SCHEDULING AND/OR-NETWORKS ON IDENTICAL PARALLEL MACHINES

Abstract Scheduling precedence constrained jobs on identical parallel machines is a well investigated problem withmany applications. AND/OR-networks constitute a useful generalization of standard precedence constraintswhere certain jobs can be executed as soon as at least one of their direct predecessors is completed. For theproblem of scheduling AND/OR-networks on parallel machines, we present a 2-approximation algorithm forthe objective of minimizing the makespan. The main idea of the algorithm is to transform the AND/OR con-straints into standard constraints. For the objective of minimizing the total weighted completion time on onemachine, scheduling AND/OR-networks is as hard to approximate as L ABEL C OVER . We show that list schedul-ing with shortest processing time rule is an O(pn)-approximation for unit weights on one machine and ann-approximation for arbitrary weights. 1 Introduction Scheduling precedence constrained jobs on identical parallel machines is a well investigated problem with manyapplications. A precedence constraint of the form i ˚ j means that job j can be started only after the completionof job i. If there are several jobs i with i ˚ j, the job j can be started only when