We consider a single machine lot scheduling problem. A number of customer orders of different sizes may be processed in the same lot. We consider first the setting that splitting orders between consecutive lots is allowed. We focus on minimizing the number of tardy orders. A polynomial time solution algorithm is introduced for this problem. We then study the extension to minimizing the weighted number of tardy orders. This problem is NP-hard, and a pseudo-polynomial dynamic programming is provided and tested. We also study the setting of no-split. The problem of minimizing the number of tardy orders in this context is proved to be strongly NP-hard, and an efficient heuristic is introduced.

我们考虑单个机器批次调度问题。可以在同一批中处理许多不同大小的客户订单。我们首先考虑允许在连续批次之间分割订单的设置。我们致力于最大限度地减少延迟订单的数量。针对此问题引入了多项式时间求解算法。然后，我们研究扩展以最小化延迟订单的加权数量。这个问题是NP难的，并且提供并测试了伪多项式动态编程。我们还研究了不拆分的设置。在这种情况下，最小化延迟订单数的问题被证明是强烈的NP-hard，并且引入了一种有效的启发式方法。