Rescheduling can help to improve the quality of a schedule with respect to an initially given sequence. In this paper, we consider the possibility of rescheduling jobs arriving for processing at a single machine under the following limitations: (a) jobs can only be moved toward the end of the schedule and not toward the front, and (b) when a job is taken out of the sequence, it is put on a buffer of limited capacity before being reinserted in its new position closer to the end of the sequence. The buffer is organized as a stack with a last-in/first-out policy. As an objective function, we consider the minimization of the weighted number of late jobs. For this NP-hard problem, we first provide two different integer linear programming (ILP) formulations. Furthermore, we develop a branch-and-bound algorithm with a branching rule based on the movement of jobs. Then a new pseudo-polynomial dynamic programming algorithm is presented which utilizes dominance criteria and an efficient handling of states. Our computational experiments with up to 100 jobs show that this algorithm performs remarkably well and can be seen as the current method of choice.

重新安排可以帮助提高相对于最初给定序列的安排的质量。在本文中，我们考虑了在以下限制下重新安排到达单台机器处理的作业的可能性：(a) 作业只能移动到调度的末尾，而不能移动到前面，以及 (b) 当一个作业从序列中取出，它被放在一个容量有限的缓冲区上，然后重新插入到靠近序列末尾的新位置。缓冲区被组织为具有后进/先出策略的堆栈。作为一个目标函数，我们考虑最小化后期工作的加权数量。对于这个 NP-hard 问题，我们首先提供两种不同的整数线性规划 (ILP) 公式。此外，我们开发了一种分支定界算法，该算法具有基于作业移动的分支规则。然后提出了一种新的伪多项式动态规划算法，该算法利用优势准则和有效的状态处理。我们对多达 100 个作业的计算实验表明，该算法的性能非常好，可以看作是当前的首选方法。