Measuring the slack between lower bounds for scheduling on parallel machines

This paper considers the problem of scheduling independent jobs with release dates and tails on m identical machines to minimize the makespan. The three main bounds are the preemptive bound, the energetic bound and the Jackson Pseudo Preemptive bound. It is known that they are very close in practice. The aim of this paper is to provide worst case instances where the slack between them is maximal and to prove tight bounds on the slack. We show that the slack is smaller than the maximal processing time.