Semi-on-line scheduling with ordinal data on two uniform machines

We investigate the problem of semi-on-line scheduling of jobs on two uniform machines where the order of jobs by their processing times is known as a priori. We propose an algorithm for any machine speed ratio s greater than or equal to 1. We also present a comprehensive lower bound, which is a piecewise function of s. The algorithm is optimal for the majority of s is an element of [1, infinity). The total length of the intervals of s where the competitive ratio does not match the lower bound is less than 0.7784 and the big est gap between them never exceeds 0.0521. (C) 2001 Elsevier Science B.V. All rights reserved.