Production flow analysis

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 $b_$, rank order clustering is an algorithm characterized by the following steps:

# For each row i compute the number $\sum_^b_*2^$
# Order rows according to descending numbers previously computed
# For each column p compute the number $\sum_^b_*2^$
# 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 proceedsAdapted from MCauley, Machine grouping for efficient production, Production Engineer 1972 https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04913845 by the following steps:

# Compute the similarity coefficient $s_=n_/(n_+u)$ for all with $n_$ 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, $s_=max(s_,s_)$
# 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

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Industrial engineering