The paper is concerned with the two-machine scheduling problem where each job is to be processed on the first-stage machine and after that on the second-stage machine. In order to be processed, each job requires storage space that it seizes at the start of its processing on the first-stage machine and releases only at the completion of processing on the second-stage machine. The storage space is limited and its consumption varies from job to job. The goal is to minimise the time needed for the completion of all jobs. All instances of the considered scheduling problem are classified by means of five parameters. This leads to the sixty four families of instances. For each family, the paper establishes its computational complexity and, in the case of polynomial-time solvability, presents a polynomial-time algorithm, constructing an optimal schedule.

本文涉及两机调度问题，其中每个作业都将在第一阶段的机器上处理，然后在第二阶段的机器上处理。为了进行处理，每个作业都需要一个存储空间，该存储空间在开始在第一阶段计算机上进行处理时会占用，并仅在第二阶段计算机上的处理完成后才释放。存储空间有限，其消耗因工作而异。目标是最大程度地减少完成所有工作所需的时间。所考虑的调度问题的所有实例均通过五个参数进行分类。这导致了64个实例族。对于每个家庭，本文确定了其计算复杂性，并且在多项式时间可解性的情况下，提出了一种多项式时间算法，构造了一个最佳计划。