In this paper we consider three machine scheduling problems with the special feature that jobs may be rejected at a certain penalty. There are n jobs which are characterized by a release date, a processing time and a penalty. Each job is either accepted and then processed by one machine, or rejected and then a rejection penalty is paid. The objective is to minimize the maximum completion time of all accepted job plus the total penalties of all rejected jobs. When jobs have identical release dates, we present a (\(\frac{3}{2}-\frac{1}{2m}\))-approximation algorithm for the parallel machine problem. When jobs have general release dates, we propose a \(\frac{4}{3}\)-approximation algorithm for the single machine problem and a (\(1+\max \{0.618,1-\frac{1}{m}\}\))-approximation algorithm for the parallel machine problem, respectively.

在本文中，我们考虑了三个机器调度问题，这些问题的特殊之处在于可能会在一定的惩罚下拒绝工作。有n个作业，其特征在于发布日期，处理时间和罚款。每个作业要么被接受，然后由一台机器处理，要么被拒绝，然后支付拒绝罚款。目的是最大程度地减少所有接受的工作的最大完成时间以及所有拒绝的工作的总罚款。当作业具有相同的发布日期时，针对并行机问题，我们提出（\（\ frac {3} {2}-\ frac {1} {2m} \））近似算法。当作业具有一般发布日期时，我们针对单机问题提出一个\（\ frac {4} {3} \） -近似算法，并提出一个（\（1+ \ max \ {0.618,1- \ frac {1} {m} \} \））-分别针对并行机问题的近似算法。