On-line scheduling of unit time jobs with rejection: minimizing the total completion time

Authors:
Leah Epstein;John Noga;Gerhard J. Woeginger
Affiliations:
School of Computer and Media Sciences, The Interdisciplinary Center, P.O. Box 167, 46150 Herzliya, Israel;Department of Computer Science, California State University, 18111 Nordhoff Street, Northridge, CA 91330-8295, USA;Department of Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands and Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, A ...
Venue:
Operations Research Letters
Year:
2002

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Abstract

We consider on-line scheduling of unit time jobs on a single machine with job-dependent penalties. The jobs arrive on-line (one by one) and can be either accepted and scheduled, or be rejected at the cost of a penalty. The objective is to minimize the total completion time of the accepted jobs plus the sum of the penalties of the rejected jobs. We give an on-line algorithm for this problem with competitive ratio 12(2+3)~1.86602. Moreover, we prove that there does not exist an on-line algorithm with competitive ratio better than 1.63784.