In Journals Format

8/13/2019 In Journals Format

1/51

1 I NTRODUCTION

Industries across the world, in recent years, are witnessing a momentous shift from the

conventional manufacturing processes towards the automation and flexible mechanization

systems. Indeed, in order to increase the productivity, accuracy and precision in operations,

the automation systems are rapidly replacing the manual systems and correspondingly

reducing the overall human intervention. Most often, these automation solutions include

robots and integrated robotic applications. Robotic systems, along with the aforesaid

advantages, also lead to reduction in monotony and risk factors. However, the overall gains

achieved using robots, in terms of increase in productivity of operations, is largely dependent

on the appropriate selection of the particular robot for the application concern. onse!uently,

the selection of appropriate robot, from the vast spectrum of the various robots and their

models from various manufacturers available today, for the particular application in hand becomes one of the most crucial decision making exercise for the modern system designers.

"everal researchers have proposed different approaches for the selection of robotic

manipulators. onventionally, the selection of robotic manipulators based on the

performance#based attributes like, speed of operation, accuracy, precision, dexterity,

singularity etc., have been proposed by Hinson $%#&'. (he workspace and payload capacity,

have been listed as selection criteria by )orf and *of $+' and Rivin $ '. Manipulability based

selection attribute, i.e. ease of changing the position and orientation of the end#effector, have been proposed by -oshikawa $ '. However, most of these approaches attach overtly high

weightage to performance factors and do not consider other !ualitative factors. / production

engineering based approach for robot selection giving weightage to the !ualitative and

!uantitative factors alike was presented by 0nott and 1etto $2' and (owill $3'. "ince then,

many researchers have proposed different approaches based on data evaluation analysis

techni!ue incorporating both !uantitative and !ualitative factors to determine the best robot

alternative $4#%4, && '.If the developments in the selection techni!ues over the years are tracked, it is observed that

initially researchers focused more on the analytical framework of decomposing the main

problem at hand into its bases and these bases were further factorized into root issues and

attributes. (he attributes were systematically divided into sub5ective and ob5ective attributes.

(hese multiple attribute decision making approaches later branched out, developing into

techni!ues based on (opsis, fuzzy logic etc. 1radually, the concern of the researchers shifted

from mere decision making to the computational efficiency aspects of the techni!ues. (he

/nalytical hierarchical approaches 6/H78 and fuzzy techni!ues were proposed. More


2/51

other approaches are being developed. urrently, the trend is towards analyzing the intra#

dependencies among the attributes and various clusters and inter#dependencies across the

various clusters of attributes, which remain un#captured in the /H7. (hus, the /H7

methodologies are extended to more general and versatile techni!ue, viz. /nalytical *etwork

7rocesses. "ince /*7 does not re!uire independence among the elements and among the

clusters and also allows for provisions of feedback, /*7 is considered more versatile than

the /H7.

(hus, 9artholomew and -annacopoulou $4' presented the robot selection and evaluation

based on the utility theory. "election of robotic manipulators considering twenty#two

attributes including accuracy, repeatability, reliability, programming languages, diagnostic

capability, safety, etc. is presented using the singly attribute, multiple attribute and mutual

independence utility theories. Imang and "chlesinger $:' presented decision models for robot

selection and compared ordinary least s!uares and linear goal programming methods.

9oubekri et al. $%;' presented a comprehensive system for industrial robot selection taking

into account the functional and organizational parameters along with the economic

considerations. / module Robofile that provides the user with a detailed description of each

robot in the knowledge base was also presented. hao#-en


3/51

Hierarchy 7rocess for Robot "election in which a selection considering eighty#nine attributes

was done $&&'. /s an illustration, the selection has been presented considering only three

attributes. /pplied to the robot selection, in this techni!ue, the decision problem is first

broken into a hierarchy of decision elements? next numerical pair wise comparisons of the

decision elements is done followed by obtaining a relative weights of decision elements. (he

relative weights of are then combined to determine the overall score for each of the robots.

