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

1.For each row i compute the number ${\displaystyle \sum _{p=1}^{m}b_{ip}*2^{m-p}}$

2.Order rows according to descending numbers previously computed

3.For each column p compute the number ${\displaystyle \sum _{i=1}^{n}b_{ip}*2^{n-i}}$

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[2] by the following steps:

1.Compute the similarity coefficient ${\displaystyle s_{ij}=max(n_{ij}/n_{i},n_{ij}/n_{j})}$ for all with ${\displaystyle n_{ij}}$ being the number of products that need to be processed on both machine i and machine j

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, ${\displaystyle s_{rk}=max(s_{ri*},s_{rj*})}$

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.

## References

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 http://www.tandfonline.com/doi/abs/10.1080/00207548008919662#.UeAI5eGLe1E
2. Adapted from MCauley, Machine grouping for efficient production, Production Engineer 1972 http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04913845