Scheduling of Identical Jobs with Bipartite Incompatibility Graphs on Uniform Machines. Computational Experiments

Abstract

Abstract. In the paper we consider the problem of scheduling of unit-length jobs on 3 or 4 uniform parallel machines to minimize schedule length or total completion time. We assume that jobs are subject to some kind of mutual exclusion constraints, modeled by a bipartite graph of bounded degree. The edges of the graph correspond to pairs of jobs that cannot be processed on the same machine. Although the problem is generally NP-hard, we show that under some conditions imposed on machine speeds and the structure of  incompatibility graph our problem can be solved to optimality in polynomial time. Theoretical considerations are accompanied by computer experiments  with some particular model of scheduling.