sdarticle important cell.pdf

7/29/2019 sdarticle important cell.pdf

1/12

Computers ind. Eng ng Vol. 12, No. 2, pp. 131-142, 1987 0360-8352/87 $3.00 + 0.00Printed in Great Britain Pergamon Journals Ltd

C E L L F O R M A T I O N I N G R O U P T E C H N O L O G Y :A N E W A PPRO A CH

S . K . K H A T OR a n d S . A . IRANIIndustrial and Management Systems Engineering, University of South Florida,Tampa, FL 33620, U.S.A.

(Received fo r publication 27 August 1986)Abs tra ct- -In the U.S .A. , mach ine-component cluster formation is considered a poor alternativeto classification and coding as a planning tool for Cellular Manufacture. This paper introduces aheuristic procedure, the Occupancy Value method, for identifying clusters in a mac hine-c ompo-nent matrix created from route card data. A unique feature of this method is that it progressivelydevelo ps block diagonalization starting from the northwest corner of the matrix. The flexibility ofthe procedure is illustrated in detail through a small example. Another large matrix is analyzed todemonstrate the inherent simplicity of the method. Further extensions of this method toimplement the manufacturing cells from these initial clusters are discussed.

INTRODUCTIONGroup Technology (GT) is an organizational principle that promises widespread benefitsto small medium batch manufacturers. There are numerous modes of application tothis important concept. One approach is the analysis of the material flows and machiningrequirements of the components constituting a company's products. Families of compo-nents are identified based on similar machine requirements. These machines are broughttogether into groups (called manufacturing cells) which are further equipped with othertypes of compatible equipment necessary to restrict the flow of those families of partswithin the cells. Recognizing the contribu tion that GT can make to the implementationof Computer Integrated Manufacture (CIM), Merchant [1] says, "the appropIiate initialstep, to lay a sound foundation for the gradual evolution of a factory to full computercontrol, is to institute group technology cellular organization".

APPROACHES TO FAMILY AND CELL FORMATIONM eth od 1: classif ication and coding

Each o f the different design attributes of a componen t e.g. dimensions, overall shape,raw material characteristics, accuracy, surface finish, type of internal or external shapefeature, etc. are represented by a single code number. Families of components wouldpossess identical code numbers. The machine tools are selected by analyzing the routecards of those components. This method is prevalent in the U.S. even though it is anindirect approach to the c reation of manufacturing cells. Much time and effort goes intoaccurate coding and the creation of an elaborate data base which provides a weakconnection between component features and machine tool grouping.Method 2 : mach ine -componen t group ana lys i s

By virtue of using route card data directly, this method is quick and sufficientlyaccurate to indicate to the company the scope for rearranging the shop floor intoindependent manufacturing cells. The basic input data is the list of machines that eachcomp onen t visits, ignoring the exact visitation sequence of those machines. This methodis not a one step solution to the creation of cells. It is part of a more comprehensivesystem design tool, called Production Flow Analysis [2]. The same principles can beextended to the planning of Flexible Manufacturing Systems.

131


2/12

132 S. K. KHATOR nd S. A. IRANIUsing route card data, a machine-component matrix is prepared, in which the rowsrepresen t machines and the columns represent components, or vice-versa. If a cell entryAij = 1, it indicates that machine "i" makes component "j ", or, if Aq = 0, there is norelation between the two. So, the complete matrix is a random array of O's and l's. Theclustering algori thms which this paper discusses rely on the essential assumption that the

machines and components can be partitioned into matched groups of machines andcomponents . These will be represented as clusters along the diagonal of the matrix. Thisvisual presentation of the possible constitution of the cells is the key merit ofthese methods. Some measure of common machine requirements among clusters willbe directly indicated by the relative dispersion of entries along the diagonal of thematrix.

EXISTING APPROACHES TO MATRIX ANALYSIS FOR CLUSTER FORMATIONWhile the literature yielded nearly 20 approaches to cell formation, this paper con-

cerns an analysis of only three methods:(a) Rank Order Clustering Algorithm [3](b) Direct Clustering Algorithm [4](c) Module Synthesis (Group Analysis Phase of Production Flow Analysis) [5].

Ra nk Order C lustering AlgorithmThe Rank Order Clustering Algorithm (ROC) [3] represents route card data as a

binary matrix. Using a positional weighting technique for the "1" entries in the matrix,the rows and columns are alternately rearranged in order of decreasing rank. The resultis a diagonalization of the l's into several clusters. If independent machine-componentgroups do exist in the sample data provided, each machine will occur in only one cluster.Components will be uniquely assigned to any one of the clusters. Using this algorithm,the analyst can obtain a visual assessment of the machine groups and the associatedfamilies of parts simultaneously. With such an approach, a very valuable preliminaryassignment of machines can be obtained because, if a large number of machines is sharedover several clusters, plans for cellular manufacture can be shelved at the outset.

