We study problems of scheduling jobs on related machines so as to minimize
the makespan in the setting where machines are strategic agents. In this
problem, each job $j$ has a length $l_{j}$ and each machine $i$ has a private
speed $t_{i}$. The running time of job $j$ on machine $i$ is $t_{i}l_{j}$. We
seek a mechanism that obtains speed bids of machines and then assign jobs and
payments to machines so that the machines have incentive to report true speeds
and the allocation and payments are also envy-free. We show that