(he /H7 is shown to be more efficient than the (opsis method in $&+#& '. 9hangale et al.

$& ' did the selection of robots and ranked them using the attribute (opsis and graphical

methods. "imilarly, a fuzzy (opsis method for robot selection is proposed by hu and =in

$%3', wherein the ratings of various alternatives versus various sub5ective criteria and the

weights of all criteria are assessed in linguistic terms represented by fuzzy numbers. (he

primary ob5ective here is to counter the shortcomings of =iang and


4/51

1.1 A NALYTICAL N ETWORK P ROCESS

Introduced by "aaty $&2', /*7 is particularly useful in decision making problems which

include cross hierarchical dependencies, influences within the clusters and between the

alternatives and does not necessarily include the assumption of independence of higher#level

elements from lower level elements and about the independence of the elements within a

level. @igure % shows a schematic representation of a network in %6a8 which involves

feedbacks, interdependencies and cross hierarchical influences as compared to a hierarchical

structure, in %6b8, used in /H7.

6a8 a *etwork 6b8 a Hieraricy

@igure %A "tructural )ifference between a *etwork and Hierarchy

It can be seen that the /H7 is a special case of /*7, methodology. *ote that, the nodes

represent the levels in hierarchy and components in the network, as proposed by "aaty $&2'.

(he arrows represent the relationships in the network and the direction of dependence.

Moreover, the feedback control is represented by the closed loops as shown in @ig. %6a8.

/nalytical *etwork 7rocess 6/*78 has been used by different researchers for decision

making in various applications including strategic I( outsourcing decision making $&3#&4',

supplier selection $&:', strategic decision making in supply chain management $+;', selection

of RB) pro5ects $+%', personnel selection in firms $+&', knowledge management in industries

$++', process selection in chemical industries $+ ', analyzing organizational pro5ect

alternatives for agile manufacturing processes $+ ', real estate sector $+2', and other fields

like military logistics policy formulation, financial crises forecasting, "


5/51

sub5ective and ob5ective criteria and parameters are involved in robot selection and most of

them have complicated cross dependencies across the hierarchies. 9esides, there exist a

looseDconditional correlation also between some elements and criteria in the robot selection.

"ince, both these things, viz., intra#dependencies and conditional correlation of criteria, can

be modeled appropriately in /*7 only, /*7 is presented here as an efficient techni!ue for

decision making and selection of robots.

1.2 O RGANIZATION OF THE P APER

(he paper is organized as followsA /fter a brief background and the literature survey, /*7 is

presented as a decision making techni!ue in multiple attribute environment in "ection &. (he

step#wise details are presented and the importance of the /*7 as a decision making tool for

the robot selection is highlighted. In "ection + the /*7 methodology is applied for a general

robot selection decision making process. robot selection using /*7 techni!ue is presented.

>arious attributes and parameters affectingDinfluencing the robot selection for a particular

application at hand are identified. (he attributes are then clustered as per the characteristics

of their influences, into determinant, dimension and enabler levels. "ubse!uently the super

matrices and the desirability matrices are obtained to estimate the overall weightage indices

6C


6/51

@igure &A *etwork for a control and attribute hierarchy

parameters which are similar in the overall influence on the alternatives are then clustered

together, as shown in @ig. &. and mapped together in the network. *ote that, the /*7 does

not re!uire the strictly hierarchical structure. / mapping of the dependencies and influences

among the various attributes and the alternatives in the network is done. @igure & represents a

schematic structure after such a problem structuring step, for four possible alternatives, ten

influencing attributes and their hypothetical inter#dependencies. *ote that, the dependenciesand influences among the various attributes, various clusters, intra cluster feedbacks and the

overall influences of the clusters on the alternatives is mapped using the arrows. (he

directions of the arrows give the direction of dependence.

