Generating a binary product-machines matrix (1 if a given product requires processing in a given machine, 0 otherwise)
Methods differ on how they group together machines with products. These play an important role in designing
manufacturing cells.
Rank order clustering
Given a binary product-machines n-by-m matrix , rank order clustering[1] is an algorithm characterized by the following steps:
For each row i compute the number
Order rows according to descending numbers previously computed
For each column p compute the number
Order columns according to descending numbers previously computed
If on steps 2 and 4 no reordering happened go to step 6, otherwise go to step 1
Stop
Similarity coefficients
Given a binary product-machines n-by-m matrix, the algorithm proceeds[2] by the following steps:
Compute the similarity coefficient for all with being the number of products that need to be processed on both machine i and machine j, u comprises the number of components which visit machine j but not k and vice versa.
Group together in cell k the tuple (i*,j*) with higher similarity coefficient, with k being the algorithm iteration index
Remove row i* and column j* from the original binary matrix and substitute for the row and column of the cell k,
Go to step 2, iteration index k raised by one
Unless this procedure is stopped the algorithm eventually will put all machines in one single group.