Semi On-Line Scheduling Problem for Maximizing the Minimum Machine Completion Time on Two Uniform Machines

Abstract

In this paper, we consider a semi on-line version on two uniform machines Mi, i = 1,2, where the processing time of the largest job is known in advance. A speed si(s1 = 1, 1≤ s2 = s) is associated with machine Mi. Our goal is to maximize the Cmin. We give a Cmin 2 algorithm and prove its competitive ratio is at most \(\frac{2s+1}{s+1}\). We also claim the Cmin 2 algorithm is tight and the gap between the competitive ratio of Cmin 2 algorithm and the optimal value is not greater than 0.555. It is obvious that our result coincides with that given by He for s = 1.