1.47-Approximation algorithm for a preemptive single-machine scheduling problem

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|rj, pmtn|∑jwjCj in the notation of Lawler et al. 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.