The two-machine permutation flow shop scheduling problem with buffer is studied for the special case that all processing times on one of the two machines are equal to a constant $c$⁠. This case is interesting because it occurs in various applications, for example, when one machine is a packing machine or when materials have to be transported. Different types of buffers and buffer usage are considered. It is shown that all considered buffer flow shop problems remain NP-hard for the makespan criterion even with the restriction to equal processing times on one machine. However, the special case where the constant $c$ is larger or smaller than all processing times on the other machine is shown to be polynomially solvable by presenting an algorithm (2BF-OPT) that calculates optimal schedules in $O(nlogn)$ steps. Two heuristics for solving the NP-hard flow shop problems are proposed: (i) a modification of the commonly used NEH heuristic (mNEH) and (ii) an Iterated Local Search heuristic (2BF-ILS) that uses the mNEH heuristic for computing its initial solution. It is shown experimentally that the proposed 2BF-ILS heuristic obtains better results than two state-of-the-art algorithms for buffered flow shop problems from the literature and an Ant Colony Optimization algorithm. In addition, it is shown experimentally that 2BF-ILS obtains the same solution quality as the standard NEH heuristic, however, with a smaller number of function evaluations.

针对两机其中一台的所有加工时间都等于一个常数的特殊情况，研究了带缓冲区的两机置换流水车间调度问题。$C$⁠。这种情况很有趣，因为它出现在各种应用中，例如，当一台机器是包装机或必须运输材料时。考虑了不同类型的缓冲区和缓冲区使用。结果表明，即使限制一台机器上的处理时间相等，所有考虑的缓冲流水车间问题对于完工时间标准仍然是NP难的。然而，常量的特殊情况$C$大于或小于另一台机器上的所有处理时间 通过提出计算最优调度的算法 (2BF-OPT) 可以多项式求解$欧(n日志n)$脚步。提出了解决NP难流水车间问题的两种启发式方法：(i) 对常用的 NEH 启发式方法 (mNEH) 的修改，以及 (ii) 使用 mNEH 启发式方法计算它的迭代局部搜索启发式方法 (2BF-ILS)初步解决方案。实验表明，所提出的 2BF-ILS 启发式算法比文献中针对缓冲流水车间问题的两种最先进算法和蚁群优化算法获得了更好的结果。此外，实验表明，2BF-ILS 获得与标准 NEH 启发式算法相同的解决方案质量，但功能评估次数较少。