Parallel environment (alpha in Graham’s notation): • 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 Sometimes the number of processors is fixed: for example, P2, F2, or Pm.

We consider the uniform parallel machine scheduling problem with the objective of minimizing maximum lateness. We show that an extension of the EDD rule to a uniform parallel machine setting yields a maximum lateness value which does not exceed the optimal value by more than pmax, where pmax is the maximum job processing time. c © 2000 Elsevier Science B.V. All rights reserved.

We consider the multistage flexible flow shop scheduling problem with uniform parallel machines in each stage and the objective of minimizing makespan. We develop a general class of heuristics for this strongly NP-hard problem that extend several well-known heuristics for the corresponding embedded serial flow shop problem, and obtain absolute performance guarantees for heuristics in this class...

The single-stage scheduling problem to minimize the makespan of identical jobs on uniform parallel machines is known to be solvable in polynomial-time. We extend this work to consider multi-stage systems with flowshop configuration. We show that the 2-stage problem may also be solved in polynomial-time and for the number of stages greater than two, the problem is shown to be NP-hard. We present...

Parallel simulation is emerging as the dominant technique for studying parallel computers. However, the interconnection networks of these machines can be modeled at many different levels of abstraction, allowing researchers to trade off accuracy and performance. In this paper, we use the Wisconsin Wind Tunnel, a parallel simulator for cache-coherent shared-memory machines, to study the trade-of...