We consider the problem of scheduling permanent jobs on related machines in an on-line fashion. We design a new algorithm that achieves the competitive ratio of $3+\sqrt{8}\approx 5.828$ for the deterministic version, and $3.31/\ln 2.155 \approx 4.311$ for its randomized variant, improving the previous competitive ratios of 8 and $2e\approx 5.436$. We also prove lower bounds of 2.4380 on the competitive ratio of deterministic algorithms and 1.8372 on the competitive ratio of randomized algorithms for this problem.