Scheduling with shutdowns and sequence dependent set-up times

This paper considers a single machine scheduling problem with ready and due times constraints on jobs, shutdown constraints on the machine and sequence dependent set-up times among jobs. The shutdown is a disruptive event such as holiday, breaks or machine maintenance, and has a prespecified period when the machine will be interrupted. If no pre-emption is allowed for jobs, shutdown constraints divide the planning horizon into disconnected time windows. An optimization algorithm based on the branch-and-bound method is developed to minimize the maximum tardiness for solving the problem. This paper further develops the post-processing algorithm that manipulates the starting time of the shutdown period so as to reduce the obtained maximum tardiness. The post-processing algorithm can determine plural schedules to reduce the maximum tardiness, and the production manager will select the objective schedule among them for the interest of overall efficiency. Computational results for the proposed algorithms will indicate that the post-processing algorithm can improve upon the original solution and the problems with multiple shutdowns and with set-up times varying widely can be satisfactorily solved.