We study a single machine due-date assignment problem with a common due-date. The objective function is minimizing the maximum earliness/tardiness cost. The scheduler may process only a subset of the jobs and the remaining jobs are rejected. Job-dependent rejection-costs are considered, and an upper bound on the total permitted rejection cost is assumed. The problem is proved to be NP-Hard. We present and test a pseudo-polynomial dynamic programming solution algorithm. An extension to the setting containing additional due-date cost component is also discussed. An efficient implementation of the algorithm is introduced, and medium size problems (containing hundreds of jobs) are shown to be solved in very reasonable running time. In addition, an intuitive heuristic is introduced, tested numerically, and is shown to produce very small optimality gaps.

我们研究具有共同到期日的单机到期日分配问题。目标函数是最小化最大提前/迟到成本。调度程序可能仅处理作业的子集，而其余作业将被拒绝。考虑与工作相关的拒绝成本，并假设总允许拒绝成本的上限。该问题被证明是NP-Hard问题。我们提出并测试了伪多项式动态规划求解算法。还讨论了包含附加到期日期成本部分的设置的扩展。介绍了该算法的有效实现，并且显示中等规模的问题（包含数百个作业）可以在非常合理的运行时间内解决。此外，还引入了直观的启发式方法，并进行了数值测试，结果表明它可以产生非常小的最优性差距。