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Scheduling two-point stochastic jobs to minimize the makespan on two parallel machines. (English) Zbl 1096.68555
Summary: Simple optimal policies are known for the problem of scheduling jobs to minimize expected makespan on two parallel machines when the job running-time distribution has a monotone hazard rate. But no such policy appears to be known in general. We investigate the general problem by adopting two-point running-time distributions, the ismplest discrete distributions not having monotone hazard rates. We derive a policy that gives an explicit, compact solution to this problem and prove its optimality. We also comment briefly on first-order extensions of the model, but each of these seems to be markedly more difficult to analyze.
MSC:
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90B35 Deterministic scheduling theory in operations research
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