A VECTOR PERTURBATION APPROACH TO THE GENERALIZED AIRCRAFT SPARE PARTS GROUPING PROBLEM

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1 Accepted fo publication Intenational Jounal of Flexible Automation and Integated Manufactuing. A VECTOR PERTURBATION APPROACH TO THE GENERALIZED AIRCRAFT SPARE PARTS GROUPING PROBLEM Nagiza F. Samatova, Thomas E. Potok, Michael Leuze Collaboative Technologies Reseach Cente Compute Science and Mathematics Division Oak Ridge National Laboatoy Oak Ridge, Tennessee, ABSTRACT: The Vecto Petubation Appoach is intoduced fo addessing the genealized pats gouping poblem, identifying pat families fo a geneal set of supplies, not ust a single supplie. This method is diven by the need fo flexible and lean supply chain systems. A vecto space model is used to epesent a set of opeation sequences as opposed to the taditional matix and intege pogamming models in Goup Technology. Using this appoach we found that we ae able to geneate pat goups fom 90% of the available pats, whee all the opeation sequences ae peseved. This contasts with the 66% of available pats gouped using the taditional methods. Futhemoe, a vecto epesentation of opeation sequences povides an intuitive means fo discoveing the natual stuctue of the pat data. Fom these esults we conclude that this technique can damatically impove the effectiveness of the entie supply chain. I. INTRODUCTION A key challenge to militay eadiness is a supply chain poblem pimaily based on the need to maintain and quickly epai damaged aicaft. This challenge equies the manufactues and distibutos of spae pats to be able to supply the militay with the ight pat, in a shot amount of time, fo a easonable pice. Histoically, this challenge has been addessed by developing and maintaining a vey lage spae pats inventoy. A solution to these types of poblems is fo pat manufactues to delive a needed pat in a matte of hous. This appoach completely bypasses the need fo an inventoy of spae pats and thus geatly educes inventoy costs, as advocated by a numbe of ust-in-time methods. These methods advocate the building of efficient manufactuing cells by gouping pats based on how they ae made, often efeed to as Goup Technology (GT). 1,2 The conventional application of GT is to ceate manufactuing cells fo pats to be poduced on a single manufactuing floo. A cell consists of a set of functionally dissimila machines dedicated to the poduction of one o moe families of simila pats. Gouping simila pats is consideed as a pat of the cell fomation poblem. 3 Most of the methods of addessing this poblem ae ooted in mathematical appoaches 4 whose obectives ae to optimize a single manufactuing envionment unde a numbe of constaints specific to this envionment. The submitted manuscipt has been authoed by a contacto of the U.S. Govenment unde contact No. DE-AC05-96OR Accodingly, the U.S. Govenment etains a non-exclusive, oyalty-fee license to publish o epoduce the published fom of this contibution, o allow othes to do so, fo U.S. Govenment Puposes.

2 A new application of GT, diven by the need fo flexible and lean supply chain management (SCM), has ecently been intoduced in the liteatue. 5 In that pape, a famewok fo appoaching the genealized pats gouping poblem was poposed based on the use of the Autonomous Intelligent Agent Technology (AIA) in combination with the extensions to taditional Goup Technology. In the genealized pats gouping, athe than gouping pats based on a known set of manufactuing capabilities, these goups ae developed fo a geneal set of pat manufactues. This pape pesents the vecto petubation appoach to the genealized pats gouping poblem while futhe extending taditional GT appoaches. The need fo this method is dictated by mao distinctions in the taditional, manufactuing oiented, and genealized, supply chain oiented, gouping poblems. The fundamental distinction between these two poblems is based on the diffeences in the obectives/constaints they seek to satisfy. Taditional Appoach In taditional GT, the existing appoaches can be distinguished as stuctual and opeational. By stuctual we mean methods that goup pats while building the manufactuing cells based on outing infomation alone. Some of these methods use this infomation in a limited sense by utilizing only a machine-pat incidence matix. 6-8 McAuley s 8 appoach is a classical example in this categoy. Methods in the second categoy, which we efeed to as opeational, build cells while incopoating opeational infomation such as pat poduction volume, cost, a pocessing time, etc. 9,10 Since opeational infomation is always manufactue specific, methods in this categoy can not be diectly applied to solve the genealized pats gouping poblem found within most poduction supply chains. The stuctue and opeational appoaches descibed above have a common obective, i.e., they stive to incease poduction effectiveness of a single manufactuing envionment. This is achieved by identifying pat goups and building manufactuing cells in such a way that each pat goup can be fully pocessed in a cell. Examples of mathematical fomulations of this obective peviously used ae to minimize the inte and inta cell moves, 8 to maximize cell independence, 6,7 and to minimize the accumulative mateial handling costs. 