We consider a single-machine scheduling problem such that the due dates are assigned to each job depending on its order, and the lengths of the intervals between consecutive due dates are identical. The objective is to minimize the total penalty for the earliness and tardiness of each job. The early penalty proportionally increases according to the earliness amount, while the tardy penalty increases according to the step function. We show that the problem is strongly NP-hard, and furthermore, polynomially solvable if the two types of processing times exist.

中文翻译：

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单机调度，具有定期的到期日，以最大程度地减少总提前期和迟到的罚款

我们考虑单机调度问题，即根据每个作业的顺序将到期日分配给每个作业，并且连续到期日之间的间隔长度是相同的。目的是最大程度地减少每项工作的过早和拖延的总罚款。早期惩罚根据提前量成比例地增加，而延迟惩罚根据阶跃函数而增加。我们表明，该问题在很大程度上是NP难题，而且，如果存在两种类型的处理时间，则该问题可以多项式求解。