*ext, the pair wise comparisons among the various clusters and then the attributes is then

done !uantify the contribution of the clusterDattribute to its upper level criterion. (he relative

importance values are determined using the "aatyEs %#: scale $&2, +&'. (hus, for a relative

importance of ith element on its upper level criterion, a numerical value of ai5 is assigned. /reciprocal value is assigned to the inverse comparison? that is, ai5F%Da5i. / local priority

vector is then derived as an estimate of relative importance associated with the elements. /

supermatrix wherein the relationships between two elements as derived above are represented

using matrix elements is formed. (hus, an initial super matrix is formed by making use of

priority vectors obtained from decision matrices. *ext, the limit supermatrix is formed via

raising the weighted supermatrix to the power of an arbitrarily large number. =imit

supermatrix exhibits the weights of factors belonging to !uantitative and !ualitative factorgroups. @inally, the results from the control hierarchies are synthesized and alternative with

/ttribute % /ttribute &

/ttribute +

Cluster 1

/ttribute 4 /ttribute :

/ttribute %;

Cluster 3

/ttribute /ttribute

/ttribute 2

Cluster 2

/lternative % /lternative &

/lternative +

Alter !t"#es

/lternative

/ttribute 3


7/51

the largest overall priority is selected. (he selection of best alternatives is done by

determining the overall weightage index 6C


8/51

maximum overload capacity, precision, manipulability, dextricity etc. and form

high criteria for considerations for robotic selection.

6v8 ompatibility of robot with the existing set up at installation site A It may be

important to assess the role of compatibility criteria which includes the influence

of existing set#up at the customer end on his decision choices. (hus, eg., if a

particular manufacturing company has a set of robots of company / 6say8, and it

is planning for expansion then there are high chances of manufacturing company

selecting the robots of company / as it provides leverage in compatibility with

existing set up of power supply, electrical controls, spares maintenance etc. (hus

this criteria is also of high importance.

(he above five criteria will be taken up as five determinants for estimating the overall

weighted index 6C


9/51

in the given range. +4# ;'

&


10/51

%

7rogrammingflexibility andcapacity of

ontroller cards6 8

(he selection criteria includes interfaces, like touch screens andother peripherals like programming, controller chips etc.

$3, 4, %;,%&, & , +

%2(ype of cableand harness6 H8

able#routing and harness specifications must be matching with the pro5ect specifications making them important for considerationduring installation of the robot.

$& '

%3 )extricity 6)J8

It is a comprehensive parameter which includes the affect ofgeometric constraints on the manipulability, speed, singularity andother aspects of robot performance. / robot with higher dextricity ismore capable of performing intricate 5obs and hence becomes achoice of robot selectors.

$& '

%4 "ingularity 6"=8

(he geometric constraints in the robot linkages manifest itself insuch a way that some locations, inspite of falling inside theworkspace may re!uire huge computational or input efforts. (hesesingularities must be avoided. are must be taken at the time of

selection of appropriate robot.

$& '

%: *o. of axis6*/8

@or some applications, such as simple pick#and#place assembly, therobot may need simple 5oints and less no. of axis. However, formore sophisticated applications, such as weldingDpainting etc., robotmay re!uire additional no. of axis. (his is achieved by selectingappropriate robot architecture suitable for the application.

$3, %;, %& '

&; 7recision67"8 (he repeatability of the robot, determined by its precision, ensuresappropriate reiteratability in the robot operations.

$3, 4, %;,% , &&, &+4'

&% "ervos 6"M8(he servos selected can be geared or direct drive. Moreover, thegear trains may be epicyclical or direct. (hus, the servos haveimpact on overall performance and repeatability of the robots.

$3, %;, &&

& , +4'

&&Reasons of breakdown6R98

/s a decision maker in robot selection, it may be imperative for theselector to know the reasons for breakdown of a particular robot. Ifthe breakdowns are due to poor workmanships of machine designs,the repeatability of the robot and its reliability are effected.

$4, & '

&+

Mean (ime9etween@ailures6M(9@8

(he meantime between failures provide a reasonable estimation oftotal breakdown time for the robot. (hus, for reliable performancethe M(9@ should be as large as possible.

