Production flow analysis

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 , Rank Order Clustering^[1] is an algorithm characterized by the following steps:

1. For each row i compute the number
2. Order rows according to descending numbers previously computed
3. For each column p compute the number
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

Although Rank Order Clustering is one of the widely used production flow algorithms, there are some limitations to this method such as lack of consideration of real-world manufacturing data during clustering^[2] and if the initial matrix is rearranged, then the resulting product-machine matrix would be different. To overcome these drawbacks, a robust Modified Rank Order Clustering algorithm was proposed by Nagdev Amruthnath^[3] in 2016^[2].

Modified Rank Order Clustering

Modified Rank Order Clustering (MROC) is a weight based rank order clustering approach which was proposed in 2016, to facilitate the needs of the real-world manufacturing environment. In this approach, machine performance data (such as cycle time, OEE and KPI's) and part information (such as volume) could be normalized and used as weights for machines and parts^[2]. The initial machine and part matrix are set up based on the order of weights in descending order. By setting up the matrix using this approach, only one resulting final matrix is obtained and manufacturing data is embedded as weights overcoming the drawbacks of rank order clustering. MROC^[2] algorithm is characterized by the following steps:

1. Develop weight factors for part and machines and
2. If there are more than weight factors then, convert each weight factor into percentage and then sum it. Else assign the weight to the part numbers
3. Create a n*m matrix (binary number for part and machine). Where n is parts and m is machines
4. Rearrange the parts and machines in descending order based on weights
5. For each row of i compute,
6. Rearrange the rows in descending order based on the computed numbers
7. For each row of j compute,
8. Rearrange the columns in descending order based on the computed numbers
9. Repeat step 1 until there is no change is observed in step 3 and 5
10. Stop

Similarity coefficients

Given a binary product-machines n-by-m matrix, the algorithm proceeds^[4] by the following steps:

1. 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.
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,
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