11 Some poduction constaints used ae the desiable numbe of cells, the maximum numbe of machines in each cell, o the maximum pocessing time available on each machine. Genealized Appoach In the genealized pats gouping poblem, the obective is to goup pats into families in ode to optimize the efficiency of the entie supply chain athe than a single manufactuing floo. This pocess involves the following key stages: 1) Gouping pats based on how they ae made 2) Selecting a supplie fo building each family of pats fom a boad set of supplies 3) Aanging the selected manufactuing envionment to efficiently build these pat families Any solution to this poblem at a minimum is subect to the following constaints: The supply chain must espond to the immediate need fo a spae pat (time constaints) The cumulative inventoies within the supply chain have to be minimized (waste constaints) Pats fom the supply chain must be affodable (cost constaints) Based on the above discussion, we conclude that 1) the taditional cell manufactuing poblem and the genealized supply chain poblem ae quite diffeent; 2) thee is a need fo the methods that povide a flexible solution to gouping pats fom a boad set of supplies athe than a single manufactuing floo and that conside the obectives/constaints specific to the supply chain opeation in ust-in-time envionment. This pape pesents a genealized pats gouping method that meets these equiements. The emainde of the pape is oganized as follows. The next section povides details of the vecto petubation method that we developed to goup pats based on opeation sequences and discusses its advantages

3 and limitations. Diffeent measues of pats dissimilaity ae intoduced fo futhe evaluation. We then illustate the method numeically. Finally, conclusions ae given based on the esults fom this study. II. METHOD DESCRIPTION This Vecto Petubation Appoach extends the cuent liteatue in GT by epesenting the opeation sequences equied to manufactue pats as a vecto space model. Fom this model we can then identify independent pat families. We define the opeation sequence of a pat as the odeing of the manufactuing opeations equied to constuct the pat. We chose the opeation sequence epesentation ove the outing cad epesentation due to the fact that outing cads descibe the specific machiney at a given manufactue. In the genealized pats gouping poblem, we need to conside opeations ove the entie supply chain, as opposed to a given supplie. Theefoe, we believe that the opeation sequence is an appopiate abstaction fo the machiney used thoughout a given supply chain. In addition to this highe level of abstaction that opeation sequences povide, we also need the capability to peseve the ode of the opeations. In the genealized gouping poblem, pat families must be as closely tailoed to a supplie s capabilities as possible. This poblem is not solved by meely poviding a supplie with a family of pats that can potentially be built using a supplie s opeations alone. The pats must flow though the supplie s manufactuing cell in a pope sequence fo the pats to be built. Theefoe the sequence of opeations is a key input to the genealized gouping poblem. This vecto petubation method contains the following essential steps: 1) Repesenting the odeed opeations of a pat in the fom of d-dimensional pat vectos 2) Evaluating a elationship between each pai of pat vectos using a dissimilaity function 3) Applying an appopiate similaity coefficient based clusteing algoithm to detemine pat families based on the dissimilaity matix computed in step 2). 4) Finding a moe optimal solution by changing the petubation paamete δ. II.1. Data Repesentation Typically, to epesent the opeations equied to build pats, a 2-dimensional matix is used. Thee ae a numbe of poblems with this type of epesentation. Most notably, these ae the loss of opeation sequences infomation, the lack of suppot fo visualizing the infomation, and the difficulty in discoveing the natual stuctue of the data. To ovecome these limitations we popose a new appoach fo epesenting pat opeation sequences. We begin with a set P of pat opeation sequences and a deived value d of distinct opeations listed in all these sequences. We model each opeation sequence as a vecto υ in the d-dimensional space R d. This allows fo one coodinate fo each of the d opeations. The th coodinate of a vecto υ is a numbe that elates the th opeation with the given opeation sequence. The value of the th coodinate can be expessed mathematically as follows 0,? =? + d ode(), if the opeation sequence does not contain opeation othewise (2.1) whee ω is the weight assigned to each opeation. This weight epesents a non-opeation based facto that may influence the gouping of the pats, fo example, the cost of equipment, the unit opeation time, its aveage wokload, etc. δis the petubation paamete used to epesent the impotance of the sequencing of opeations ode( ) is the numbe that defines the ode in which the opeation occus in the opeation sequence

