Sistemas Expertos Para Tecnologia de Grupos

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Defence Science Journal, Vo147. No I. JanuaIY 1997. W. 83-88(Q1997,DES~ I

Expert System for Group TechnologyM. Srinivasulu and Shravan KurnarUniversity of Roorkee, Roorkee -247 667

ABSTRACTAn expert Sf stem for solving group technology (GT) problems hai been developed, considering

simplified mopells of industrial GT problems. It solves problems of varying characteristics usingin-built algorithms, namel)! average linkage clustering algorithms (ALC), cluster identificationalgorithms (CI) andigeneralised p-median model. Depending upon the characteristics of GT problem,a suitable algorithm is selected. The algorithm takes the required inputs for the problem and gives theoutput. which consists of m.achi~e cells with corresponding part families and the bottleneck parts, ifany. ,

This paper de~ls with an expert s~stem whicsolv~s the GT problem with varying characteristicsusing Cluster analysis algorithms. The system based on the idea jsuggested by Kusiak3. Thougthe system can be used for various attributes, th.discussion proceeds taking into consideration thmachine attribute of the part.

I. INTRODUCTIONGroup Technology (GT) is defined as a

approach to identify things as I?arts,equipment, tools, people. and customer

needs by using th~ir attributes (like. visual,functional or environmental). These,

are then anal,ysed to identify similarities,the things; the things are grouped into

a9cord'ing to similarities and thesesimilarities are used to increase the efficiency andIof .hanuf~cturing process. Theconcept of GT was first introduced/by Mitrafanov.Burbidge 1, one of ~he pioneers of IGT, used it in.IdeveJoping the concept of pr~duction flowanalysis. Hitomi, el ar. have done co"nsiderableresearch i~ GT and extended its scope to entireproduction ( manage~ent.1 in adtlition, considerableresearch has been done ih this field to make GT auniversally Ilccepted I~hilo~ophy for flcx ihlcmanufactu~ing system(FMS) and computerintegrated manufacture !CIM) applications.I

2. FEATURES OF THE PROBLEMThe grouping process of machines and parts

simple when the number of machines and parts small. But, it becomes impossible to solve thproblem manua.lly when their number increas~s ttens ,and hundreds. .In industry, we, generally deawith the later type of problems. ~Iuster analysisused fOT problem solving is concerned withgrouping of objects iQto homogeneous clustersbased on object attributes. The method initiallyrcllllircN 1IIrnlcllillR IIIC rrohlcl11 11111(1IICII N(llvillgthis model using a particl,llar methJd. Three typeof model formlllali()ns are used.

R~eived 28 Octorer 1996


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DEF sa 1, VOL 47, NO I, lANUARY 1997fMatrix rormulatioll Methods

These methods are productioll flow unalysisl,coefficien't meth-ods4,5, cluster

algorithm6 and others. .Here a,machine-part incidence matrix consists' of 0.1

entry 1(0) indicates that machine,(not used) to process part, column, j.

Mathematical Pro.gramming FormulationMethodsThese methods are .generalised Ip-median

quadratic programming model and fract-model and algorithm is selected. Based on the typof algorithm selected, it P?ses questions regardingadditional constraints if the user intends to havany (this facility is available only for one of thalgorithms used).

Graph Formulation Methods.,These methods are bi-pariate graph, transitiongraph methods. They are ~uitable

a particular type of problem and each has acomputational complexity. Based on thelysis, the features of a GT problem are:

4. MODELS & ALGORITHMS'IFor each of the thr~e different fomlulations,mentioned ih the features .section, the following,three characteristics, have been considered fo

selecting an algorithm:IHuge amount of data,

Possiblefonnulation in anumberofways, and(a) Limited numberlof part families (or machine,.cells), IVariati3n in the computational complexity of

these fonD ulations. f(b) .Limited number of parts i!l each part family, andThese types of problems are most suitablyexpert system approach8. The system

the data and uses the advantages ofmodel and algorithms.

(c) Costs (e.g., su~contractin8, production)4.1 Extended Cluster Identi(ication AlgorithmIIt is a heuristic methpd of GT problem solvingdeveloped by Chow and: Kusiak6. This method iused by the system when the user. is choosy abou~he contents and the number of part families. It ithe case where the: additional constr'aints blockshown in Fig. 1 comes into role, ~and the constraints, , ,are fed by the user. The algorithm can be used withor without considetation of subcoptracting costsIts input is bachine-part incidence matrix and cos

.Imatnx.