$4, & '

& Mean (ime toRepair 6M((R8

In case of a breakdown , the robot is do be serviced to bring it inworking order as soon as possible. / large M((R is indicative ofserious breakdowns, low availability of spares, poor service networkof the supplier, etc. and hence is detrimental to selection of robot bythe decision makers.

$4, & '

&"upplier service!ualityDcontract6"G8

(he company procuring the robot may have contractual agreementswith some specific suppliers. (his may provide the company the benefits of economics of scale. "uch contracts influence theselection of decision makers and hence must be given due weightage.

$%&, %3, && , +4'

&2 "upplier rating6"R8

9ased on the previous purchases, after sales services and

performance of their robots the user companies generally assignratings to the robot suppliers. (hese ratings play important role innew decision making by the company for new procurements and

$%+, & '


11/51

&3 (otal cost 6 (8

ost of the robot is undoubtedly an important decisive criterion.However, note that, cost alone is not the overall governing criteria but various aspects of !uality and return on investments complimentthe cost as selection criteria.

$3, %&, %+% , %3, && , +4'

&4 /vailability ofspares 6"/8Guick availability of spare parts reduce the downtime of the robotsand positively influence the decision of robot selection. $%+, & '

&:


12/51

3.3 P AIR (WISE C O'PARISONS OF T HE D ETER'INANTS

In this step the attributes and decision elements at determinant level are compared pair#wise

with respect to their importance towards the attainment of ob5ective 6robot selection8.

ach determinant level criterion is pair#wise compared with other determinant level

criteria with

(otal cost 6 (8 /vailability

of spares 6"/8


13/51

@igure +A /*7 based model for robot selection in multiple attribute based decision makingenvironment

/ 9


14/51

respect to the contribution to the goal. It will suffice here to outline the techni!ue adopted, in

this paper, to obtain the pairwise comparative rating between two criteria, at any level of

classification, namely determinant, norm and facilitators. In order to get the genuine

ratings of each parameter viz#a#viz other parameters, a three pronged strategy has been

adopted. @irst a set of re!uest proposals have been developed wherein a brief description

of various attributes 6at various levels8, as presented in "ection +.%, are put in a

comparative matrix format. (he !uestions are then given to a panel of experts on the

sub5ect who are re!uested to rate them pairwise. (he ratingDrelative importance values

are determined with "aatyEs %#: scale, where a score of % represents e!ual importance

between the two elements and a score of : indicates the extreme importance of one

element 6row component in the matrix8 compared to the other one 6column component in

the matrix8. / reciprocal value is assigned to the inverse comparison? that is, ai5F%Da5i,

where ai5 6a5i8 denotes the importance of the ith 65th8 element.

/s the third part of the strategy for determination of pair#wise ratings, the geometric mean of

the various ratings, between two given criteria, given by different experts is taken. (he

geometric mean, then, represents the pair#wise comparative value to be taken for the

determination of priority vectors between two elements.

"ince the pairwise comparison matrices are formed using the group decision making followed

by geometric averaging of individual 5udgments, the effect of the individual biases have

been eliminated from the analysis. (his is in accordance with )yer and @orman $ %' whohave suggested 6i8 consensus, voting in groups, and 6iii8 geometric mean of the

individualEs 5udgments as methods to include ob5ective opinion rankings and eliminate

individual biases from the analysis.

*ote that, similar procedure is adopted to get the weighted rankingsDvalues of pairwise

comparisons between attributes at cluster#norm and facilitator level.

(able & shows the the matrix showing the pairwise comparison of determinants. / set of local

priority vectors 6also known as eigen#vectors or e#vectors8, as an estimate of relativeimportance associated with the elements, is also shown. (he local priority vectors are

determined by solving the e!uation

/K w F LmaxKw 6%8

where / is the matrix of pairwise comparison, w is the eigenvector, and Lmax is the largest

eigenvalue of /. In this paper, the following three#step procedure is used to determine

the priority vectors $&2, +++'A

%. "um the values in each column of the pairwise comparison matrix?&. )ivide each element in a column by the sum of its respective column. (he resultant matrix


15/51

+. "um the elements in each row of the normalized pairwise comparison matrix, and divide

the sum by the n elements in the row.

