In this paper, we consider the parallel-machine scheduling problem with release dates and submodular rejection penalties. In this problem, we are given m identical parallel machines and n jobs. Each job has a processing time and a release date. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on one of the m identical parallel machines. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalty of the rejected jobs which is determined by a submodular function. Our main work is to design a 2-approximation algorithm based on the primal-dual framework.

中文翻译：

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具有发布日期和子模块拒绝惩罚的并行机调度问题的近似算法

在本文中，我们考虑了具有发布日期和子模块拒绝惩罚的并行机调度问题。在这个问题中，我们有m 个相同的并行机和n个作业。每个作业都有处理时间和发布日期。一项工作要么被拒绝，在这种情况下必须支付拒绝罚款，要么在m 台相同的并行机之一上接受和处理。目标是最小化接受作业的完工时间和被拒绝作业的拒绝惩罚的总和，这是由子模块函数确定的。我们的主要工作是设计一种基于原始对偶框架的 2-近似算法。