SYSTEM ARCHITECTUREI.A rule-based system archItecture as suggestedKusiak I s used (Fig. 1 . The; architecturean expert system which gathers data about

parts (machine-part incidencecost (In case it is. being consider~d) and

li~e number of clusters. The expertanalyses a GT problem (data) and

fupon its type and size, an appropriate


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SRINIVASULU & SHRAVAN KUMAR : EXPERT SYSTEMIConsider Ian ideally clustered-binalry(I). I algorithm. This concept of the algorithm wadeveloped by Iri, which was the principle for th

present algorithm.,A (k) is the machine-part incidence matrix aftek ..IIteratIons.AlgorithmStep 0.

Set iteration nufJ1ber k =Step

Crossing all entries i~ the Iilatrix (I) by fiveI

Vs2 V3I V4

Select those machines (rows of matrix A) thatbased on user's knowledge, are potential candidatesfor inclusion in niachine cell, MC-k. Drawhorizontal lines h through each row of matrix A (kcorresponding to these machines. In the absence othe user's expertise, any machine can be selected.Step 2. ,For each column in A (k) corresponding to theentry of 1 crossed by any of the horizontal line hidraw a vertical line vFStep 3.

For each rowo n A (k) corresponding to the entryof 1 crossed by any of vertical lines Vj, drawn inStep 2, draw a horizontal line hi..-6ased on the machines corresponding to all thehorizontal lines drawn in Step 1 and Step 3, atemporary I machin~ cell MC-k is for~~d. If theuser's expertis,e indicates that some machines can-not be included in MC-k, erase the corresppndinghorizontal lines result in MC-k. Delete from matrix0 A(k) parts (columns) that are to be manufactured onat leastOone of the machines already included inMC-k. Place these parts on the list of parts to bemanufactured in a functional machining facility orsubcontracted. Draw a vertical line Vj through eachcrosscd-ol1cc cl1tric~ of 1 in matrix A(k) which docsnot .involve other machines than tbose included inMC-k.

I ,One can notice that matrix (2) h.as theproperty: Euch entry '1: in n cluster is

by two lines (a h'prizontal and abblonging'to this cluster. For example, all

'1' in the upper left ct)rner cl\lster incrossed b't exactly two vertical lines

1, v2, and two hoiizon~al lines h 1, h2 This prop-llscd to dcvclop thc clustcr idcntificntion

I

StepFor all the crossed-twice entries of 1 in A (k)

.form 11mtlchinc ccll MC-k Iln


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DEF sa I, VOL 47, NO JANUARY 1997generated based on a thr~shold value of thesimilarity co,fficient. A .disadvantage with SLCAis thnt it rcq:Uircs n thrcshold vnluc; othcrwisc ifails to recG>gnise the individually separableclusters- resulting from eli.minating bottleneckmachines. TQ recognise the Ibottlendck machines,S'eifoddini and' Wolfe4 used the a.,.erage linkageclustering. They defined the s\milaiity coefficientbetween any two clusters as,an average of thesimilarity coefficient between all members of thetwo clusters. The total number of intercellularmovements (ICM) between two machine cells is.Icomputed as

Step 5.Transform the incidence matrix A (k) by

removing aJJ lhe rows and COJUlW1S orrespondingto MC-k and PF-k..Step 6.

If matrix A (k+ 1) = O (where O denotes a nullmatrix), stop; otherwise set k :;: k + 1 'and go tofStep 1.When cost is to be considered, with each

column of the machine-part incidence matrix A and,Cj of part j is associated. In this case, the contentsof part families are such that rcosts in Ihandling thebottleneck parts are minimum. Different solutionsare obtained by selecting a different startinglrow inStep 1 and for each solution, the costs arecompared.

(4)ICM;jn= L d3(Vik'Vjk)Ik=l

where, if-L, aik ~ 04.2 Average Linkage Clustering AlgorithmThis is developed by Seifoddini and Wolfe 4 as

an extension to single linkage cluster analysis(SLCA) al~orithm developed by Mc Auley5, so asto find independant clusters and bottleneck parts.It is used by the system when there are noconstraints regarding the number and contents ofthe part family and cost is not a consideration. TheSLCA is based on the similarity coefficient Sijmeasure between two machines i and j and iscomputed as

\I';k =

When d3 (V k, V ~) = 1, it ipdicates that part krequires processing in both macbine cells MC-i andMC-j and thus part k is a bottleneck part. Thisproblem can be solved eithe~ by removing part kfrom the two machine cel~s ' or by adding anidentical machine to each mach~ne cell.

