Lecture 1: Scheduling on Parallel Machines

Classes of scheduling problems can be specified in terms of the three-field classification α|β|γ where • α specifies the machine environment, – P parallel identical – Q uniform machines: each machine has a given speed speed i, and all jobs have a size sizej, the processing time is given by sizej/speed i – R unrelated machines: the processing time of job j on machine i is given by pi,j, without any other constraints • β specifies the job characteristics, – ri: jobs with release dates; job i is submitted to the system at time ri – di: jobs with deadlines or due dates; job i must complete by the date di – pmtn: jobs may be subject to preemption; the execution of a job could be stopped at any time to be resumed later for the point it was stopped – prec: there may be precedence constraints between jobs • γ describes the objective function – Cmax = maxiCi: makespan or maximum completion time – maxi(Ci − ri): maximum flow time Parallel environment (alpha in Graham’s notation): Sometimes the number of processors is fixed: for example, P2, F2, or Pm.