Scheduling Parallel Machines with a Single Server: A Dedicated Case

The model in this paper is abstracted from a key course of batch annealing process in the steel industry: heating or cooling. We mainly investigate scheduling parallel dedicated machines with a single sever as well as additional constraints on setups and removals. It generalizes classical parallel machine scheduling problem with a single server which needs to perform setup operation of each job only. The single server in our problem do not only load a job on a machine which takes a certain setup time immediately before processing but also unload a job from the machine which takes a certain removal time after processing. The objective is to minimize make span. A polynomial time approximate algorithm is proposed with a tight worst-case bound at most twice as large as the optimal value.