We study a single-machine scheduling problem with two competing agents. The objective function of one agent is minimizing total late work, whereas the maximum cost of the jobs of the second agent cannot exceed a given upper bound. We introduce and test a pseudo-polynomial dynamic programming algorithm for this NP-hard problem. Our tests indicate that the algorithm can handle large-size instances (containing hundreds of jobs) fairly quickly. We then extend the setting to that of job rejection, where the scheduler may decide to process only a subset of the jobs. The dynamic programming algorithm is modified accordingly, and our numerical tests verify that medium-size instances (containing less than 100 jobs) are solved in reasonable time.

我们研究了具有两个竞争代理的单机调度问题。一个代理的目标功能是最大程度地减少总的后期工作，而第二个代理的工作的最大成本不能超过给定的上限。我们针对此NP-hard问题引入并测试了伪多项式动态规划算法。我们的测试表明，该算法可以相当快地处理大型实例（包含数百个作业）。然后，我们将该设置扩展到拒绝作业的设置，在该位置调度程序可以决定仅处理一部分作业。动态编程算法进行了相应的修改，我们的数值测试证明，中等大小的实例（包含少于100个作业）可以在合理的时间内解决。