard and polynomial-time solvable instances of the problems with respect to the ratio between the storage size and the maximum operation length.

我们考虑双机流水车间调度问题的两个版本，其中每个作业从第一个操作开始到第二个操作结束都需要额外的资源。我们将此资源称为存储空间。每个作业的存储要求由其第一个操作的处理时间决定。这两个问题的不同之处在于为每个作业分配资源的方式。在第一种情况下，作业在处理第一个操作开始时捕获所有必要的存储空间单元。在第二种情况下，作业在执行第一个操作时逐渐占用存储空间。在这两个问题中，目标都是最小化完工时间。在我们的论文中，我们根据存储大小和最大操作长度之间的比率，在问题的 NP 困难实例和多项式时间可解实例之间建立了精确的边界。