We consider the on-line version of the original m-machine scheduling p
roblem: given m machines and n positive real jobs, schedule the n jobs
on the m machines so as to minimize the makespan, the completion time
of the last job. In the on-line version, as soon as a job arrives, it
must be assigned immediately to one of the m machines. We study the c
ompetitive ratio of the best algorithm for m-machine scheduling. The l
argest prior lower bound was that if m greater-than-or-equal-to 4, the
n every algorithm has a competitive ratio at least 1 + 1 / square-root
2 almost-equal-to 1.707. We show that if m greater-than-or-equal-to 3
454, then the competitive ratio of every algorithm exceeds 1.837. The
best upper bound on the competitive ratio is now 1.945.