Waiting time and idle time are among the main cost sources in production systems. They can also affect the feasibility of operations from a technological perspective; hence, both such times have to be kept as small as possible. This paper studies four single-objective variants of the permutation flowshop scheduling problem, where two objectives are considered: the weighted sum of the makespan and the core waiting time, and the weighted sum of the makespan and the core idle time. For each objective, both the problem with the assumption of semi-active solution and the one without it are considered.

A general solution framework for tackling the above-mentioned problems is provided. First, two Mixed Integer Linear Programming (MILP) formulations (based on positional and precedence variables, respectively) and one Constraint Programming (CP) formulation are presented. Second, a MILP-based local search approach based on the positional MILP formulation and the concept of sliding windows are defined. An extensive set of computational experiments on benchmark instances show that the positional MILP formulation strongly outperforms the other two formulations in all the considered cases. The experiments also show that the sliding window local search heuristic achieves much better performances than other state-of-the-art local search heuristics. Indeed, it is able to improve the state-of-the-art in 2384 instances out of 2400.

等待时间和空闲时间是生产系统中的主要成本来源。它们还可以从技术角度影响操作的可行性；因此，这两个时间都必须尽可能短。本文研究了置换流水车间调度问题的四种单目标变体，其中考虑了两个目标：完工时间和核心等待时间的加权和，以及完工时间和核心空闲时间的加权和。对于每个目标，都考虑了假设半主动解决方案和没有半主动解决方案的问题。

提供了解决上述问题的通用解决方案框架。首先，提出了两个混合整数线性规划 (MILP) 公式（分别基于位置变量和优先级变量）和一个约束规划 (CP) 公式。其次，基于位置 MILP 公式和滑动窗口概念的基于 MILP 的局部搜索方法被定义。对基准实例进行的大量计算实验表明，位置 MILP 公式在所有考虑的情况下都明显优于其他两个公式。实验还表明，滑动窗口局部搜索启发式算法比其他最先进的局部搜索启发式算法具有更好的性能。事实上，它能够在 2400 个实例中的 2384 个实例中改进最先进的技术。