On the Optimal Stochastic Scheduling of Out-Forests

This paper presents new results on the problem of scheduling jobs on K ≥ 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...

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Bibliographic Details
Published in:Operations research Vol. 40; no. 1-supplement-1; pp. S67 - S75
Main Authors: Coffman, E. G., Liu, Zhen
Format: Journal Article
Language:English
Published: Linthicum, MD INFORMS 01.01.1992
Operations Research Society of America
Institute for Operations Research and the Management Sciences
Subjects:
Applied sciences
Counterexamples
Exact sciences and technology
Forest conservation
Job shops
Mathematical analysis
network/graphs: tree algorithms
Operational research and scientific management
Operational research. Management science
Operations research
Optimal policy
Parallel processing
Plant roots
Probabilities
production/scheduling: stochastic sequencing
Random variables
Roots of functions
Scheduling
Scheduling, sequencing
Stochastic models
Trees
Tree(graph)
Processor
Forest(graph)
Scheduling
Graph theory
Stochastic method
Optimization
ISSN:0030-364X, 1526-5463
Online Access:Get full text
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Summary:This paper presents new results on the problem of scheduling jobs on K ≥ 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 ≥ 2.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ObjectType-Article-1
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.40.1.S67