But, there are a few weaknesses in this algorithm which affect its performance, causedby two types of cell entries which prevent cluster formation and create dispersion awayfrom the diagonal. These are:(1) Exception elements. These are a few cell entries that occur outside a pair ofclusters. However, only one cluster can contain that machine, resulting in an inter-cellmove of the other components requiring that machine to complete their processing. Theoccurrence of such entries is expected but the ROC solution is disrupted, due to themethod adopted for ranking. It relies on pairwise comparisons of cell entries in theleftmost column (when ranking rows) and topmost row (when ranking columns). So ifthe positional occurrence of these elements is such that they influence the ranking, poorcluster formation will result.(2) Bottleneck machines. These are machines that are used by a large number ofcomponents. Since these components can be expected to be dispersed over more thanone cluster, such machines must appear in more than one row in the matrix. Otherwise,the ranking procedure creates large, dispersed clusters with many machines and com-ponents contained in them.The ROC Algorithm works only after these two types of elements are (i) identified and(ii) suppressed after visual analysis of the initial matrix solutions. Such prior assumptionsbias the solution, especially as the algorithm must indicate exceptions and bottleneckmachines, not rely on their temporary suppression to be effective. Other drawbacks ofKing's method are:(a) An inability to analyze large matrices since the binary word lengths increase. Rowsand columns are compared pairwise increasing the number of comparisons necessary fora solution. The ranking being dependent on the positional coordinates of the entries in


3/12

Cell formation n group technology 133the matrix, the complete matrix needs to be analyzed, which increases computationaltime.

(b) Inconsistency in the number of clusters, the identity of the exceptional elementsand the machi ne-component constitution of the clusters, depending on the initial inputmatrix.

(c) Total neglect of load figures to decide the allocation of bottleneck machines amongthe clusters. King assumes that these machines can be freely duplicated if they arerequired in several clusters. He ignores the fact that some clusters would need to bemerged to optimize the utilization of those machines. This same assumption tends toview an exception more as an array-related problem. And not as one due to the non-availability of sufficient load to justify the inclusion of at least one machine in the clusterin which the component occurs.Direct Clustering Alg orithm

The Direct Clustering Algorithm (DC) [4] is a poor version of the ROC Algorithm,except that it eliminates the sensitivity of the latter to the configuration of the initialmatrix. The number of positive cell entries K in each row and column is counted. Theinput machine- compon ent matrix is rearranged with columns in decreasing order of Kbut rows in increasing order of K. So, approximate diagonalization is created and themachine-component matrix is input in the same format always to the algorithm. Other-wise, this algorithm has the same handicaps as the ROC Algorithm, and uses a limitedbinary comparison procedure for ranking, by neglecting subsequent comparisons toresolve ties in ranking. Even the approach suggested for handling large matrices suffersfrom the problems of:

(a) Deciding the allocations of components to be entered in each of the smallermatrices. They are obtained by breaking up the matrix for all the machines andcomponents, and combining machine requirements of several components into one toinclude them in further analysis.

(b) The number of entries in the rows and columns which will increase in the matricesanalyzed later, creating cluster dispersion similar to the influence of the bottleneckmachines, and exception elements.Burbidge's me thod o f mo dule synthesis in group analysis

This approach has been surprisingly ignored by researchers as an effective meth od formachine-component group formation. His basic assumption is that clusters can bedeveloped by adding machines to those making a small number of components. Amodule is defined as "a set of machines and a set of parts for which there is a highprobability that they will exist togethe r in only one group" [5]. This method succeeds inreducing a large machine-component matrix to a smaller machine-module matrix,whose size is determined only by the number of machines included in the analysis.Refinements in this method are necessary because:

(1) No algorithm is used for identifying clusters in the modul e-machine matrix.(2) Individual componen ts lose their identity in the module.(3) Excessive machine duplication occurs when it would be better to suppress some

machines from unnecessarily repeating in several modules before entering them in themachine-module matrix.(4) Choice of successive nucleus machines is made solely on the basis of minimumnumber of components that have not been modularized. (The "minimum F-Ef value"controls only one dimension of the machine-componen t matrix.) But, the routes of those

components could contain a large number of machines. This could lead to the formationof a large dispersed cluster.(5) Even though the modules are essentially small machine-component clusters, theconnect ion between successive modules is prevented. This is because no at tempt is made

to create modules from the machines, other than the nucleus machines entered in thefirst few modules.


4/12

134 S.K .. KHATOR an d S. A. IRANIT H E O C C U P A N C Y V A L U E M E T H O D

T h e O c c u p a n c y V a l u e ( O V ) m e t h o d b e i n g p r e s e n t e d i n t h is p a p e r e l im i n a t e s l im i -t a t io n s o f t h e e a r l i e r m e t h o d s b y :

( a ) C r e a t i n g c o m p a c t c l u s t e r s w i t h o u t a n y p r e l i m i n a r y a s s u m p t i o n s o r v i s u a l i d e n t i f i -c a t i o n o f e x c e p t i o n a l e l e m e n t s o r b o t t l e n e c k m a c h i n e s .

( b ) B u i l d i n g u p c l u s t e r s a l o n g t h e d i a g o n a l b y u s i n g sm a l l s e l e c t e d s e c t i o n s o f t h el a r g e r o r i g i n a l m a t r i x . T h i s a l l o w s t h e a n a l y s t fl e x i b il i ty t o r e i t e r a t e w h e n e v e r d i s p e r s i o no f c el l e n t r i e s o u t s i d e a c l u s t e r is o b s e r v e d , d u e t o t h e o c c u r r e n c e o f b o t t l e n e c km a c h i n e s . S o , g i v e n a n y s e e d o r s t a r ti n g m a c h i n e , i ts c o m p o n e n t s w i ll i n d i c a te t h e o t h e rm a c h i n e s t h a t w i ll o c c u r in th e c l u s t e r . O n l y a g o o d c h o i c e o f s e e d m a c h i n e i s r e q u i r e d .

( c) U s i ng t h e m a c h i n e - c o m p o n e n t m a t ri x o n ly as a m e a n s f o r d a t a r e p r e s e n t a t i o n a n dn o t f o r a r r a y m a n i p u l a t i o n s l ik e t h e R O C o r D C A l g o r i t h m s .

