In this paper we consider n jobs and a number of machines in parallel. The machines are identical and subject to breakdown and repair. The number may therefore vary over time and is at time t equal to m(t). Preemptions are allowed. We consider three objectives, namely, the total completion time, ∑ Cj, the makespan Cmax, and the maximum lateness Lmax. We study the conditions on m(t) under which various rules minimize the objective functions under consideration. We analyze when the jobs have deadlines to meet and when the jobs are subject to precedence constraints.
