In this paper we study single-machine preemptive scheduling to minimize the total weighted late work with assignable due dates or assignable weights. For the problem with assignable due dates, we show that it is binary NP-hard, solvable in pseudo-polynomial time, and solvable in polynomial time when all the jobs have agreeable processing times and weights. For the problem with assignable weights, we show that it is solvable in polynomial time. For the problem with assignable due dates and assignable weights, we show that it is binary NP-hard, solvable in pseudo-polynomial time, and solvable in polynomial time when all the jobs have the same processing times.

中文翻译：

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具有可分配截止日期或可分配权重的单机抢占式调度，以最大限度地减少加权延迟工作总数


在本文中，我们研究了单机抢占式调度，以最小化具有可分配截止日期或可分配权重的总加权延迟工作。对于具有可分配截止日期的问题，我们表明它是二进制 NP 困难的，可以在伪多项式时间内求解，并且当所有作业都具有令人满意的处理时间和权重时，它可以在多项式时间内求解。对于可分配权重的问题，我们表明它是可以用多项式时间解决的。对于具有可分配截止日期和可分配权重的问题，我们表明它是二进制 NP 困难的，可在伪多项式时间内求解，并且当所有作业具有相同的处理时间时，可在多项式时间内求解。