( d ) U s i n g t h e O V t o d e la y t h e e n t r y o f b o t t l e n e c k m a c h i n e s a n d c o m p o n e n t s w i t h al a r g e n u m b e r o f m a c h i n e s i n t h e i r r o u t e s i n t o t h e m a t r i x . O t h e r w i s e t h i s w i ll c r e a t e l a r g ec l u s t e r s , u s e l e s s f o r t r a n s f o r m i n g i n t o c e l l s .

( e ) S i m p l i fy i n g th e i d e n t i f ic a t i o n o f b o t h e x c e p t i o n a l e l e m e n t s a n d b o t t l e n e c km a c h i n e s b y g r o u p i n g c o r r e c t l y a ll th e m a c h i n e s w h i c h w o u l d o c c u r in o n l y o n e c l u s t e r.T h e O c c u p a n c y V a l u e ( O V ) f o r a c o m p o n e n t

T h e r o u t e o f a c o m p o n e n t , p , c o n si st s o f a se t o f m a c h i n e s 11. A l l c o m p o n e n t s v i s it in go n e o r m o r e o f t h e s e m a c h i n e s c a n b e r e p r e s e n t e d b y a s e t J . S o m e o f t h e s e c o m p o n e n t sm i g h t b e u s i n g a d d i t i o n a l m a c h i n e s , r e p r e s e n t e d b y a s e t 1 2 . T h e m a c h i n e s i n 1 1 a n d 1 2a n d c o m p o n e n t s i n J r e p r e s e n t a m a c h i n e - c o m p o n e n t s u b m a t ri x w h o s e O c c u p a n c yV a l u e i s d e f i n e d a s

E E A ij Z m jO V p - j e J i e { l l U i 2 } _ j e . I s i n c e M ] = ~ A i jm x n m n

iw h e r e m = n u m b e r o f r o w s o f t h e s u b - m a t r i x

n = n u m b e r o f c o l u m n s o f t h e s u b - m a t r ix .F o r t h e s u b - m a t ri x s h o w n b e l o w , c o m p o n e n t 1 u s es m a c h i n es A a n d B . T h e r e f o r e ,I~ = { A , B } . C o m p o n e n t s 1 t h r o u g h 5 u s e o n e o r b o t h o f t h e s e tw o m a c h i n e s . T h e r e f o r e ,J = { 1 , 2 ,3 , 4 ,5 } . T h e a d d i t io n a l m a c h i n e s r e q u i r e d b y t h e s e c o m p o n e n t s a r e m a c h i n e s Ca n d D , i . e . 12 = { C , D } .

C o m p o n e n t1 2 3 4 5

M a c h i n eA 1B 1CDM i 2

1 1 11 1 1

1 1 11 1 1

2 3 3 411 U 12 = {A , B , C , D }

J - - { 1 , 2 , 3 , 4 , 5 }m = n u m b e r o f r o w s in t h e s u b - m a t r i x = 4n = n u m b e r o f c o l u m n s in t h e s u b - m a t r i x = 5

Z ~ = 2 + 2 + 3 + 3 + 4 = 1 4j e J


5/12

C e l l fo r m a t i o n i n g r o u p t e c h n o l o g yT h e r e f o r e , t h e O c c u p a n c y V a l u e f o r C o m p o n e n t 1 = O V1

135

- - j e j - - _ _ 1 4 _ 0 . 7m x n 4 x 5

B a s i s o f t h e O V m e t h o dT h e m e t h o d s ta r ts t o r e a r r a n g e a n i ni ti al m a c h i n e - c o m p o n e n t m a t r ix b y i nt r o d u c in g a

c o m p o n e n t i n to th e n o r t h w e s t c o r n e r o f t h e n e w m a c h i n e - c o m p o n e n t m a t r ix . A c o m -p o n e n t w i t h t h e s m a l l e s t m a c h i n e u s a g e v a l u e i s s e l e c t e d fi rs t a n d t h e m a c h i n e ( s ) u s e d f o ri ts p r o c e s s i n g a r e b r o u g h t i n t o t h e n e w m a t r i x . T h e r e m a i n i n g o p e r a t i o n s o f a ll t h ec o m p o n e n t s t h a t u s e o n e o r m o r e o f th e s e m a c h i n e s is d e c r e a s e d a c c o r d i n g l y . A t t h i sp o i n t a n e w c o m p o n e n t h a v i n g a m i n i m u m n u m b e r o f r e m a i ni n g m a c h i n e s is b r o u g h ti n t o t h e n e w m a t r i x . T h i s n e w c o m p o n e n t w i l l i n d i c a t e t h e n e w m a c h i n e ( s ) t o e n t e r t h em a t r ix . T i e s f o r m o r e t h a n o n e c o m p o n e n t h a v in g t he s a m e n u m b e r o f r e m a i n i n gm a c h i n e s a r e b r o k e n b y c a lc u l a ti n g t h e i r O c c u p a n c y V a l u e ( O V ) ( a s e x p l a i n e d in t h en e x t s e c t i o n ) . A h i g h e r o c c u p a n c y v a lu e w il l m e a n a d e n s e m a t r ix . T h e r e p e a t e da p p l i c a t i o n o f th i s m e t h o d w i ll r e s u l t i n t h e d i a g o n a l i z a t io n o f th e m a c h i n e - c o m p o n e n tm a t r ix . A d o w n w a r d f lo w o c c u r s w h e n m o r e m a c h i n e ty p e s ar e a d d e d a n d h o r i z o n t a lf lo w a s m o r e c o m p o n e n t s a r e a d d e d . I f i n d e p e n d e n t c l u s t e rs e x is t , t h is m e t h o d w il lp e r f o r m a s w e l l a s t h e R O C A l g o r i t h m [ 3 ] . I t s a c t u a l m e r i t s l i e i n i t s a b i l i t y t o f o r mc l u s t e r s , a n d t o i n d i c a t e e x c e p t i o n s a n d b o t t l e n e c k m a c h i n e s ( i . e . a m a c h i n e w i t h h i g hu s a g e v a l u e ) d i r e c t l y , as th e e x a m p l e p r o b l e m s w i ll s h o w . S i n c e th e m e t h o d p r o g r e s s i v e l yc r e a t e s a n e w m a c h i n e - c o m p o n e n t m a t r i x w i t h c l u s t e r s , i t a l l o w s r e s t r i c t e d m a c h i n ed u p l i c a t i o n t o s o l v e th e p r o b l e m o f b o t t l e n e c k m a c h i n e s i n g e tt in g i n d e p e n d e n t c e ll s.S t e p s i n th e O V h e u r i st ic

( 1 ) D e v e l o p a n o r i g i n a l m a c h i n e - c o m p o n e n t m a t r i x c o n s i s t i n g o f l ' s a n d O ' s . E a c he n t r y i n c e l l ( i , j ) w i ll b e 1 i f m a c h i n e i is u s e d i n t h e p r o c e s s i n g o f c o m p o n e n t j , w i ll b ez e r o o th e r w i s e . F o r m a n o t h e r i n i t i a l m a c h i n e - c o m p o n e n t m a t r ix i d e n ti c al t o t h e o r ig i na lm a t r i x .

( 2 ) F o r e a c h c o m p o n e n t j i n t h e i n it ia l m a t r i x fi n d t h e t o t a l n u m b e r o f m a c h i n e s u s e d( M ) .

( 3 ) S c a n t h e c o m p o n e n t li st f o r s e l e ct i n g c o m p o n e n t ( s ) w i t h th e m i n i m u m n u m b e r o f( r e m a i n i n g ) m a c h i n e s . ( a ) I f o n l y o n e c o m p o n e n t r e s u lt s fr o m t h e a b o v e s c a n , g o t o S t e p5 . ( b ) I f t h e r e a r e t ie s i n t e r m s o f m o r e t h a n o n e c o m p o n e n t h a v i n g t h e sa m e m i n i m u mn u m b e r o f o p e r a ti o n s , g o t o S t e p 4.

( 4 ) C a l c u l a te t h e O c c u p a n c y V a l u e f o r e a c h o f t h e c o m p o n e n t s f o u n d i n S t e p 3 ( a so u t l i n e d i n t h e p r e v i o u s s e c t i o n ) . S e l e c t t h e c o m p o n e n t w i t h t h e h i g h e s t O c c u p a n c yV a l u e . T i e s f o r t h e h i g h e st O c c u p a n c y V a l u e c a n b e b r o k e n a t r a n d o m .( 5 ) E n t e r t h e s e l e c t e d c o m p o n e n t a n d t h e m a c h i n e s u s e d i n t o t h e n e w m a t r i x .

( 6 ) U p d a t e t h e i n it ia l m a c h i n e - c o m p o n e n t m a t r i x f o r a ll t h e m a c h i n e s i n t h e f o l lo w i n gm a n n e r : C r o s s o u t th e r o w s c o n t a in i n g m a c h i n e s s e l e c t e d i n S t e p 5. F o r e a c h c o m p o n e n tr e m a i n i n g i n t h e i n it i al m a t r i x d e c r e a s e i t s M j v a l u e b y 1 i f a c r o s s e d o u t m a c h i n e w a su s e d b y t h is c o m p o n e n t .

( 7 ) E n t e r a n y a d d i t io n a l c o m p o n e n t s i n th e n e w m a t r i x i f it s M j v a lu e i s z e r o .( 8 ) If a ll m a c h i n e s a n d c o m p o n e n t s a r e e n t e r e d i n t h e n e w m a t r i x , g o t o S t e p 9.

O t h e r w i s e , g o t o S t e p 3 .( 9 ) U s i n g c e l l e n t r i e s f r o m t h e o r i g i n a l m a c h i n e - c o m p o n e n t m a t r i x a s i n p u t , c o m p l e t e

t h e n e w m a t r i x .


6/12

136Example

Ste p 1 .

M a c h i n e

S. K. KHATOR nd S. A. IRANI

T h e o r i g i n a l m a c h i n e - c o m p o n e n t m a t r ix [ O ] is s h o w n b e l o w :C o m p o n e n t

1 2 3 4 5 6 712345

11

1 11 1 11 1 1 11 1 1

1 1 1

C r e a t e a n i d e n t i c a l in i ti a l m a c h i n e - c o m p o n e n t m a t r ix [I] f o r u s e in a l l s u b s e q u e n t s t ep s .S t e p 2 . F o r e a c h c o m p o n e n t , j , i n [ I ] , s c a n i t s c o l u m n t o f i n d t h e t o t a l n u m b e r o f

m a c h i n e s i t u s e s , M j .

S t e p 3 .

S t e p 4 .

