The on-line multiprocessor scheduling problem with known sum of the tasks

In this paper we investigate a semi on-line multiprocessor scheduling problem. The problem is the classical on-line multiprocessor problem where the total sum of the tasks is known in advance. We show an asymptotic lower bound on the performance ratio of any algorithm (as the number of processors gets large), and present an algorithm which has performance ratio at most root6+1/2<1.725 for any number of processors. When compared with known general lower bounds, this result indicates that the information on the sum of tasks substantially improves the performance ratio of on-line algorithms.