Problems related to the flow management of a flexible manufacturing system (FMS) are here formulated in terms of combinatorial optimization. The authors consider a system consisting of several multitool automated machines, each one equipped with a possibly different tool set and linked to each other by a transportation system for part moving. The system operates with a given production mix. The focused flow-management problem is that of finding the part routings allowing for an optimal machine workload balancing. The problem is formulated in terms of a particular capacity assignment problem. With the proposed approach, a balanced solution can be achieved by routing parts on a limited number of different paths. Such a balancing routing can be found in polynomial time. The authors also give polynomial-time and -space algorithms for choosing, among all workload-balancing routings, the ones that minimize the global amount of part transfer among all machines.
