Semi on-line scheduling problem for maximizing the minimum machine completion time on two uniform machines

In this paper, we consider a semi on-line version on two uniform machines M i , i = 1,2, where the processing time of the largest job is known in advance. A speed s i (s 1 = 1, 1≤ s 2 = s) is associated with machine M i . Our goal is to maximize the C min. We give a C min 2 algorithm and prove its competitive ratio is at most 2s+1/s+1. We also claim the C min 2 algorithm is tight and the gap between the competitive ratio of C min 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. © Springer Science + Business Media, Inc. 2006.