An exact algorithm for parallel machine scheduling with conflicts

Daniel Kowalczyk and Roel Leus

No 485437, Working Papers of Department of Decision Sciences and Information Management, Leuven from KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven

Abstract: We consider an extension of classic parallel machine scheduling where a set of jobs is scheduled on identical parallel machines and an undirected conflict graph is part of the input. Each node in the graph represents a job and an edge implies that its two jobs are conflicting, meaning that they cannot be scheduled on the same machine. The goal is to find an assignment of the jobs to the machines such that the maximum completion time (makespan) is minimized. We present an exact algorithm based on branch and price that combines methods from bin packing, scheduling and graph coloring, with appropriate modifications. The algorithm has a good computational performance even for parallel machine scheduling without conflicting jobs.

Keywords: Scheduling; Combinatorial optimization; Parallel machines; Coloring; Branch and price (search for similar items in EconPapers)
Date: 2015
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Published in FEB Research Report KBI_1505

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