Production flow analysis

Rank Order Clustering

Given a binary product-machines n-by-m matrix b i p , Rank Order Clustering is an algorithm characterized by the following steps:

1. For each row i compute the number ∑ p = 1 m b i p ∗ 2 m − p
2. Order rows according to descending numbers previously computed
3. For each column p compute the number ∑ i = 1 n b i p ∗ 2 n − i
4. Order columns according to descending numbers previously computed
5. If on steps 2 and 4 no reordering happened go to step 6, otherwise go to step 1
6. Stop

Similarity coefficients

Given a binary product-machines n-by-m matrix, the algorithm proceeds by the following steps:

1. Compute the similarity coefficient s i j = n i j / ( n i j + u ) for all with n i j 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.
2. Group together in cell k the tuple (i*,j*) with higher similarity coefficient, with k being the algorithm iteration index
3. Remove row i* and column j* from the original binary matrix and substitute for the row and column of the cell k, s r k = m a x ( s r i ∗ , s r j ∗ )
4. 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.