Discrete–continuous scheduling problems: Mean completion time results

Problems of scheduling independent, nonpreemptable jobs on m parallel machines with an additional continuously divisible, renewable resource to minimize the mean completion time are considered. A jobs is described by its processing demand and its processing rate being a continuous, nondecreasing function of the amount of the continuous resource allotted to it at a time. Properties of optimal schedules are proved and two special cases with efficient solution algorithms are presented.