(able &A 7airwise comparisons of determinants 6 RF4.&48

SC WTH %LT PER CO' Pr"*r"t- #e+t*r

S+* e *, Cust*/"0!t"* SC % + & .1456

W*rt7 WTH %D+ % .1851

%u!l"t- %LT N % N . 961

Per,*r/! +e PER & & & % %D+ .2 44

C*/ !t":"l"t- CO' & & + % .3681

(hese final numbers provide an estimate of the relative priorities for the elements beingcompared with respect to its upper level criterion. (he resultant set is priority vector

associated with the pairwise comparison matrix. *ote that, priority vectors must be

derived for all comparison matrices. (he priority vectors from pairwise comparisons of

determinants, shown in (able#&, will be used for the calculation of overall weighted

index 6C


16/51

3.8 P AIR (WISE C O'PARISONS OF T HE F ACILITATORS &ENA$LER ATTRI$UTES

In this step, the pairwise comparison of attributes and parameters at the facilitator level is

conducted with respect to their relative influences towards their controlling criterion.

(hus, pairwise comparison for a determinant is done among the applicable enablers

within a given dimension cluster. (he number of such pairwise comparison matrices

depends on the number of determinants and dimensions in the /*7 model. In the present

case, there are five parameters at determinant level and six dimensions at cluster norms

level. Hence, in total there will be +; 6F2x 8 number of matrices. Cne such pairwise

comparison matrix for onfiguration of robot 6 R8 dimension under "cope of

customization 6" 8 determinant is shown in (able . @or the pairwise comparison, the

!uestion asked to the decision#maker isA Owhat is the relative impact on the configuration

of robot by enabler a 6say payload8 when compared to enabler b 6say workspace8 in

improving scope of customization available to the robot user and the supplierPQ

It is observed from (able that the relative importance of 7 when compared to


17/51

&. It is also observed from (able that enabler 7", M/ and C of robots have higher

influence 6;.%23 , ;.%2 % and ;.%+%3 respectively8 on configuration of robot in

improving "cope of customization between the robot user and the supplier. "imilarly,

computational efficiency 6 8 has the least influence 6;.;&%&8 on the robot configuration

in improving the scope of customization. (he priority#vectors obtained from these

matrices will be used in "uper matrix determination.

3.6 P AIR (WISE C O'PARISONS F OR I NTERDEPENDENCIES A 'ONG THE

F ACILITATORS &ENA$LER ATTRI$UTES

In this step, the interdependencies of the attributes at facilitator level are mapped by doing the

pairwise comparisons among themselves. (hus, the pairwise comparison of attributes

and parameters at the facilitator level is conducted to capture the effect of one controlling

facilitatorDenabler level attribute on the other enabler attributes in a particular cluster and

determinant group. (he number of such pairwise comparison matrices depends on the

number of determinants and dimensions in the /*7 model. Cne such pairwise

comparison matrix for mapping the effects of configuration of robot 6 R8 dimension

under "cope of customization 6" 8 determinant with payload capacity 67 8 as the

controlling criteria on the other attributes at facilitator level in the same cluster is shown

in (able . @or the pairwise comparison, the !uestion asked to the decision#maker isA

Owhen considering payload capacity with regard to increasing scope of customization,what is the relative impact on the enabler a 6say workspace8 when compared to enabler b

6say overload capacity8 in the given configuration of robot clusterPQ (he method of

rating the attributes is similar to that used in "ection In accordance with the network.

It is observed that workspace 6


18/51


19/51

3.> S UPER ' ATRI? F OR'ATION

In this step, a super#matrix, which synthesizes the priority vectors from various pair#wise

comparison matrices is formed for overall criteria prioritization and alternative rankings.

