The complexity of mean flow time scheduling problems with release times

Authors:
Philippe Baptiste;Peter Brucker;Marek Chrobak;Christoph Dürr;Svetlana A. Kravchenko;Francis Sourd
Affiliations:
Aff1 Aff2;Universität Osnabrück, Fachbereich Mathematik/Informatik, Osnabrück, Germany 49069;Department of Computer Science, University of California, Riverside, USA 92521;CNRS LIX, Ecole Polytechnique, Palaiseau, France 91128;United Institute of Informatics Problems, Minsk, Belarus 220012;CNRS LIP6, Université Pierre et Marie Curie, Place de Jussieu, Paris, France 75005
Venue:
Journal of Scheduling
Year:
2007

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Abstract

We study the problem of preemptive scheduling of n} jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. In this paper, show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard.