We consider the problem of scheduling n independent jobs on m unrelated parallel machines. Each job has to be processed by exactly one machine, processing job j on machine i requires p; j time units, and the objective is to minimize the makespan, ie the maximum job completion time. We focus on the caSe when n is fixed and develop a fully polynomial approximation scheme whose running time depends only linearly on n. In the second half of the paper we extend this result to a variant of the problem, where processing job j on machine i also incurs a cost of cij, and thus there are two optimization criteria: makespan and cost. We show that for any fixed m, there is a fully polynomial approximation scheme that, given values T and C, computes for any fixed E> 0 a schedule in O (n) time with makespan at most (1+ e) T and cost at most (1+ e) C, if there exists a schedule of makespan T and cost C.