M a c h i n e

1 2 3 4 5 6 72 3 3 3 2 2 3

S c a n t h e M j v a lu e s i n t h e c o m p o n e n t l i st fo r s e l e ct in g c o m p o n e n t ( s ) w i t h t h em i n i m u m n u m b e r o f ( r em a i n i ng ) m a c h i n e s .C o n d i t i o n 3 ( a ) i s v i o l a t e d .C o n d i t i o n 3 ( b ) i s f u l fi l le d .T h r e e c o m p o n e n t s t i e w i t h M 1 = M 5 = M 6 = 2 . G o t o S t e p 4 .C a l c u l a t e t h e O c c u p a n c y V a l u e f o r e a c h c o m p o n e n t s e l e c t e d i n S t e p 3 ( b ) .T h e s u b - m a t r i c e s a n d O V c o m p u t a t i o n s a r e s h o w n b e l o w :

C o m p o n e n t 1S u b m a t r i x

C o m p o n e n t1 2 3 4 5 6 7

1 123 145 1M i 2 3 3~ m j = 1 8J

1 1 111 1 1 1 1

1 1 11 1 13 2 2 3

m = 5 n = 7 18OW l - 5 )


7/12

C e l l fo r m a t i o n i n g ro u p t e c h n o l o g yC o m p o n e n t 5

S u b m a t r i xC o m p o n e n t1 3 4 5 7

137

M a c h i n e1 1 1 1 13 1 1 1 14 1 1 15 1 1

2 3 3 2 3

~ M j = 13 m = 4J

n = 5 13OV5 - 4 ----5 - 0.65

C o m p o n e n t 6S u b m a t r i xC o m p o n e n t

1 2 3 4 6 7

M a c h i n e

S t e p 5 .S t e p 6 .

1 1 1 12 13 1 1 1 1 1 14 1 15 1 1 1 1M j 2 3 3 3 2 3

16~ m j = 1 6 m = 5 n = 6 O V 6 = 5 x 6 = 0 . 5 3 3JC o m p o n e n t 5 r e t u r n s t h e h i g h e s t O c c u p a n c y V a l u e , 0 . 6 5 .E n t e r c o m p o n e n t 5 a n d m a c h i ne s 1 a n d 4 in t o th e n e w m a c h i n e - c o m p o n e n tma t r i x [N] .The i n i t i a l ma t r i x [ I ] i s now upda t e d us i ng t he r e su l t s f rom S t e p 5 :(i ) Set al l A i j v a l u e s in t h e r o w s c o r r e s p o n d i n g t o t h e e n t e r in g m a c h i n e s z e r o ,a nd ( ii ) r e c o m pu t e a l l Mj va l ue s a s show n be l ow:

C o m p o n e n t1 2 3 4 5 6 7

M a c h i n e1 023 145M j 1

0 0 011 1 1 1 10 0 0

1 1 1 13 1 2 0 2 2

St e p 7 .S t e p 8 .

N o o t h e r c o m p o n e n t e n t e rs t h e n e w m a t ri x.M a c h i n e s 2 , 3 a n d 5 h a v e n o t y e t b e e n e n t e r e d i n t o t h e n e w m a t r i x . G o t oS t e p 3 .


8/12

138I t e r a t i o n 2

S t e p 3 .

S t e p 4 .

S t e p 5 .S t e p 6 .

S . K . K H A T OR a n d S . A . I RA N I

S c a n th e c o m p o n e n t l is t f o r n e w m i n i m u m M j v a l ue s : M 1 = M 3 = l . E a c hc o m p o n e n t r e q u i re s o n l y o n e m o r e m a c h i n e t o c o m p l e t e its r o u te . G o t oS t e p 4 .I n t h i s c a s e b o t h c o m p o n e n t s r e q u i r e t h e s a m e m a c h i n e 3 . S i n c e t h e O c c u -p a n c y V a l u e s f o r b o t h t h e c o m p o n e n t s w i ll b e e q u a l , n o O V c a l c u l a ti o n isr e q u i r e d .E n t e r a n y o n e o f th e t w o c o m p o n e n t s s e l e c t e d in S t e p 4 ( s a y 1) a n d m a c h i n e 3i n t o t h e n e w m a t r ix .S c a n t h e r o w f o r m a c h i n e 3 t o u p d a t e A 3 j a n d M j v a l u e s :

C o m p o n e n t1 2 3 4 5 6 7

M a c h i n e12345M,. 0

010 0

0 0 0O 0 O 00 0 0

1 1 1

2 0 1 0 1 1

S t e p 7 .S t e p 8 .

I t e r a t i o n 3S t e p 3 .S t e p 4 .

S t e p 5 .S t e p 6 .

C o m p o n e n t 3 e n t e r s t h e n e w m a c h i n e - c o m p o n e n t m a t r ix si nc e M 3 = 0 .M a c h i n e s 2 a n d 5 r e m a i n t o b e e n t e r e d i n t o [ N ], g o t o S t e p 3 .

M 4 = M 6 = M 7 = 1 . C o n d i t i o n 3 ( b ) i s f u l fi l le d . G o t o S t e p 4 .O c c u p a n c y V a l u e s f o r a l l t h e c o m p o n e n t s i n t h e p r e v i o u s s t e p w i l l b e t h es a m e . O n l y m a c h i n e 5 is r e q u i r e d t o c o m p l e t e t h e r o u t e s o f al l t h r e ec o m p o n e n t s .E n t e r c o m p o n e n t 4 a n d m a c h i n e 5 i n t o I N ] , si n c e it o c c u r s fi rs t i n a l e f t - t o -r i g h t s c a n o f Mj v a l u e s i n [ I ] .U p d a t e t h e m a t r i x [ O ] a s s h o w n b e l o w :

C o m p o n e n t1 2 3 4 5 6 7

M a c h i n e

M j 0

01

0 00

0 0 00 0 0 00 0 0

0 0 01 0 0 0 0 0

S t e p 7. E n t e r c o m p o n e n t s 6 a n d 7 i n t o [N ] s i n c e M 6 = M 7 = 0 .S t e p 8. M a c h i n e 2 r e m a i n s t o b e e n t e r e d . G o t o S t e p 3 .

