This paper studies the single machine scheduling problem with availability constraints and optional job rejection. We consider the non-resumable and resumable variants, and show that the problems remain ordinary NP-hard, even with the rejection possibility extension, by presenting pseudo-polynomial dynamic-programming (DP) solutions. We also present an enhanced running time implementation of the algorithm of Kellerer and Strusevich (Algorithmica 57(4):769–795, 2010) for the resumable scenario without job rejection. This solution is adapted to efficiently solve the machine non-availability problem with a floating interval and the problem of two competing agents on a single machine, with and without optional job rejection. Numerical experiments support the efficiency of our DP implementation.

本文研究了具有可用性约束和可选作业拒绝的单机调度问题。我们考虑了不可恢复和可恢复的变体，并通过提出伪多项式动态规划 ( DP ) 解决方案，表明问题仍然是普通的 NP-hard，即使有拒绝可能性扩展。我们还提出了 Kellerer 和 Strusevich (Algorithmica 57(4):769–795, 2010) 算法的增强运行时间实现，用于没有工作拒绝的可恢复场景。该解决方案适用于有效地解决具有浮动间隔的机器不可用问题和单个机器上的两个竞争代理问题，有和没有可选的作业拒绝。数值实验支持我们DP的效率 执行。