On scheduling malleable jobs to minimise the total weighted completion time

Abstract

This paper is about scheduling parallel jobs, i.e. which can be executed on more than one processor at the same time. Malleable jobs is a special class of parallel jobs. The number of processors a malleable job is executed on may change during the execution. In this work, we consider the NP-hard problem of scheduling malleable jobs to minimize the total weighted completion time or mean weighted flow time. For this problem, we introduce an important dominance rule which can be used to reduce the search space while searching for an optimal solution.