Optimal multi-class job scheduling on a single machine with sequence-dependent set-up and variable processing times

The scheduling of jobs belonging to different classes over a single machine is considered in this paper. The processing time of any job of a given class is a continuous variable whose value ranges from a lower bound up to a higher bound, corresponding to the nominal processing time. The switch from a job of a class to a job of another class requires a sequence-dependent set-up. The cost function to be minimized in the scheduling problem takes into account the overall job tardiness, the sum of the costs due to the deviation of the actual processing time from the nominal value, and the set-up costs. The decision variables are those concerning job sequencing and execution times. In the paper, a solution to this problem - in terms of optimal control strategies - is provided.