4 Fo example, conside a hypothetical set of opeation sequences fo two pats as shown in Table 1. Thee ae fou (d = 4) distinct opeations, esulting in a 4-dimentitional space. The opeational sequence vectos ae illustated in Table 2. TABLE 1. Routing Sequences fo Two Pats. Pat No. Routing sequence P 1 O 2 O 1 O 4 P 2 O 3 O 4 O 1 O 2 TABLE 2. Vectos Coesponding to Pats P 1 and P 2 Vecto No. Vecto components υ 1 (1 + 2 δ, 1 + δ, 0, δ) (1 + 3 δ, δ, 1 + δ, δ) υ 2 II.2. Analysis of the Relations Using Dissimilaity Functions Now that we have epesented the data, we need to analyze the elations between pats, i.e., the similaity, o dissimilaity between them. To do this, five diffeent dissimilaity coefficients ae intoduced and compaed to each othe. 1) Euclidean squae distance D e (υ i,υ ) showing the most natual elations fo vectos in the Euclidean space. It is defined by D (2.2) k = d 2 i,? ) = ik? e k ) k= 1 Notice that clustes defined by Euclidean distance will be invaiant to tanslations o otations of the pat vectos, due to the isotopic popety of the Euclidean space. Howeve, they will not be invaiant to linea tansfomations o othe tansfomations that distot the distance elationship. Thus, intoducing weighting tems fo the opeations can esult in a diffeent gouping of the pats into clustes. 2) Dissimilaity coefficient D c (υ i,υ ) computed as the contaction of the Euclidean distance between two pat vectos by a facto popotional to the numbe of common non-zeo vecto components, o the numbe of common opeations in the pat opeation sequences Dc D i,? ) =?(nc i,? )),? ) e i (2.3) i,??(nc i,? )) (2.,? ) Dc De i 3) whee ψ (n c (υ i, υ )) is a function of the total numbe n c (υ i, υ ) of common non-zeo vecto components. Fo this analysis we set ψ (n c (υ i, υ )) = 1 / (1 + n c (υ i, υ )), to avoid division by zeo. The Euclidean distance measuement is stongly influenced by the dissimilaities of the vecto coodinates. This dissimilaity measue distinguishes two pais of pat vectos at the same Euclidean distance as being diffeent if the numbe of common opeations between thei pat pais is diffeent.. The poposed dissimilaity coefficient weighs the Euclidean distance between vectos based on the similaities of the vectos. 3) City-block distance D b (υ i,υ ) (i.e., Manhattan distance) defined by D b i,? ) = k = d k= 1 4) McAuley s 8 dissimilaity coefficient D M (υ i,υ ) defined by n c i,? ),? ) = 1 (2.5) D? ik? k (2.4)

5 whee n c (υ i, υ ) is the total numbe of common non-zeo vecto components as defined above and n t (υ i,υ ) is the total numbe of non-zeo vecto components of both vectos. 5) Dissimilaity coefficient D (υ i,υ ) defined by the atio D i,? ) = 1+ n c D 1 i,? ),? ) e If two vectos ae the same, i.e. D e (υ i,υ ) = 0, then the dissimilaity coefficient D (υ i,υ ) is defined to be equal to 0, to avoid division by zeo. Of paticula note hee is the obsevation that 0 D (υ i,υ ) 1 and it is equal to 1 when thee ae no common non-zeo components. Thus, the two pats ae less dissimila when the numbe of commons, n c, opeations in thei outing sequences is lage and the Euclidean distance D e (υ i,υ ) is smalle. It is also inteesting to note hee that if the petubation paamete is ignoed (in Equation (2.1) δ=0), the dissimilaity coefficient D (υ i,υ ) educes to McAuley s dissimilaity coefficient. The esults fo a gouping poblem theefoe, can be veified using this special case and compaed with McAuley s fo vaious changes of the petubation paamete. i (2.6) II.3. Advantages and Limitations of the Vecto Petubation Appoach The poposed vecto petubation method fo gouping the pats has seveal advantages ove existing appoaches, paticulaly, when it is evaluated in tems of the genealized gouping poblem. The poposed appoach is the fist known method in the GT liteatue that builds a vecto space model fo a set of opeation sequences. This model allows the epesentation of pat opeation sequences infomation, the ability to visualize the infomation and analyze the natual stuctue of the data. Additionally, one can apply geometic and linea algeba methods in analyzing pat infomation within this type of model. Most of the existing clusteing techniques ae stongly dependent on the shape, size and density of the clustes. With ou vecto epesentation thee is the potential to tansfom the n-dimensional space into foms well suited fo the clusteing techniques. A choice of a paticula clusteing algoithm may also depend on the similaity measue used to define the elations between pats. At the simplest level, the vecto epesentation of opeation sequences natually suggests numeical similaity metics fo pats, based on the Euclidean distance. Howeve, many othe elated metics (Mahalanobis distance, cityblock distance, etc.) o nonmetic similaity functions (cosine measue, etc.) to elate two vectos can be intoduced based on the natue of the data. The poposed method takes into account both the 1) commonality of opeations and 2) the similaity in opeation sequences. These ae the two essential featues by which the similaity of pats can be chaacteized in the genealized pats gouping poblem. The vaiation of the vecto petubation paamete povides a desiable compomise between the ease of esouce assignment and the incease in poduction thoughput by taking advantage of inteleaving vaious pats though a common set of sequenced opeations. Moeove, in eal wold applications all the opeations may be not equally impotant due to thei diffeence in costs, unit pocessing time, etc.. This new method allows model heteogeneity among opeations by assigning vaious weights to diffeent opeations.

