We consider two single-machine scheduling problems in which two competing projects share one common resource. Each project has multiple interim assessments, and its own jobs are ordered completely. A tardy job incurs a tardiness penalty cost which can be avoided by compressing some jobs, which requires an additional cost. The performance measure of each project is the total tardiness penalty cost plus the total compression cost. The first problem minimizes the weighted sum of the performance measures of two projects, and the second problem minimizes the performance measure of one project with a constraint on that of the other. We show that the first problem is solvable in strongly polynomial time and the second is weakly NP-hard. Furthermore, we analyze how the computational complexity of each problem changes if the number of projects is more than two.

中文翻译：

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在单机环境中以可控的处理时间安排两个项目

我们考虑两个单机调度问题，其中两个相互竞争的项目共享一个公共资源。每个项目都有多个中期评估，其自身的工作是完全有序的。迟到的作业会产生迟到惩罚成本，这可以通过压缩一些作业来避免，这需要额外的成本。每个项目的性能度量是总延迟惩罚成本加上总压缩成本。第一个问题最小化两个项目的绩效度量的加权总和，第二个问题最小化一个项目的绩效度量，并限制另一个项目的绩效度量。我们证明第一个问题在强多项式时间内是可解决的，第二个问题是弱 NP-hard 问题。此外，