This study addresses a two-machine job-shop scheduling problem with fixed lower and upper bounds on the job processing times. An exact value of the job duration remains unknown until completing the job. The objective is to minimize a schedule length (makespan). It is investigated how to best execute a schedule, if the job processing time may be equal to any real number from the given (closed) interval. Scheduling decisions consist of the off-line phase and the on-line phase of scheduling. Using the fixed lower and upper bounds on the job processing times available at the off-line phase, a scheduler may determine a minimal dominant set of schedules (minimal DS), which is based on the proven sufficient conditions for a schedule dominance. The DS optimally covers all possible realizations of the uncertain (interval) processing times, i.e., for each feasible scenario, there exists at least one optimal schedule in the minimal DS. The DS enables a scheduler to make the on-line scheduling decision, if a local information on completing some jobs becomes known. The stability approach enables a scheduler to choose optimal schedules for most feasible scenarios. The on-line scheduling algorithms have been developed with the asymptotic complexity $O\left(n^2\right)$ for n given jobs. The computational experiment shows the effectiveness of these algorithms.

中文翻译：

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计划执行两台机器的车间，以在不确定的处理时间下最大程度地缩短工期

这项研究解决了两台机器的车间调度问题，在工作处理时间上上下限固定。在完成作业之前，作业持续时间的确切值仍然未知。目的是最大程度地减少计划时间（makespan）。如果作业处理时间可能等于给定（封闭）时间间隔内的任何实数，则会研究如何最好地执行计划。计划决策包括计划的离线阶段和在线阶段。使用离线阶段可用的工作处理时间的固定上限和下限，调度程序可以基于已证明的足够的时间表优势条件，确定最小的主要调度集（最小DS）。DS最佳地涵盖了不确定（间隔）处理时间的所有可能实现，即 对于每种可行方案，最小DS中至少存在一个最佳计划。如果已知有关完成某些作业的本地信息，则DS使调度程序可以做出在线调度决策。稳定性方法使调度程序可以为大多数可行方案选择最佳调度。具有渐近复杂度的在线调度算法$Ø（{ñ}^2）$对于ñ获得就业机会。计算实验表明了这些算法的有效性。