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Machine–part cell formation through visual decipherable clustering of self-organizing map

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1
Machine-Part cell formation through visual decipherable clustering of Self Organizing Map
Manojit Chattopadhyay
1
,Surajit Chattopadhyay
2
, Pranab K. Dan
3
1,2
Department of Computer Application, Pailan College of Management & Technology, Kolkata-700104
3
Industrial Engineering, School of Engineering & Technology, West Bengal University of Technology, Kolkata 700 064
1
chattomanojit@yahoo.com,
2
surajit_2008@yahoo.co.in
3
dan1pk@hotmail.com
ABSTRACT
Machine-part cell formation is used in cellular manufacturing in order to process a large variety, quality, lower work in process levels, reducing manufacturing lead-time and customer response time while retaining flexibility for new products. This paper presents a new and novel approach for obtaining machine cells and part families. In the cellular manufacturing the fundamental problem is the formation of part families and machine cells. The present paper deals with the Self Organising Map (SOM) method an unsupervised learning algorithm in Artificial Intelligence, and has been used as a visually decipherable clustering tool of machine-part cell formation. The objective of the paper is to cluster the binary machine-part matrix through visually decipherable cluster of SOM color-coding and labelling via the SOM map nodes in such a way that the part families are processed in that machine cells. The Umatrix, component plane, principal component projection, scatter plot and histogram of SOM have been reported in the present work for the successful visualization of the machine-part cell formation. Computational result with the proposed algorithm on a set of group technology problems available in the literature is also presented. The proposed SOM approach produced solutions with a grouping efficacy that is at least as good as any results earlier reported in the literature and improved the grouping efficacy for 70% of the problems and found immensely useful to both industry practitioners and researchers.
Key words:
machine-part cell formation, cellular manufacturing, self organising map, component plane, u-matrix, pc projection, histogram, scatterplot,
visually decipherable cluster
1. Introduction
Cell formation has been emerged as a production strategy in implementing cellular manufacturing and consists of decomposing the shop in distinct manufacturing cells, each one dedicated to the processing of a family of similar part types. Group Technology (GT) as defined by Burbidge (1979) is the management philosophy that believes similar activities should be done similarly. Cellular Manufacturing (CM) is the application of GT. A manufacturing cell is a cluster of dissimilar machines placed in close proximity and dedicated to the manufacture of a family of parts. In the design of a CM system,
2 similar parts are grouped into families and associated machines into groups as cell formation problem(CF), so that one or more part families can be processed within a single machine group. CM has been proven as a methodology to lower work in process levels, reducing production lead-time while retaining flexibility for new products. The potential benefits include reductions in material handling, setup times, lot sizes, work-in-process inventories and lead times and increase in throughput, productivity and quality (Wemmerlov and Hyer, 1989). In CF, a binary machine/part matrix of
pm
dimension is usually provided. The m rows indicate m machines and the p columns represent p parts. Each binary element in the
pm
matrix indicates a relationship between parts and machines where ‘‘1’’ or ‘‘0’’ represents that the pth part should be worked on the mth machine or otherwise. The matrix also displays all similarities in parts and machines. The objective is to group parts and machines in a cell based on their similarities. If there are no ‘‘1’’ outside the diagonal block and no ‘‘0’’ inside the diagonal block then it is called as perfect result. That is, the two cells are completely independent where each part family will be processed only within a machine group. On the other hand, if in the machine/part matrix there is ‘‘1’’ outside the diagonal block then this is called an ‘‘exceptional part’’ because it can work on two or more machine groups, and corresponding machine is called a ‘‘bottleneck machine’’ as it processes two or more part families. There may also be a ‘‘0’’ inside the diagonal block which is called a ‘‘void’’. In general, an optimal result for a machine/part matrix by a CF clustering method is desired to satisfy the following two conditions: (a) To minimize the number of 0s inside the diagonal blocks (i.e., voids); (b) To minimize the number of 1s outside the diagonal blocks (i.e., exceptional elements). There are many cell formation approaches in the literature viz., visual inspection, classification and coding (Singh and Rajamani, 1996), Similarity coefficients(Yin and Yasuda, 2006), Cluster Analysis (Chu and Tsai,1990), array manipulation (Murugan and Selladurai, 2007), Graph Theoretic Approach (Mukhopadhyay, 2009),mathematical programming (Kioon
et al
., 2007), Heuristic algorithms (Mukattash
et al
., 2002), Soft computing technique (Jang
et al
., 2002), Fuzzy clustering (Li, 2007;Tavakkoli-Moghaddam,2007), Metaheuristic techniques like simulated annealing (Lin,2008), genetic algorithm (Pillai
et al
., 2008; Tay and Ho, 2008), Tabu Search (Wang
et al
., 2006), combinatorial search methods(Jeffrey Schaller, 2005), Ants Colony Systems (Kao
3 and Li ,2008), ART1(Yang and Yang,2008;Carpenter and Grossberg, 1987), competitive learning rule (Malave and Ramachandran,1991), Kohonen’s self-organizing feature maps (Venkumar P and Haq AN, 2006a,2006b), Fuzzy ART neural network(Suresh
et al
.,1999). Recently, in most neural network models, competitive learning algorithm (Malave and Ramachandran, 1991) and SOM (chattopadhyay
et al
., 2009; Guerrero
et al
