We revisit the problem of scheduling or assigning jobs non-preemptively so as to minimize the total completion time on $m$ identical machines and on $m$ uniformly related machines. This problem is polynomially solvable if all jobs are presented at once, even for unrelated machines. An online algorithm receives jobs one by one, such that every job is scheduled before the next job is presented. A robust algorithm with migration factor $\gamma >0$ also receives jobs one at a time to be assigned immediately, but when a job of size $p$ arrives, the algorithm can re-assign a subset of jobs of total size $\gamma \cdot p$. That is, it can remove the jobs of one such subset from their positions and schedule them again in an arbitrary way. The goal is to obtain optimal or almost optimal solutions. We use the term schedule for a solution where every job is scheduled to a time slot on a machine, and the term assignment is used for a solution where a job is assigned to a machine and an optimal ordering of jobs (by SPT) is always used for every machine. We show that a nearly optimal schedule cannot be obtained for $m\ge 1$ machines for any constant migration factor. For the variant of creating assignments, for one machine already the online problem is trivial, and we prove that an optimal assignment cannot be obtained for any constant migration factor $\gamma$ for any $m\ge 2$ and identical machines. Then, we deal with the problem of finding almost optimal assignments. We provide a fully polynomial time approximation scheme (FPTAS) for identical machines with constant migration factor, show how its running time can be reduced, and extend our result to the case of uniformly related machines. Our approximation schemes work even for the case where job departures may occur.

我们重新审视了非抢占式调度或分配作业的问题，从而最大程度地减少了 $米$ 相同的机器 $米$统一关联的机器。如果同时显示所有作业，即使对于不相关的机器，此问题也可以解决。在线算法一个接一个地接收作业，以便在呈现下一个作业之前安排每个作业。具有迁移因子的鲁棒算法$\gamma >0$ 也一次接收一次要立即分配的作业，但是当一个作业 $p$ 到达后，该算法可以重新分配总大小的作业子集 $\gamma \cdot p$。也就是说，它可以从一个这样的子集中删除其职位，并以任意方式再次安排它们。目的是获得最佳或几乎最佳的解决方案。我们将术语计划用于解决方案，其中每个作业都计划在计算机上的一个时隙中，术语分配用于解决方案，在该解决方案中，将作业分配给计算机，并且始终以最佳作业顺序（通过SPT）进行排序用于每台机器。我们表明，无法获得以下最佳计划：$米\ge \mathrm{1个}$机器的任何恒定迁移因子。对于创建分配的变体，对于一台机器而言，在线问题已经微不足道，并且我们证明，对于任何恒定的迁移因子，都无法获得最佳分配$\gamma$ 对于任何 $米\ge 2$和相同的机器。然后，我们处理寻找几乎最佳分配的问题。我们为具有恒定迁移因子的相同机器提供了完全多项式时间近似方案（FPTAS），显示了如何减少其运行时间，并将结果扩展到统一关联机器的情况。即使在可能发生工作变动的情况下，我们的近似方案也可以使用。