6 Pats that ae pocessed by the same opeation moe than once cause a special poblem when unidiectional mateial flows in the manufactuing cells ae assumed. So fa, the poposed method assumes that the opeation sequences do not contain backtacking opeations. Reseach is undeway to extend the method by making it sensitive to backtacking opeations. III. CASE STUDY In this section, the poposed method is applied to the poblem used by Bubidge 1 and fequently cited in the Goup Technology liteatue. A list of pats and thei opeation sequences is shown in Table 3. Each element in the opeation sequence denotes an opeation and not a machine as specified by Bubidge. Since the method does not cuently addess backtacking, we have adusted the data as follows. If an opeation appeas moe than once in a outing sequence, only one of these occuences was left to avoid backtacking; the est ae eliminated (cossed out in Table 3). The obective is to goup 43 pats into families based on the similaity of thei opeation sequences. TABLE 3. Opeation Sequences fo 43 pats and 16 opeations Example Poblem Opeation Sequence P P P P4 8 P P P P P P P P P P P P16 4 P P P P P P P P P P26 9 P P P P P P P P P P36 2 P P P P P P P Fist, the input data has to be analyzed as to whethe it has any sequencing poblems. In the selected example, thee ae many pat pais that may cause poblems when assigned to the same family, assuming that this family is pocessed in a unidiectional flow cell. Fo example, if the pats P 5 =(7-4-

7 14-3) and P 21 =(3-14-7) ae gouped togethe then any odeing of opeations 3, 4, 7, and 14 within the poduction cell esults in backtacking of mateial flow and theefoe, such pais ae consideed as pohibited pais. Using the Bubidge input data, the values of a dissimilaity matix have been computed fo each of the dissimilaity coefficients descibed in Section II.2. To illustate the method we set the opeation weight ω = 1 in Equation (2.1). Fo example, the dissimilaity between pats P 5 and P 21 computed by McAuley s is D M (υ 5,υ 21 ) = 1 (3/4) = 1/4. The dissimilaity coefficient D (υ 5,υ 21 ) between the opeation sequences of these pats is D (υ 5,υ 21 ) = 1 / (1 + 3 / (1+2 δ+10 δ 2 )). If we set the value of δ=0.2, then D (υ 5,υ 21 ) 0.37, which shows the effect of adding sequence infomation in detemining pat similaity. The next step in pats clusteing is to goup pats accoding to the dissimilaity coefficients that wee calculated. In this pape, the hieachical agglomeative clusteing algoithm that utilizes Wad s Minimum Vaiance citeia is used fo pats gouping. 12 Figue 1 is a Phyllips tee, o dendogam, epesenting the beakdown of how the 43 pats, (Table 3), wee actually gouped based on the McAuley s measue. The length of the banches shows how close one goup of pats is to anothe. Fo all the dissimilaity matices, thee ae five basic well-sepaated pat goups. When the value of the petubation paamete is small, the sepaation of the goups of pats is detemined by thei diffeences in equiements of opeations. And only close to the leaves, ae the diffeences in the odes of opeations moe appaent, (see Table 5 and Table 6). Figue 1. Dendogam fo McAuley s dissimilaity matix D M To evaluate the pats families geneated fo diffeent dissimilaity measues we used the simple matching measue of compaison. 13 This measue is based on the following 2 x 2 contingency table as that in Table 4 in which all pat pais ae classified fo two patitions into fou classes. Table 5 shows the compaison between the McAuley s patition and each of the consideed dissimilaity coefficient based patitions fo diffeent numbe of pat families. Each enty in Table 5 is in a fom of a / (b + c). When the numbe of goups inceases, the numbe of diffeent assignments, o misses, is getting lage and the numbe of the same assignments, o hits, is getting smalle. TABLE 4. Contingency Table fo Paied Compaisons between Patitions Patition1/Patition a b

