Stochastic Machine Scheduling with Precedence Constraints

We consider parallel, identical machine scheduling problems where the jobs are subject to precedence constraints, release dates, and the processing times of jobs are governed by independent probability distributions. The objective is to minimize the expected value of the total weighted completion time. Building upon a linear programming relaxation by Möhring, Schulz and Uetz (Journal of the ACM 46, 1999, 924-942) and an idle time charging scheme by Chekuri, Motwani, Natarajan, and Stein (SIAM Journal on Computing 31, 2001, 146-166) we derive the first constant-factor approximation algorithms for this model.