 
Summary: SIAM J. COMPUT. c 2005 Society for Industrial and Applied Mathematics
Vol. 34, No. 4, pp. 788802
STOCHASTIC MACHINE SCHEDULING WITH
PRECEDENCE CONSTRAINTS
MARTIN SKUTELLA AND MARC UETZ
Abstract. 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 M¨ohring,
Schulz, and Uetz [J. ACM, 46 (1999), pp. 924942] and a delayed list scheduling algorithm by Chekuri
et al. [SIAM J. Comput., 31 (2001), pp. 146166], we derive the first constantfactor approximation
algorithms for this model.
Key words. approximation algorithms, stochastic scheduling, parallel machines, precedence
constraints, release dates, list scheduling algorithms, LPrelaxation
AMS subject classifications. 68M20, 68Q25, 68W25, 68W40, 90B36, 90C05
DOI. 10.1137/S0097539702415007
1. Introduction. This paper addresses stochastic parallel machine scheduling
problems with the objective of minimizing the expected value of the total weighted
completion time. Machine scheduling problems have attracted researchers for decades
since such problems play an important role in various applications from the areas of
