Production flow analysis

In operations management and industrial engineering, production flow analysis refers to methods which share the following characteristics:


 * 1) Classification of machines
 * 2) Technological cycles information control
 * 3) 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 $$b_{ip}$$, rank order clustering is an algorithm characterized by the following steps:


 * 1) For each row i compute the number $$\sum_{p=1}^{m}b_{ip}*2^{m-p}$$
 * 2) Order rows according to descending numbers previously computed
 * 3) For each column p compute the number $$\sum_{i=1}^{n}b_{ip}*2^{n-i}$$
 * 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 $$s_{ij}=n_{ij}/(n_{ij}+u)$$ for all  with $$n_{ij}$$ 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, $$s_{rk}=max(s_{ri*},s_{rj*})$$
 * 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.