We address in this paper the two-machine open shop problem with set-up time considerations to build schedules that minimize the overall completion time, known as the makespan. In the model we are considering, the set-up, handled by a single server, consists of a preparation phase separated from the processing phase. Once the server completes the preparation of a job, it becomes again available for setting up other jobs, leaving the current one to complete its processing. We prove several $\mathcal{NP}$-completeness results, exhibit a linear time algorithm for a special case, and develop heuristic and hyper-heuristic algorithms to solve the general problem along with an experimental study.

我们在本文中讨论了两台机器的开放车间问题，并考虑了设置时间，以建立可最大程度减少整体完成时间（称为工期）的进度表。在我们正在考虑的模型中，由单个服务器处理的设置包括与处理阶段分离的准备阶段。服务器完成作业的准备后，它将再次可用于设置其他作业，而使当前作业可以完成其处理。我们证明几个$\mathcal{NP}$-完备性结果，展示一种特殊情况的线性时间算法，并开发启发式算法和超启发式算法来解决一般问题，并进行实验研究。