In this paper, we investigate a semi-on-line version for a special case of three machines M1, M2, M3 where the processing time of the largest job is known in advance. A speed si(s1 = s2 = 1, 1 ≤ s3 = s) is associated with machine Mi. Our goal is to maximize the C min — the minimum workload of three machines. We give a C min 3 algorithm and prove its competitive ratio is [Formula: see text] and the algorithm is the best possible for 1 ≤ s ≤ 2. We also claim the competitive ratio of algorithm C min 3 is tight.
Semi-on-line scheduling problems for maximizing the minimum machine completion time