A PTAS for Minimizing the Total Weighted Completion Time on Identical Parallel Machines

We consider the problem of scheduling a set of n jobs on m identical parallel machines so as to minimize the weighted sum of job completion times. This problem is NP-hard in the strong sense. The best approximation result known so far was a 1 2 1+ p2 approximation algorithm that has been derived by Kawaguchi and Kyan back in 1986. The contribution of this paper is a polynomial time approximation scheme for this setting, which settles a problem that was open for a long time. Moreover, our result constitutes the rst known approximation scheme for a strongly NP-hard scheduling problem with minsum objective. Key words: scheduling theory, approximation algorithm, approximation scheme, worst-case ratio, combinatorial optimization

• Type: Journal
• Year: 2000
• Where: MOR
• Authors: Martin Skutella, Gerhard J. Woeginger
• Keywords: Approximation, Approximation Scheme, MOR 2000, Polynomial Time Approximation Scheme