4. 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 1234 1,6 2 2,3,7, 8, 9, 12, 13, 15 3 3,5,10,14 4 5 6 7 2, 7, 8, 11, 12, 13 3,5, 10, 11, 14 1,4,5,9,10 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 (10 points) b) Show that the determination of the cells can be based on the minimal spanning tree solution and show the solutions for 1 cell, 2 cells and 3 cells. (10 points)

Fig: 1