Single-machine bicriterion group scheduling with deteriorating setup times and job processing times

This paper considers a group scheduling problem with two ordered criteria where both setup times and job-processing times are increasing functions of their starting times. It is assumed that the jobs be classified into several groups and the jobs of the same group have to be processed contiguously. We consider two objectives where the primary criterion is the total weighted completion time and the secondary criterion is the maximum cost. A polynomial time algorithm is presented to solve this bicriterion group scheduling problem with deteriorating setup times and job-processing times. This algorithm can also solve single-machine group scheduling problems with deteriorating setup times and job-processing times in several ordered maximum cost and arbitrary precedence.