/ super#matrix is a partitioned matrix where each sub#matrix is composed of a set of

relationships between and within the levels as represented by the decision#makerEs

model. (hus the priority vectors from the pair#wise comparison matrices are used to

determine the overall relative importance of the enablers for each of the determinants.

(he super#matrix M, for the scope of customization determinant is presented in (able 3

in which the relative importance of each of the attributes at facilitatorDenabler level on

the scope available for the customization is presented.

"ince, the elements of the super#matrix are imported from the pairwise comparison matrices

of interdependencies 6(able 8, and there are +; such pairwise comparison matrices, one

for each interdependent enabler attribute in the scope of customization determinant, there

will be +; nonzero columns in this super#matrix. ach of the non#zero values in acolumn is the relative importance weight associated with the interdependent pairwise

comparison matrices. *ote that in total there will be as much super matrices as the

number of determinants 6attributes at the determinant level8. (hus, there exist five super#

matrices for the /*7 model shown in @igure %.

3.4 L I'IT SUPER ' ATRI? F OR'ATION

*ext, the super#matrix is made to converge to obtain a long#term stable set of weights. @or

convergence to occur, the super#matrix needs to be column stochastic $+3, &'. In other

words, the sum of each column of the super matrix needs to be one. Initial super matrix

is now raised to a high power to get the limit super matrix. Raising the super#matrix to

the power &k %, where k is an arbitrarily large number, allows convergence $ &'. In this

example, convergence is reached at M%4. (he converged super#matrix is shown in (able


20/51

(able 3A "uper#matrix M for "cope of customization before convergence

PC WS OC AC RS CE 'A =T PR PS WR SP ED HD CC CH SL D? NA PC S' R$ 'F 'R S% SR CT WT SA NW

PC ; ;.;2%& ;.%; & ;.;32: ;.%% & ;.% ;.% ;.;:42 ;.;:: ;.%;;3 ;.%; % ;.%%3: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

WS ;.%4&2 ; ;.;4&3 ;.;:&+ ;.;:42 ;.%;+ ;.; 3 ;.;:; ;.;:2% ;.;:+4 ;.;4:: ;.;:3: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

OC ;.%2;% ;.;4+: ; ;.;: + ;.;2&2 ;.;4; ;.;3& ;.;32+ ;.%;43 ;.;32% ;.;+:: ;.; ;& ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

AC ;.;+ ;.;2:& ;.;4 ; ;.;: + ;.;3:: ;.;42 ;.;2% ;.;2%+ ;.;44 ;.;:%& ;.;&: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

RS ;.;+ ;.;:34 ;.; 23 ;.;3 + ; ;.;:%& ;.%%; ;.;4+ ;.;:4 ;.%; + ;.; :: ;.;:+ ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

CE ;.%;3& ;.%;;& ;.;2%4 ;.;2%4 ;.;4 ; ;.;3% ;.; % ;.;:+2 ;.;3% ;.;3+: ;.%;%4 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

'A ;.;:+ ;.%%4 ;.;234 ;.%;3 ;.; :3 ;.;4;4 ; ;.%;2% ;.;:2 ;.;2++ ;.;4&2 ;.;4: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

=T ;.;4 & ;.; +% ;.;:;3 ;.;4 & ;.%+& ;.%&22 ;.%%+& ; ;.%%% ;.;:4 ;.;:%% ;.;3 % ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

PR ;.;32; ;.;4:& ;.;43: ;.%&2 ;.;: ;.;43& ;.%%3+ ;.%; ; ;.%& % ;.% + ;.% % ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

PS ;.; 4 ;.;:+% ;.%%%+ ;.% &: ;.;:4& ;.;:%+ ;.;:% ;.%;+ ;.; ; ; ;.% 3% ;.% ;2 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

WR ;.; 3 ;.% ;.%%4+ ;.; :3 ;.; 4 ;.;2:2 ;.; :4 ;.%&%+ ;.;332 ;.%;3& ; ;.; + ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

SP ;.%&:% ;.%++2 ;.%+ % ;.;24+ ;.%; % ;.;4:2 ;.;33 ;.%;&: ;.%%23 ;.;3&% ;.;3 4 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