I t e r a t i o n 4S t e p 3 - 8 . C o m p o n e n t 2 a n d m a c h i n e 2 w i l l e n t e r t h e n e w m a c h i n e - c o m p o n e n t

m a t r i x [ N ] n o w .


9/12

St e p 9 .

M a c h i n e

Cell formation in gro up technologyT h e f in a l m a c h i n e - - c o m p o n e n t m a t r i x w o u l d a p p e a r a s:

C o m p o n e n t5 1 3 4 6 7 21 1 1 11 1 11 1 1 1 1 1

1 1 1 1 1

139

Analysis o f resul tsT h i s d is c u s s io n p r e s e n t s t h e b a s ic d i f f e r e n c e b e t w e e n t h e O V m e t h o d a n d t h e R O C [3 ]a n d D C [ 4] A l g o r i th m s . A s s u m e t h a t o n l y o n e m a c h i n e o f t y p e s 1 , 2 , 4 an d 5 i s a v a i la b l e .

M a c h i n e 3 is c l e ar l y a b o t t l e n e c k m a c h i n e . A t l e a st 2 m a c h i n es o f it s t y p e s h o u l d b ea v a i l a b l e f o r t w o c l u s t e r s t o b e f o r m e d , C o m p o n e n t s 5 , 1 , a n d 3 b e l o n g t o c l u s t e r 1 .C o m p o n e n t s 6 a n d 2 b e l o n g t o cl u s te r 2 . F o u r o p e r a t i o n s r e p r e s e n t e d b y th e m a c h i n e -c o m p o n e n t p a i r s 1 - 4 , 4 - 7 , 5 - 4 a n d 5 - 7 q u a l i f y a s e x c e p t i o n o p e r a t i o n s .T h e a s s i g n m e n t s o f c o m p o n e n t s 4 an d 7 w il l d e p e n d o n w h e t h e r c a p a c i t y r e q u i r e m e n t sy i e l d a be t t e r u t i l iz a t ion fo r ma c h i ne 3 i n c l us t e r 1 o r 2 . C o m po ne n t 4 wi ll y i e l d a ne x c e p t i o n o p e r a t i o n 1 - 4 o r 5 - 4 d e p e n d i n g o n w h e t h e r i t i s a s s i g n e d t o c l u s t e r 2 o r 1 ,r e s p e c t i v e l y . S i m i l a r l y , c o m p o n e n t 7 w i l l y i e l d a n e x c e p t i o n o p e r a t i o n , 4 - 7 o r 5 - 7 ,de pe ndi ng on whe t he r i t i s a s s i gne d t o c l us t e r 2 o r 1 , r e spe c t i ve l y . One of t he f i na l c e l la s s i gnme nt s wi l l a ppe a r a s :

14

M a c h i n e 3352

* E x c e p t io n O p e r a t i o n

C o m p o n e n t5 1 3 4 6 7 2

1 *

1 1 1 11 1 1 1

1

D e m o n s t r a ti o n o f t h e O V m e th o dK i n g ' s m a t r ix f o r a 1 6 m a c h i n e -4 3 c o m p o n e n t e x a m p l e [ 3] w a s c h o s e n t o d e m o n s t r a t e

h o w t h e O V m e t h o d e a s i l y a c o m m o d a t e s t h e p r o b l e m s w h i c h t h e D C a n d R O C A l g o r -i t hms de sc r i be . F i gure 1 i s t he In i t i a l Ma t r i x . F i gure 2 is t he so l u t i on g o t by a pp l y i ng t heO V m e t h o d . F o r t h i s s m a l l m a t r i x , t h e O V m e t h o d s i m p l y c h a n g e d t h e o r d e r i n w h i c hm a c h i n e s w e r e l i st e d . T h e n , i t u s e d t h e M j = 0 c r i te r i o n t o o r d e r t h e s e q u e n c e o f e n t r y o ft h e c o m p o n e n t s . T h e t w o b o t t l e n e c k m a c h i n e s , 6 an d 8 , t h o u g h i n c l u d e d i n t h e a n a ly s i s,d i d no t a f fe c t t he c l us t e r s . The y we re no t dup l i c a t e d t o c re a t e 5 pe r fe c t c l us t e r s , a s t h i sv i o l a t e s p ra c t ic a l c ons t ra i n t s o n ma c h i ne a va i l a b il i ty in a j ob sho p . H ow e v e r , i f t hosem a c h i n e s a r e d u p l i c a te d , o n e w i ll n o t i c e t h e e x c e p t i o n s , l i s te d b e l o w :

