We consider single machine lot scheduling problems. A number of customer orders of different sizes may be processed in the same lot. Splitting orders between consecutive lots is allowed. Three scheduling measures are considered: makespan, total completion time and total weighted completion time. In all cases, the goal is minimizing the relevant scheduling measure, subject to an upper bound on the total permitted rejection cost. All three problems studied here are NP-hard. We introduce efficient pseudo-polynomial dynamic programming algorithms for all cases. Our numerical tests indicate that the proposed algorithms can solve efficiently large-size problems.

我们考虑单机调度问题。可以在同一批中处理许多不同大小的客户订单。允许在连续的批次之间拆分订单。考虑了三种调度方法：工期，总完成时间和总加权完成时间。在所有情况下，目标是最大程度地减少相关的调度措施，但要以允许的总拒绝成本为上限。这里研究的所有三个问题都是NP难的。我们针对所有情况介绍了有效的伪多项式动态规划算法。我们的数值测试表明，所提出的算法可以有效地解决大型问题。