There is a set J of n jobs, and a set M of m machines. Each job j has a xed size sj 0 and may only be assigned to some machine in a xed set of...

There is a set J of n jobs, and a set M of m machines. Each job j has a fixed size sj ≥ 0 and may only be assigned to some machine in a fixed set of machines Mj ⊆ M. The goal is to assign each job j to a machine in Mj so that the maximum load on any machine will be as small as possible.