View source for Engineering:Production flow analysis

{{Short description|Concept in operations management & industrial engineering}}
In [[Social:Operations management|operations management]] and [[Industrial engineering|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>b_{ip}</math>, Rank Order Clustering<ref>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</ref> is an algorithm characterized by the following steps:

# For each row i compute the number <math>\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>\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<ref>Adapted from MCauley, Machine grouping for efficient production, Production Engineer 1972 http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04913845</ref> by the following steps:

# Compute the similarity coefficient <math>s_{ij}=n_{ij}/(n_{ij}+u)</math> for all  with <math>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>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==
{{Reflist}}

[[Category:Industrial engineering]]

{{Sourceattribution|Production flow analysis}}