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 , rank order clusteringKing, 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 is an algorithm characterized by the following steps:
For each row i compute the number Order rows according to descending numbers previously computed For each column p compute the number 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 for all with 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, 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.
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