## On the optimal stochastic scheduling of out-forests.(English)Zbl 0764.90042

Summary: This paper presents new results on the problem of scheduling jobs on $$K\geq 1$$ parallel processors to stochastically minimize the makespan. The jobs are subject to out-forest precedence constraints, i.e. each job has at most one immediate predecessor, and job running times are independent samples from a given exponential distribution. We define a class of uniform out-forests in which all subtrees are ordered by an embedding relation. We prove that an intuitive greedy policy is optimal for $$K=2$$, and that if out-forests satisfy an additional, uniform root-embedding constraint, then the greedy policy is optimal for all $$K\geq 2$$.

### MSC:

 90B35 Deterministic scheduling theory in operations research 93E03 Stochastic systems in control theory (general)
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