Group scheduling jobs on a single machine: A multi-objective approach with preemptive priority structure

We characterize the properties of optimal schedules, for a single machine group scheduling problem, to obtain all optimal scheduling alternatives efficiently. The optimality criterion considered is the minimization of mean completion time. Further, in the group scheduling context, we introduce a new concept of holding time and cost and consider a multi-objective scenario with preemptive priority structure. We present an efficient scheme to determine an optimal schedule with minimization of mean completion time, makespan, and holding time (or cost) being primary, secondary, and tertiary criteria respectively.