Semi-on-line multiprocessor scheduling with given total processing time

We are given a set of identical machines and a sequence of jobs, the sum of whose weights is known in advance. The jobs are to be assigned on-line to one of the machines and the objective is to minimize the makespan. An algorithm with performance ratio 1.6 and a lower bound of 1.5 is presented. These results improve on the recent results by Azar and Regev, who proposed an algorithm with performance ratio 1.625 for the less general problem that the optimal makespan is known in advance.