Parallel machine scheduling in a flexible manufacturing system

We consider the problem of assigning parts and tools on a Flexible Manufacturing System composed by W identical parallel workstations, so that the workload of the workstations is well balanced. The goal is to minimize the total number of tools needed on all workstations, including multiple copies, if any. We give a mixed integer programming formulation of this problem and a branch and cut procedure to solve it. Several computational experiences have been carried out in order to evaluate the performance of the proposed procedure.