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 i p {\displaystyle b_{ip}} , rank order clustering is an algorithm characterized by the following steps:
For each row i compute the number ∑ p = 1 m b i p ∗ 2 m − p {\displaystyle \sum _{p=1}^{m}b_{ip}*2^{m-p}}
Order rows according to descending numbers previously computed For each column p compute the number ∑ i = 1 n b i p ∗ 2 n − i {\displaystyle \sum _{i=1}^{n}b_{ip}*2^{n-i}}
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 by the following steps:
Compute the similarity coefficient s i j = n i j / ( n i j + u ) {\displaystyle s_{ij}=n_{ij}/(n_{ij}+u)} for all with n i j {\displaystyle n_{ij}} 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 r k = m a x ( s r i ∗ , s r j ∗ ) {\displaystyle s_{rk}=max(s_{ri*},s_{rj*})}
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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