Scheduling on (Un-)Related Machines with Setup Times

We consider a natural generalization of scheduling n jobs on m parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches from processing jobs of one class to jobs of a different class. During such a setup, a machine cannot process jobs and the duration of a setup may depend on the machine as well as the class of the job to be processed next. For this problem, we study approximation algorithms for nonidentical machines. We develop a polynomial-time approximation scheme for uniformly related machines. For unrelated machines we obtain an O(log n + log m)-approximation, which we show to be optimal (up to constant factors) unless NP ⊂ RP. We also identify two special cases that admit constant factor approximations.