M a c h i n e C o m p o n e n t11 916 714 2C A I E 1 2 : 2 - B


10/12

14 0 S . K . K H A T OR a n d S . A . I R AN II t er a t i o n 1 M i n M j = 1C o m p o n e n t N o . 2 6 2 2 4 3 6 1 6M a chi ne N o . 1 0 1 2 9 3 5O V e 6 = 0 . 6 0 7 , OVz2 = 0 .6 , O V 4 = 0 . 5 2 9 , O V 3 6 = 0 . 5 5 , O V I 6 = 0 . 5 3 8M a c h i n e s e n t e r e d 1 0 7 6 8C o m p o n e n t s e n t e r e d 2 6 2 5 1 3 3 9 1 3 1 1 2I t er a t i o n 2 M i n M j = 1C o m p o n e n t N o . 2 2 1 1 2 0 4 6 3 4 3 6 1 6 1 5 8M ach ine N o. 12 12 11 9 14 3 3 5 5 5O V 2 2 = 0 . 6 , O V 2 o = 0 . 6 6 7 , O V a = 0 . 5 6 , O W 6 = 0 . 4 5 , O V 3 4 ~ - 0 . 5 3 3 , O V 1 6 = 0 . 5 3 8 ,OV l l = 0 . 6 , OV 3 6 = 0 . 5 3 3 , OV t5 = 0 . 5 3 8 , OV 8 = 0 . 5 3 8M a chi ne s en tere d 1 1 1 2 1 3C o m p o n e n t s e n t e r e d 2 0 2 2 3 0 1 1 2 7 2 4 3I t er a t i o n 3 M i n M jC o m p o n e n t N o .M a c h i n e N o .O V a = 0 . 5 6 , O V 6 =O V s = 0 . 6 1M a c h i n e s e n t e r e d 5C o m p o n e n t s e n t e r e d 1 6

14

= 14 6 34 36 16 15 89 14 3 3 5 5 5

0 . 4 5 , O V 3 4 = 0 . 5 3 , 0 1 / ' 1 6 = 0 . 6 1 , O V 3 6 = 0 . 5 3 , O V 3 5 = 0 . 6 1 ,4 15

15 819 21

9 23 29 33 41 43 5

I t er a t i o n 4 M i n M j = 1C o m p o n e n t N o . 4 6 3 4 3 6M a c h i n e N o . 9 1 4 3 3O V 4 = 0 . 5 6 , O W 6 = 0.45 , OV34 = 0 .53 , O V 3 6 = 0 . 5 3M a chi n es en tered 9 2 1 6 1 1 4C o m p o n e n t s e n t e r e d 4 2 8 4 0 1 8 1 0 3 2 3 8 3 7 4 2 2I t er a t i o n 5 M i n M j = 1M a c h i n e e n t e r e d 3C o m p o n e n t s e n t e r e d 1 7 35 7 34 36

C O M P O N E N T S

1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 41 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3

I2 I I3 I4 1 1 15 1 1 1 1 1 16 1 1 1 1 1 1 1 17 1 18 1 1 1 1 1 1 1 19 1 1 1

1 0 1 1 11 1 1 11 2 11 3 11 4 1 11 5 1 11 6 1 1 1

1 1I 1 1 1 1 1

1 1 1 11 1 1 11 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 11

1 1 1 1 1 1 1 1 1 1 1 I1 1 1 1 1 1 1

1 1 1 11 1 1 1

1 1 1 11

1 11 1 1 1 1

1 1 1 1 1

M. 4 6 3 1 3 2 3 3 4 3 2 3 3 4 2 1 3 2 5 2 4 1 4 4 2 1 3 3 2 2 2 4 3 2 2 1 6 4 2 3 3 5 4JF i g . 1 . I n i ti a l m ach i n e - com p on en t m at ri x.


11/12

1076811

121354

1592

16I

143

M.2

C e l l f o r m a t i o n i n g r o u p t e c h n o l o g y 14 1C O M P O N E N T S

2 2 1 3 3 1 2 2 3 1 2 2 1 1 2 2 3 4 4 1 1 2 2 4 1 1 3 3 3 4 1 3 3 36 5 3 9 1 1 2 0 2 0 1 7 4 3 6 5 8 9 3 9 3 1 3 5 4 9 1 4 8 0 8 0 2 8 7 2 2 6 7 5 7 4 61 1 1 1 1 1 1

1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 *1 1 1 1

1 1

1 1

1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1

1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 11 1 1 1 1 1 1 *

1 1* 1 1 1

1 1 1 1 1

1 2 3 2 4 2 3 2 1 2 2 3 4 3 1 2 3 4 4 2 3 3 ~ 3 4 5 4 1 3 3 2 3 4 4 6 5 6 2 3 2 3 2 1

* E x c e p t i o n E l e m e n t s i f M a c h i n e s # 6 a n d # 8 d u p l i c a t e dFig . 2 . Solution obtained using OV method.

F U R T H E R R E S E A R C H D I R E C T IO N SW h i l e f u r t h e r r es e a r c h i s n e c e s s a r y t o r ef i n e t h e c o m p u t e r i m p l e m e n t a t i o n o f t h e

p r o p o s e d h e u r i s t i c , c e rt a i n o t h e r c o n s i d e r a t i o n s n e e d t o b e d i s c u s s e d , h i t h e r t o i g n o r e d i nt h e r e s e a r c h l it e r a t u r e. I t c o n c e r n s t h e d e c i s i o n s o n t h e fi n a l m a c h i n e - c o m p o n e n tc o n t e n t s o f t h e c lu s t er s , a f t er t h e p r o b l e m s o f t h e b o t t l e n e c k m a c h i n e s a n d e x c e p t i o ne l e m e n t s a r e r e s o l v e d .

