Scheduling precedence-constrained jobs with stochastic processing times on parallel machines

Abstract

We consider parallel machine scheduling problems where the jobs are subject to precedence constraints, and the processing times of jobs are governed by independent probability distributions. The objective is to minimize the weighted sum of job completion times ∑, w, C, in expectation, where w, g 0. Building upon an LP-relaxation from [3] and an idle time charging scheme from [1], we derive the first approximation algorithms for this model.