(3)I4.3 Generalised p-Medi~n Model., ,,This model is an extension of the p.:median

model and it considers different process plans forp:oducing a p~rt9. So in the machine-:Eart, ncidencematrix for every par(, more than one column isused, each corresporl,ding to a ~ifferent processplan. The system uses this algorit~m if one wantsto choose best process plan amqng differentalternatives. ~The mod.el .requires the number ofprocess families (p ) at start. If P1is not known, thenil stflrts with a small number of pfocess familiesp = Po and 'solves the model. If .the quality ofprocess families is not ratisfactory,! p is increasedby 1, ~nd model is again resolved. The model can

where1 -Jl. if ajk=ajk='ld (ajk. aj~ -1'otherwise2 -fl. ,if ajk= ajk= 1d (ajk. aj~ -1 otherwise

a.. = Element of matrix AI)

To solve the GT problem using SLCA,similarity coefficients for all possible pairs ofmachines are computed. Machine cells are

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SRINIVASULU & SHRAVAN KUMAR : EXPERT SYSTEMof part families 7 which ensures that part family ibelongs to part family j only when this part familyis formed. The third constraint9 ensures integrality.5. WORKING OF THE SYSTEM

I The present system can be used to solve a largescaJe GT probJem in a suffici.entJy Jess time. TheformuJations used in this paper are simplifiedmodels of the industrial GT p~oblem. The systemposes a questionnaire to the user so as to gathercharacteristics mentioned in models and algorithmssection. The selection of the model depends on the.characteristics of the problem to be solved and theselection is shown In Tabie 1.

IIwork taking into consideratiop the costs. Theinteger pro$ramming Jodel for this is asI I

n ~umber of partsI,q Number of process plans,\F k I Number of process 'plan stfor part k,k= 1,2,3 n Ip Required number of process faniliesI Idij Distance measure between process plans i1 andj. I

(5) Table 1.n'

dU = r Z(Pik1 ajVk=1 Choose con.tents of PF

Cost con.sidered

Modelimitednumberof PF's

InputsI 11, if aik * ajk =Z (aik. ajk ~ = 1 otherwise

NoYesNo

A.A.C.P

00 A.C.P

NoNo or YesNo or Yes

NoNo or YesNo or Yes

ALCCIGen: pIThe objective functi~n minimises the total sum

dnd production costs.I .= Ad'ditional constraints can be given interactively...Gen,p = Generalise4 p-median model,p in the second and third cases is optional,

Iq q I

min L L d;jx;j +iI CjX;ji=l j=l(6)

After detennining the model to be used, thealgorithms mentioned above are used. for solvingthe problem taking the inputs given in Table 1. Thealgorithms are developed in C-language.(7)

qL L Xij = I f~r all k ~ I, 2 niFK =l

(8)q

L Xij=Pj=l IXij ~~jj for alIi = 1,2... qI andj= 1,2...qJXjj = b,l for all i = 1,2... qI

I apdj::;,1,2...q

5(9)

5.1 Trial Run jWhen i~put were p = 2

Part number1 2 3 4

Process plan number123 45 67 89

1 1 1 1 11011

l'I (10) 12 MIC3 Number4

1A = 1ne constDaint 7 ensures that fo~ e~ch part

nother .constraintS specifies th~ required number1 1 1 11 ,.

1 II1 11 11 1 1 1 1 1'= I

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DFF SCI I, VOL 47. NO 1, JANUARY 199T/III3. Chow Wi\1g, S. & Kusiak!, Andrew. DecomPO-,MC-1 = { 2. 4} sition of Ii1anufacturing systems. IEEE J. Robot.

I,1C-2= {1, 3} Auto.,198~,4(5),457-71. , ,The solution given isPF-l = {2, 7}PF-2 = {5, 9, 1} ~

Seifo"ddini, H. & Wolfe P.M. Ap~lication of thesimilarity coefficient methods in GT. .IEEETrans., 1986, 18(3), 271-77. .',

4.6. CONCLUSION IThis expert system has been developedconsidering simple models of industrial GT

problem. An actual problem has many otheradditional constraints, like proc~ssing timeavailable at each machine, frequency of trips ofmaterial-handling carriers, dimension of themachine cell, etc, which wer~ not considered. Thesystem can be further developed considering theseconstraints so as to make it more realistic.

5 ..Auley, J. Mc. Machine grouping for efficientproduction. Production, Engineer. 1972, 53,271-77.

.6.

'7,

Chow Wing, S. & Kusiak, Andrew. An efficientcluster identification algorithm. IEEE Trans. SystMan and Cybern., 1987, S;MC-17(4), 696-99.1

Kusiak, Andrew. the ,generalised GT concept.Int. J. Pro(i. Res., 1987, 25(4), 561-69.

REFERENCES Kumaran S.R.T e, al. Expert systems in industrialengineeripg. Int! .J. Prod. Res., 1986, 24(5),1107-25. I

8.Burbidge, J.L. Simplification of material flowsystem. Int. I. Prod. Res., 1982,20(3),339-47.1

Kusiak, Andrew.( Intelligent manufacturingsystem. Prentice Hall International, 1990,,pp. 206-46.

9,am, I.; Hitomi, K. & Yoshida, T. Grouptechnology application to production manage-ment. Kluwer Nijhoff Publishing.

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