# Engineering:Production flow analysis

From HandWiki

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

- Classification of machines
- Technological cycles information control
- 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:

- For each row i compute the number [math]\displaystyle{ \sum_{p=1}^{m}b_{ip}*2^{m-p} }[/math]
- Order rows according to descending numbers previously computed
- For each column p compute the number [math]\displaystyle{ \sum_{i=1}^{n}b_{ip}*2^{n-i} }[/math]
- 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 [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.
- 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, [math]\displaystyle{ s_{rk}=max(s_{ri*},s_{rj*}) }[/math]
- 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

- ↑ 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
- ↑ Adapted from MCauley, Machine grouping for efficient production, Production Engineer 1972 http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04913845

Original source: https://en.wikipedia.org/wiki/Production flow analysis.
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