In our current fast-paced era, customers are often willing to pay extra premium for shorter lead times, which motivates further research on the scheduling problem with due-date assignment and customer-specified lead times. As part of this effort, we extend the classic minsum ‘DIF’ scheduling model to allow optional job-rejection, thus adding an important component of real-life applications, namely, the possibility that the scheduler decides to process only a subset of the jobs and outsource the disjoint set. The scheduler is penalised for rejecting certain jobs by setting job-dependent rejection costs, and he is limited by a given upper bound on the total rejection cost. The most general version of the minsum DIF problem includes job-dependent cost parameters and lead-times, and it is strongly NP-hard. Therefore, we study six variants of the problem, where either only the cost parameters or the lead-times are job dependent. All alternatives are extended by optional job-rejection that possibly bounds the constraints or the underlying cost functions. We establish that all studied problems are NP-hard in the ordinary sense and present pseudo-polynomial dynamic programming algorithms and extensive numerical studies for most solutions.

在我们当前快节奏的时代，客户往往愿意为更短的提前期支付额外的费用，这激发了对到期日分配和客户指定提前期的调度问题的进一步研究。作为这项工作的一部分，我们扩展了经典的 minsum 'DIF' 调度模型以允许可选的作业拒绝，从而增加了现实生活应用程序的一个重要组成部分，即调度程序决定仅处理作业子集的可能性并外包不相交的集合。通过设置依赖于作业的拒绝成本，调度器因拒绝某些作业而受到惩罚，并且他受到总拒绝成本的给定上限的限制。该minsum DIF问题的最一般的版本包括相关的作业成本参数和交货时间，并且它是强 NP 难的。因此，我们研究了该问题的六个变体，其中只有成本参数或提前期与工作相关。所有替代方案都通过可选的作业拒绝进行扩展，这可能会限制约束或基础成本函数。我们确定所有研究的问题在一般意义上都是 NP 难的，并为大多数解决方案提供伪多项式动态规划算法和广泛的数值研究。