Two-machine open shop problem with a single server and set-up time considerations

Abstract

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 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.