., 2002; Venugopal and Narendran, 1994) has been applied in GT. Since the competitive learning network is an unsupervised approach, it is very suitable for use in GT as the cell formation is a NP complete problem. The robustness of those SOM applications allows it to handle the data visualisation and classification effectively which provides the motivation in applying this approach for exploring into the analysis of the data problem. In this paper, an attempt is made to use the binary part-machine matrices which are obtained from artificially generated (problem#1 in table 1) and literature (Table 3) to group the parts into part families and machines into machine cells with an idea to maximize the proposed performance measure by introducing a cluster analysis approach using the self organizing map (SOM) proposed by Kohonen (2001). The SOM is a non-linear statistical technique for transforming and visualising multi-dimensional data in a lower-dimensional map (Kohonen, 1998; Mancuso, 2001). The SOM technique based solutions have been designed for problems involving visualisation and cluster analysis (Flexer, 2001; Kiang, 2001) and implemented for many applications for exploratory data analysis. SOM clustering with color coding is a way to group data, according to its properties (Kaski and Kohonen, 1998; Kaski, 2001). The SOM is a competitive learning neural network model, which preserve the distribution and topology information of input data in a low dimension map grid. After mapping, the preserved information can be extracted from which many valuable characteristics of srcinal data can be obtained, such as distribution, cluster, component correlation etc. The novelty of this proposed approach is that the clustering of machine part cell formation can be visually decipherable and thereby cell formation can be studied in depth in a simple and robust way. All experiments, in the present study were performed in the MATLAB programming language using the SOM MATLAB Toolbox (Vesanto et al., 2000).
4
2. Performance Measure
The grouping efficiency and grouping efficacy are two popular grouping measures because they are simple to implement and generate block diagonal matrices. Grouping efficiency was first proposed by Chandrasekharan and Rajagopolan (1989). It incorporates both machine utilization and inter-cell movement and is defined as the weighted sum of two functions
η1 and η2
.
The Grouping efficiency (η) is a weighted average of two functions η1 and η2.
)5...(211
r r
6...blocksdiagonalin theelementsof number Total
blocksdiagonalin theonesof Number
1
)7...(blocksdiagonal-off in the elementsof number Total
blocksdiagonal-off in the zeroesof Number
2
In equation (5) r is a weighting factor that lies between zero and one (0<r<1) and its value
is decided depending on the size of the matrix. A higher value of η is supposed to
indicate better clustering. One drawback of grouping efficiency is the low discriminating capability (i.e. the ability to distinguish good quality grouping from bad). To overcome the low discriminating power of grouping efficiency between well-structured and ill-structured incidence matrices, Kumar and Chandrasekharan (1990) proposed another measure, which they call grouping efficacy. Unlike grouping efficiency, grouping efficacy is not affected by the size of the matrix. The objective of Eq.(8) is to reach the minimization of the exceptional parts and maximization of the number of parts in cells simultaneously.
The grouping efficacy can be defined as Grouping efficacy
=µ=
)8...(NNNN
In01Out11
Where N
1
total number of 1’s in matrix;
Out1
N
total number of 1’s outside the diagonal blocks;
In0
N
total number of 0’s inside the diagonal blocks. The closer the grouping efficacy is to 1, the better will be the grouping.
In the present work we have used the grouping efficacy for measuring the performance of cell formation. The grouping efficacy for the matrices obtained from the literature after
5 deploying SOM approaches are compared with the results as reported. The comparisons are given in the table 3 in Appendices.
3. Overview of Self Organizing Map Learning Algorithm
Artificial Neural Networks (ANN) is computer algorithm, inspired by the functioning of the nervous system of the human brain, capable of learning from data and generalizing. This learning process can be described as supervised or unsupervised learning. In the supervised learning process, the ANN is shown several input-output patterns during training to enable the trained ANN to make generalizations based on the training data and to correctly produce output patterns based on new input (Jain et al., 1996). The SOM-algorithm is based on unsupervised learning, which means that the desired output is not known a priori. The goal of the learning process is not to make predictions, but to classify data according to their similarity. In the neural network architecture Kohonen proposed (Kohonen, 1998), the classification is done by plotting the data in n-dimensions onto a, usually, two-dimensional grid of units in a topology preserving manner. The former means that similar observations are plotted in each others neighborhood on the 2-D-grid. The neural network consists of an input layer and a layer of neurons. The neurons or units are arranged on a rectangular or hexagonal grid and are fully interconnected. Each of the input vectors is also connected to each of the units. The learning algorithm applied to the network (Kohonen, 2001; Kaski, 1997): An input vector is shown to the network; the Euclidean distances between the considered input vector
x
i
and all of the reference vectors
m
i
are calculated.
)1...(,...,2,1,,...,
2,1
N inT n x x xi x
)2...(,...,2,1,,...,
2,1
N inT nmmmim
The connection between the two layers represents a map of real high-dimensional data onto a low-dimensional (usually 2-D) display of the nodes. In the training process, The best matching unit m
c
, the unit with the greatest similarity with the considered input vector, is chosen according to:
)3...(m-xminmx
c
i
i

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