Electro produces 15 electronic parts on 10 machines. The company wants to group the machines into cells designed to minimize the “dissimilarities” among the parts processed in each cell. A measure of “dissimilarity,” dij, among the parts processed on machines i and j can be expressed as dij = 1 -

nij nij + mij where nij is the number of parts shared between machines i and j, and mij is the number of parts that are used by either machine i or machine j only.

The following table assigns the parts to machines:

Machine Assigned parts 1 1, 6 2 2, 3, 7, 8, 9, 12, 13, 15 3 3, 5, 10, 14 4 2, 7, 8, 11, 12, 13 5 3, 5, 10, 11, 14 6 1, 4, 5, 9, 10 7 2, 5, 7, 8, 9, 10 8 3, 4, 15 9 4, 10 10 3, 8, 10, 14, 15

(a) Express the problem as a network model.

(b) Show that the determination of the cells can be based on the minimal spanning tree solution.

(c) For the data given in the preceding table, construct the two- and three-cell solutions.