Stochastic Machine Scheduling with Precedence Constraints

• Published in: SIAM journal on computing Vol. 34; no. 4; pp. 788 - 802
• Main Authors: Skutella, Martin, Uetz, Marc
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2005
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Approximation; Computer science; control theory; systems; Computer systems performance. Reliability; Exact sciences and technology; Expected values; Job shops; Linear programming; Mathematical programming; Operational research and scientific management; Operational research. Management science; R&D; Random variables; Release dates; Research & development; Schedules; Scheduling; Scheduling, sequencing; Software; Theoretical computing; precedence constraints; 68Q25; 68W40; LP relaxation; Parallel machines; Linear programming; Processing time; Stochastic scheduling; Probability distribution; Scheduling; list scheduling algorithms; 68W25; 90C05; approximation algorithms; Approximation algorithm; Precedence constraint; Delay; 90B36; release dates; Distribution function; LP-relaxation 68M20
• ISSN: 0097-5397; 1095-7111
• DOI: 10.1137/S0097539702415007

We consider parallel, identical machine scheduling problems, where the jobs are subject to precedence constraints and release dates, and where the processing times of jobs are governed by independent probability distributions. Our objective is to minimize the expected value of the total weighted completion time. Building upon a linear programming relaxation by Mohring, Schulz, and Uetz [J. ACM, 46 (1999), pp. 924--942] and a delayed list scheduling algorithm by Chekuri et al. [SIAM J. Comput., 31 (2001), pp. 146--166], we derive the first constant-factor approximation algorithms for this model.