A technique for finding economical part-machine families in cellular manufacturing environments is described. The technique is based on trying to optimize, in an economic sense, machine replication and part sub-contracting strategies. An important feature of this work is that it allows management and facility designers to place limits on the sizes of the part-machine families. The most recent developments in graph approximations are exploited. Computational results on a number of benchmark problems from the group technology literature are presented. These results indicate the promise of the proposed technique.