Abstract This paper focuses on two components of idle time and waiting time, namely core idle time, ∑CITi, and core waiting time, ∑CWTj. Both measures are relevant indicators of the efficiency of production systems, since they are directly related to machine utilization and to the flow of jobs, and they can be used as scheduling criteria if no-idle and no-wait constraints do not have to be strictly enforced. However, they have been scarcely considered in the literature, and their relationship with other objectives in the permutation flowshop literature (makespan or Cmax and total completion time or ∑Cj), has not been studied. To bridge this gap, the alignment between ∑CITi and ∑CWTj, and the classical scheduling criteria is studied. First, it is shown that ∑CWTj (∑CITi) is tantamount to ∑Cj (Cmax) for some special cases. Secondly, the general case with randomly generated processing times is computationally analysed using exact methods. Results show alignment between ∑CWTj and ∑Cj and between ∑CITi and Cmax, being the alignment stronger for the first pair of objectives. Based on the analysis, conclusions about the possibilities for the permutation flowshop problem with these new objectives are established.

中文翻译：

---

置换流水车间调度中常用目标函数、空闲时间和等待时间的关系

摘要 本文重点讨论空闲时间和等待时间两个组成部分，即核心空闲时间∑CITi 和核心等待时间∑CWTj。这两项措施都是生产系统效率的相关指标，因为它们与机器利用率和作业流直接相关，如果不需要严格的无空闲和无等待约束，它们可以用作调度标准强制执行。然而，它们在文献中几乎没有被考虑过，并且它们与置换流水车间文献中的其他目标（完工时间或 Cmax 和总完成时间或 ∑Cj）的关系尚未研究。为了弥合这一差距，研究了∑CITi 和∑CWTj 之间的对齐方式以及经典的调度标准。首先，表明对于某些特殊情况，∑CWTj (∑CITi) 等同于∑Cj (Cmax)。第二，使用精确方法对随机生成处理时间的一般情况进行计算分析。结果显示∑CWTj 和∑Cj 之间以及∑CITi 和Cmax 之间的对齐，对于第一对物镜来说对齐更强。基于分析，建立了关于具有这些新目标的置换流水车间问题的可能性的结论。