Performance guarantees for scheduling algorithms under perturbed machine speeds

We study two local search algorithms and a greedy algorithm for scheduling. The worst-case performance guarantees are well-known but seem to be contrived and too pessimistic for practical applications. For unrestricted machines, Brunsch et al. (2013) showed that the worst-case performance guarantees of these algorithms are not robust if the job sizes are subject to random noise. However, in the case of restricted related machines the worst-case bounds turned out to be robust even in the presence of random noise. We show that if the machine speeds rather than the job sizes are perturbed, one obtains smaller bounds for the performance guarantees also for restricted machines thus yielding a stronger result.