8 0 c d (1,1) class two pats ae assigned to the same family in the two patitions (0,0) class two pats ae assigned to diffeent families in the two patitions (1,0) class two pats ae in the same family in the fist patition and in diffeent families in the second patition (0,1) class same as (1,0) class but with the opposite assignment TABLE 5. Compaison of McAuley s Pat Families with the Pat Families fo Diffeent Dissimilaity Coefficient Measues Dissimilaity Coefficient Numbe of Goups City Block Distance 135/82 119/44 107/28 97/34 66/65 58/67 159/34 106/76 82/78 66/87 47/105 43/104 Euclidean Contacted 181/0 120/42 88/66 74/71 58/79 49/82 Dissimilaity Ratio 181/0 120/42 100/50 76/66 60/74 56/70 To compae the efficiency of the poposed method, the sequence utilization measue 14 has been used. This measuement is expessed as the atio of the numbe of violated elements to the total numbe of pohibited elements. The esults of this analysis fo diffeent dissimilaity measues and diffeent numbe of goups ae illustated in Table 6. As one can see, the Euclidean distance based method pefoms the best and the McAuley s pefoms the wost out of all consideed dissimilaity measues. TABLE 6. Analysis of Sequence Utilization fo Diffeent Dissimilaity Measues Dissimilaity Coefficient Numbe of Goups McAuley s Euclidean Distance Euclidean Contacted City Block Distance Dissimilaity Ration Gouping pats at vaious levels on the dendogam gives diffeent pat families. Table 7 shows a 7-goup solution of the example poblem using McAuley s and Euclidean distance dissimilaity measues. It can be noticed that the two solutions fo the same poblems ae diffeent 82 hits vs. 78 misses fom Table 5 in the assignments of pats to pat families. The sequence utilization measue is also impoved by 21% when the Euclidean distance combined with the vecto petubation appoach is used compaed to the McAuley s appoach. The next question that comes up in the analysis of the vecto petubation appoach is whethe the poposed method is sensitive to the vaiations of the petubation paamete and what ae the suggested default values fo this paamete. Viewing the poblem geometically, when the petubation paamete is set δ = 0 and the opeation weight is set ω = 1 in Equation (2.1), each opeation sequence is mapped in one of the vetices of the d-dimensional unit hypecube. We call these vetices the esouce centes. In this TABLE 7.

9 Pat Families fo a 7-goup Solution Using McAuley s and Euclidean Distance Dissimilaity Measues McAuley Euclidean Distance Family 1 {1, 12, 13, 25, 26, 31, 39} {1, 12, 13, 25, 26, 31, 39} Family 2 {2, 10, 28, 32, 37, 38, 40, 42} {4, 10, 18, 28, 38, 40} Family 3 {6, 7, 17, 34, 35, 36} {6, 7, 17, 34, 35, 36} Family 4 {4, 8, 9, 14, 15, 18, 19, 21, 23} {8, 14, 15, 16, 23, 29} Family 5 {33, 43} {5, 19, 21, 33, 41, 43} Family 6 {3, 11, 20, 24, 27, 30} {3, 9, 11, 20, 22, 24, 27, 30} Family 7 {5, 16, 22, 29, 41} {2, 32, 37, 42} case, the opeation sequences (O 1 -O 2 -O 3 ) and (O 3 -O 2 -O 1 ) will be mapped to the same esouce cente. When sequencing is taken into account, the goal is to map each opeation sequence into a point of R d in the vicinity of its coesponding esouce cente. Thus, if L is the maximum outing length in the set of all opeation sequences, then taking δ< (1 / L) will guaantee that the distance between any pai of points in the same neighbohood will be less than the distance between any pai of points fom the diffeent neighbohoods. In all the examples above, we set δ default = (0.99 / L). Table 8 summaizes the esults of 8-goup clusteing fo diffeent petubations of the paamete δ. The esults ae the pai wise compaisons (in tems of hits and misses) of pat families obtained using the McAuley s and D dissimilaity measues with diffeent values of δ. The last ow in the table specifies the values of sequence utilization measue 14 fo each of the consideed cases. TABLE 8. Sensitivity to the Vaiations of the Vecto Petubation Paamete