. We present a new online algorithm, MR, for non-preemptive scheduling of jobs with known processing times on m identical machines which beats the best previous algorithm for m 64. For m ! 1 its competitive ratio approaches 1 + p 1+ln 2 2 ! 1:9201. 1 Introduction Scheduling problems are of great practical interest. However, even some of the simplest variants of the problem are not fully understood. In this paper, we study the classical problem of scheduling jobs online on m identical machines without preemption, i.e., the jobs arrive one at a time with known processing times and must immediately be scheduled on one of the machines, without knowledge of what jobs will come afterwards, or how many jobs are still to come. The goal is to achieve a small makespan which is the total processing time of all jobs scheduled on the most loaded machine. Since the jobs must be scheduled online we cannot expect to achieve the minimum makespan whose computation would require a priori knowledge of..