ED ; ; ; ; ; ; ; ; ; ; ; ; ; ;.&:3+ ;.&:+% ;. +3 ; ; ; ; ; ; ; ; ; ; ; ; ; ;

HD ; ; ; ; ; ; ; ; ; ; ; ; ;.% ;: ; ;.% 4 ;.&24 ; ; ; ; ; ; ; ; ; ; ; ; ; ;

CC ; ; ; ; ; ; ; ; ; ; ; ; ;.2;%3 ;. +: ; ;.%: 2 ; ; ; ; ; ; ; ; ; ; ; ; ; ;

CH ; ; ; ; ; ; ; ; ; ; ; ; ;.& 3 ;.%2+4 ;. %% ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

SL ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.++++ ;.3 ;; ; ; ; ; ; ; ; ; ; ; ;

D? ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.++++ ; ;.& ;; ; ; ; ; ; ; ; ; ; ; ;

NA ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.2223 ;.2223 ; ; ; ; ; ; ; ; ; ; ; ;

PC ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.2223 ;.& ;; ; ; ; ; ; ; ; ;

S' ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.++++ ; ;.3 ;; ; ; ; ; ; ; ; ;

R$ ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.2223 ;.++++ ; ; ; ; ; ; ; ; ;

'F ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;. 44: ;. +4: ;. 44: ; ; ; ;

'R ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;. +3 ; ;.&:3+ ;.& %: ; ; ; ;

S% ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.&24; ;.& %4 ; ;.% :+ ; ; ; ;

SR ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.%: 2 ;.% :+ ;.%2+4 ; ; ; ; ;

CT ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.%:&& ;.% 22 ;.++++

WT ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.& %+ ; ;.+32 ;.++++

SA ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;. 4:+ ;. 22& ; ;.++++

NW ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.% : ;.& %2 ;. 23; ;


21/51

(able 4A =imit "uper#matrix for "cope of customization after convergence 6 M18

PC WS OC AC RS CE 'A =T PR PS WR SP ED HD CC CH SL D? NA PC S' R$ 'F 'R S% SR CT WT SA NW

PC ;.;:++ ;.;:++ ;.;:++ ;.;:++ ;.;:++ ;.;:++ ;.;:++ ;.;:++ ;.;:++ ;.;:++ ;.;:++ ;.;:++ ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

WS ;.;:;3 ;.;:;3 ;.;:;3 ;.;:;3 ;.;:;3 ;.;:;3 ;.;:;3 ;.;:;3 ;.;:;3 ;.;:;3& ;.;:;3 ;.;:;3 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

OC ;.;33% ;.;33% ;.;33% ;.;33% ;.;33% ;.;33% ;.;33% ;.;33% ;.;33% ;.;33;: ;.;33% ;.;33% ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

AC ;.;2 ;.;2 ;.;2 ;.;2 ;.;2 ;.;2 ;.;2 ;.;2 ;.;2 ;.;2 ; ;.;2 ;.;2 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

RS ;.;32 ;.;32 ;.;32 ;.;32 ;.;32 ;.;32 ;.;32 ;.;32 ;.;32 ;.;32 & ;.;32 ;.;32 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

CE ;.;3 : ;.;3 : ;.;3 ;.;3 ;.;3 ;.;3 ;.;3 ;.;3 ;.;3 ;.;3 :2 ;.;3 ;.;3 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

'A ;.;4;: ;.;4% ;.;4% ;.;4% ;.;4% ;.;4% ;.;4% ;.;4% ;.;4% ;.;4;:2 ;.;4% ;.;4% ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

=T ;.;43 ;.;43 ;.;43 ;.;43 ;.;43 ;.;43 ;.;43 ;.;43 ;.;43 ;.;43 + ;.;43 ;.;43 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

PR ;.;:3+ ;.;:3+ ;.;:3+ ;.;:3+ ;.;:3+ ;.;:3+ ;.;:3+ ;.;:3+ ;.;:3+ ;.;:3+ ;.;:3+ ;.;:3+ ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

