A 1.47-approximation algorithm for a preemptive single-machine scheduling problem

Authors:
Michel X. Goemans;Joel M. Wein;David P. Williamson
Affiliations:
MIT, Room 2-351, 77 Mass. Ave, Cambridge, MA 02139, USA;Department of Computer Science, Polytechnic University, Five MetroTech Center, Brooklyn, NY 11201, USA;IBM T.J. Watson Research Center, Room 33-219, P.O. Box 218, Yorktown Heights, NY, 10598, USA
Venue:
Operations Research Letters
Year:
2000

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Abstract

In this note, we give a 1.47-approximation algorithm for the preemptive scheduling of jobs with release dates on a single machine so as to minimize the weighted sum of job completion times; this problem is denoted by 1|r"j,pmtn|@?"jw"jC"j in the notation of Lawler et al. (Handbooks in Operations Research and Management Science, Vol. 4, Logistics of Production and Inventory, North-Holland, Amsterdam, pp. 445-522). Our result improves on a 2-approximation algorithm due to Hall et al. Math. Oper. Res. 22 (1997) 513-544, and also yields an improved bound on the quality of a well-known linear programming relaxation of the problem.