McAuley D (d= 0.05) D ( default = 0.17) D (d= 0.25) McAuley D (d= 0.05) 92/42 D ( default = 0.17) 76/66 93/24 D (d= 0.25) 85/51 102/9 92/21 Sequence Utilization: IV. SUMMARY AND CONCLUSIONS This pape has pesented a vecto petubation appoach to the genealized pats gouping poblem. The need fo this method is dictated by mao distinctions in the taditional, manufactuing oiented, and genealized, supply chain oiented, gouping poblems. The mao featues of this method ae: 1) It builds a vecto space model to epesent pat opeation sequence infomation. This technique impoves visualization and discovey of natual pat goups as high-density sets of points in n-dimensional vecto space. We believe that this is the fist model of this type that has been poposed in the GT liteatue. 2) It goups a collection of pats fo a geneal set of supplies, not ust a single known supplie. 3) It povides a desiable compomise between the ease of esouce assignment and the incease in poduction thoughput by taking advantage of inteleaving vaious pats though a common set of sequenced opeations. This featue is due to the vaiation of the vecto petubation paamete

10 Results fom the pesented case example illustate the capability of this appoach to geneate pat goups with a 90% sequence utilization measue. This contasts to the 66% value achieved with the taditional appoaches. This demonstates the ability to pocess moe pats within a unidiectional flow line cell. This method was also applied to thee lage sets of C-130 and F-16 aicaft pat data. The esults, though peliminay, ae vey pomising. Ou conclusion is that the Vecto Petubation Appoach is well suited to addess the genealized gouping poblem, and can be used to enhance the efficiency and utilization of most supply chain systems. ACKNOWLEDGEMENTS The Oak Ridge National Laboatoy is managed by Lockheed Matin Enegy Reseach Cop. fo the U. S. Depatment of Enegy unde contact numbe DE-AC05-96OR This wok was suppoted by the Defense Logistics Agency, and the Lockheed Matin Copoation. We would like to thank Michael Bogsmille fo poviding with the softwae pogams used thoughout this poect. REFERENCES 1. Bubidge, J.L. Poduction Flow Analysis, Poduction Engineeing, 42, 1963, Bubidge, J.L., The Intoduction of Goup Technology, Heinemann, London, Wemmelov, U. and Hye, N.L., Pocedues fo the pat family/machine goup identification poblem in cellula manufactuing. Jounal of Opeations Reseach, 6, 1986, Selim H.M., Askin R.G., and Vakhaia A.J., Cell fomation in Goup Technology: eview, evaluation and diections fo futue eseach. Computes ind. Engng. 34, 1998, Potok, T.E. and Ivezic, N. A., Multi-agent spae pat gouping system fo logistics optimization, Poceedings of the 5 th Intenational Confeence on Infomation Systems Analysis and Synthesis, 3, 1999, Caie A.S., Numeical taxonomy applied to goup technology. Intenational Jounal of Poduction Reseach, 11, 1973, King J.R., Machine-component gouping in poduction flow analysis: an appoach using a ank ode clusteing algoithm, Intenational Jounal of Poduction Reseach, 18 (2), 1980, McAuley J., Machine gouping fo efficient poduction. The poduction Enginee, 52, 1972, Gupta T., Seifoddini H., Poduction data based similaity coefficient fo machine-component gouping decision in the design of a cellula manufactuing system, Intenational Jounal of Poduction Reseach, 28 (5), 1990, Vakhaia A.J. and Wemmelov U., Designing of a cellula manufactuing system: a mateials flow appoach based on opeation sequences. IIE Tansactions, 22, 1990, Selvam, R.P. and Balasubamanian, K.N., Algoithmic gouping of opeation sequences, Engineeing Costs and Poduction Economics, 9, 1985, Wad J.H., Hieachical gouping to optimize an obective function. Jounal of the Ameican Statistical Association, 58, 1963, Geen P. and Rao V.R., A note on poximity measues and cluste analysis, Jounal of Maketing Reseach, 6, 1969, Details of the analysis will be pesented in a fothcoming pape.