I f u n l i m i t e d m a c h i n e d u p l i c a t io n i s a l l o w e d w h e n e v e r a m a c h i n e i s re q u i r ed o v e r t w oo r m o r e c l u s t e r s , t h e n p e r f e c t d i a g o n a l i z a t i o n o f th e m a c h i n e - - c o m p o n e n t m a t r i x w i ll b eo b s e r v e d a s s h o w n b e l o w :

12

34

I n r e a li t y , t h e n u m b e r o f c e l ls t h a t w i l l b e f o r m e d c a n b e e x p e c t e d t o b e l e s s t h a n t h en u m b e r o f cl u st e rs s h o w n . A l t h o u g h s e v e r al t y p e s o f m a c h i n e s w il l b e f o u n d c o m m o n t ot w o o r m o r e c l u s t e rs , i t m a y n o t b e p o s s i b l e t o a l l o c a t e m a c h i n e s t o e v e r y c l u s t e r d u e t or e s tr i ct i on s o n i n v e s t m e n t a n d u n e c o n o m i c a l u t i li z a ti o n o f th e e x tr a m a c h i n e s p u r c h a s e d .

S o m e i n i ti a l c o n s t r a in t s t h a t w i l l n e e d t o b e s a t i sf ie d w i l l b e : U p p e r a n d l o w e r l i m i t f o r n u m b e r o f ce l ls . T o t a l n u m b e r o f m a c h i n e s a s s ig n e d t o a n y c el l b e t w e e n a g i v e n ra n g e . L o w e r l i m i t o n o v e r a l l u t i l iz a t i o n o f t h e e x i s t in g m a c h i n e t o o l s a f t er r e a l l o c a t i o n

a m o n g t h e c e l l s .I t w i l l a l s o b e n e c e s s a r y t o s t u d y t r a d e - o ff s b e t w e e n m a t e r i a l h a n d l i n g c o s t s a n d s e t - u pl o s s e s . T h a t i s , in c a s e o f a m a c h i n e b e i n g s h a r e d a m o n g o n e o r m o r e c l u s t er s , i t w i l l b en e c e s s a r y t o c o n s i d e r t h e p o s i t i o n o f t h e m a c h i n e i n t h e o v e r al l s e q u e n c e o f o p e r a t i o n s o ft h e p a r t s i n e a c h c l u s t e r .


12/12

142 S . K . KHATOR an d S . A. IkANtIt is proposed to resolve this problem of machine assignment using the followingprocedure. The initial clusters formed using the OV method would indicate the machine

types that are being shared among the clusters. Load calculations will indicate therelative utilizations of these bottleneck (or shared) machines among the clusters. Certainclusters, by their smaller size, will be broken up and the parts contained in themreassigned to other larger clusters, to maximize machine utilization and to minimizeoverall material handling and set-up costs. So, cluster merging can be viewed as a parts-cluster assignment problem similar to that of bottleneck machines. The allocation ofbottleneck machines either to individual cells or to a common facilities cell will involve alarge number of components using them.Unlike the bottleneck machine case, the problem of exception elimination concerns afew components in two or more clusters sharing a single machine. It is required to assignthe machine to one of the competing clusters. So, exception elimination can be viewed asa machine-cluster assignment problem.Currently, the OV method yields solutions without the need for machine duplicationarising, since the components visiting most machines generally occur together at somepoint along the diagonal. Machine duplication will be required for a larger number ofcomponent s. It is proposed to include a lookahead feature which will check if a machineneeds to be duplicated over subsequent iterations. If the capacity requirements of thecomponents remaining to be introduced in the new machine-compo nent matrix requireone or more machines of a type entered earlier, duplication will be allowed. This willallow diagonalization or cluster growth to recommence at any point.

C O N C L U S I O NThis paper was intended to introduce a heuristic approach to machine-component

grouping in cellular manufacturing applications. Using the assumption of independentmachine-component groups, a simple reordering of the listing of machines will decidethe order in which the components get listed. The block diagonalization indicatingclusters will appear. Most of the examples cited in the literature can be solved easily bythis approach. The Mj and Occupancy Values were used to control the size of theclusters. This approach is superior to the array-based ones encountered earlier. It haspotential for widespread industrial use.

R E F E R E N C E S1 . M . E . M e r c h a n t . G r o u p t e c h n o l o g y - - a s o u n d f o u n d a t i o n fo r c o m p u t e r c o n t r o l o f c e l lu l a r m a n u f a c t u r i n gs y s t e m s , 9 t h C I R P I n t e r n a t i o n a l S e m i n a r o n M a n u f a c t u r i n g S y s t e m s . C r a n f i e l d I n s t i t u t e o f T e c h n o l o g y ,

B e d f o r d , U . K . ( 1 9 7 7 ) .2 . J . L . B u r b i d g e a n d D . M . Z e l e n o v i c . U s i n g p r o d u c t i o n f lo w a n al y s is (P F A ) t o p l a n g ro u p t e c h n o l o g y ( G T )f o r a n e w f a c t o r y . M a t e r . F l o w 1, 129-140 (1983) .3 . J . R . K i n g a n d V . N a k o r n c h a i . M a c h i n e - c o m p o n e n t g r o u p f o r m a t i o n in g r o u p t e ch n o l o g y : r e v ie w a n de x t e n s i o n . In t . J . Prod. Res . 20(2) , 117-133 (1982) .4 . H . M . C h a n a n d D . A . M i l n e r . D i r e c t c l u st e r in g a l g o r i th m f o r g ro u p f o r m a t i o n i n c e l lu l a r m a n u f a c t u r e .

J . M a n u f a c t . S y s t . 1(1) , 65-74 (1983) .5 . J . L . B u r b i d g e . A m a n u a l m e t h o d o f p r o d u c t i o n flo w a n a ly s is . P r o d . E n g n g 5 6 , 3 4 - 3 8 ( 1 9 7 7 ) .

Documents

sdarticle important cell.pdf