Biomass partitioning

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

1.Classification of machines

2.Technological cycles information control

3.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 $b_{ip}$, Rank Order Clustering is an algorithm characterized by the following steps:

1.For each row i compute the number $\sum _{p=1}^m{b}_{ip}*2^{m-p}$

2.Order rows according to descending numbers previously computed

3.For each column p compute the number $\sum _{i=1}^n{b}_{ip}*2^{n-i}$

4.Order columns according to descending numbers previously computed

5.If on steps 2 and 4 no reordering happened go to step 6, otherwise go to step 1

6.Stop

Similarity Coefficients

Given a binary product-machines n-by-m matrix, the algorithm proceeds by the following steps:

1.Compute the similarity coefficient $s_{ij}=max(n_{ij}/n_i,n_{ij}/n_j)$ for all with $n_{ij}$ being the number of products that need to be processed on both machine i and machine j

2.Group together in cell k the tuple (i*,j*) with higher similarity coefficient, with k being the algorithm iteration index

3.Remove row i* and column j* from the original binary matrix and substitute for the row and column of the cell k, $s_{rk}=max(s_{ri*},s_{rj*})$

4.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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