Engineering:Production flow analysis

From HandWiki

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 [math]\displaystyle{ b_{ip} }[/math], Rank Order Clustering[1] is an algorithm characterized by the following steps:

  1. For each row i compute the number [math]\displaystyle{ \sum_{p=1}^{m}b_{ip}*2^{m-p} }[/math]
  2. Order rows according to descending numbers previously computed
  3. For each column p compute the number [math]\displaystyle{ \sum_{i=1}^{n}b_{ip}*2^{n-i} }[/math]
  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[2] by the following steps:

  1. Compute the similarity coefficient [math]\displaystyle{ s_{ij}=n_{ij}/(n_{ij}+u) }[/math] for all with [math]\displaystyle{ n_{ij} }[/math] 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, [math]\displaystyle{ s_{rk}=max(s_{ri*},s_{rj*}) }[/math]
  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.


  1. King, J. R., Machine-component grouping in production flow analysis: an approach using a rank order clustering algorithm, International Journal of Production Research, Vol.18 1980
  2. Adapted from MCauley, Machine grouping for efficient production, Production Engineer 1972