PS ;.;:;4 ;.;:;4 ;.;:;4 ;.;:;4 ;.;:;4 ;.;:;4 ;.;:;4 ;.;:;4 ;.;:;4 ;.;:;4% ;.;:;4 ;.;:;4 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

WR ;.;3&3 ;.;3&4 ;.;3&4 ;.;3&4 ;.;3&4 ;.;3&4 ;.;3&4 ;.;3&4 ;.;3&4 ;.;3&33 ;.;3&4 ;.;3&4 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

SP ;.;:&+ ;.;:&+ ;.;:&+ ;.;:& ;.;:&+ ;.;:&+ ;.;:& ;.;:& ;.;:&+ ;.;:&+ ;.;:&+ ;.;:& ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

ED ; ; ; ; ; ; ; ; ; ; ; ; ;.&323 ;.&323 ;.&322 ;.&323 ; ; ; ; ; ; ; ; ; ; ; ; ; ;

HD ; ; ; ; ; ; ; ; ; ; ; ; ;.% :% ;.% :% ;.% :% ;.% :% ; ; ; ; ; ; ; ; ; ; ; ; ; ;

CC ; ; ; ; ; ; ; ; ; ; ; ; ;.+;+% ;.+;+% ;.+;+% ;.+;+% ; ; ; ; ; ; ; ; ; ; ; ; ; ;

CH ; ; ; ; ; ; ; ; ; ; ; ; ;.&2% ;.&2% ;.&2% ;.&2% ; ; ; ; ; ; ; ; ; ; ; ; ; ;

SL ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.+3 + ;.+3 + ;.+3 ; ; ; ; ; ; ; ; ; ; ;

D? ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.&& : ;.&& : ;.&& % ; ; ; ; ; ; ; ; ; ; ;

NA ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.+::3 ;.+::3 ;. ;; ; ; ; ; ; ; ; ; ; ; ;

PC ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.+%32 ;.+%33 ;.+%32 ; ; ; ; ; ; ; ;

S' ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.+ &: ;.+ &: ;.+ +;% ; ; ; ; ; ; ; ;

R$ ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.+&: ;.+&: ;.+&:+: ; ; ; ; ; ; ; ;

'F ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.+2 2 ;.+2 2 ;.+2 2 ;.+2 2 ; ; ; ;

'R ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.&:% ;.&:% ;.&:% ;.&:% ; ; ; ;

S% ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.%: : ;.%: : ;.%: : ;.%: : ; ; ; ;

SR ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.% :+ ;.% :+ ;.% :+ ;.% :+ ; ; ; ;

CT ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.%4;% ;.%4;% ;.%4;% ;.%4;%

WT ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.& : ;.& : ;.& : ;.& :

SA ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.+&4& ;.+&4& ;.+&4& ;.+&4&

NW ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;.& && ;.& && ;.& && ;.& &

&%


22/51

3.1 A SSORT'ENT OF DATA AND T HE DESIRA$ILITY I NDICES ' ATRICES

Ssing the information inform of pairwise comparative scores among priority vectors, and

comprehensive comparative scores from the super#matrix and limit super#matrix, the

selection of best alternative is done. @irst, the selection of best alternative corresponding to

each determinant is done,. @or this the desirability indices, indicating the relative importance

of the alternatives in supporting a particular determinant, are obtained corresponding to each

determinant. (he desirability index, D ia for alternativei 6F/, 9 or in the present model8

and the determinanta , is defined as $ +'A

= =

= J

i j

K

k ikja

I kja

Dkja jaia

ja

S A A P D%

where P ja is the relative importance weight of dimension j in influencing the determinanta which

is obtained from the priority vector of the pairwise comparison matrices of cluster level normattributes? Dkja A is the relative importance weight for attribute at facilitatorDenabler level and is

obtained as the priority vector from pairwise comparison matrices of facilitator level attributes

mapping their combined effect of various dimensions under scope of various determinants? