Approximation Bounds for a General Class of Precedence Constrained Parallel Machine Scheduling Problems

Abstract

A well studied and difficult class of scheduling problems concerns parallel machines and precedence constraints. In order to model more realistic situations, we consider precedence delays, asso ciating with each precedence constraint a certain amount of time which must elapse between the completion and start times of the corresponding jobs. Release dates, among others, may be modeled in this fashion. We provide the first constant-factor approximation algorithms for the makespan and the total weighted completion time objectives in this general class of problems. These algorithms are rather simple and practical forms of list scheduling. Our analysis also unifies and simplifies that of a number of special cases heretofore separately studies, while actually improving some of the former approximation results.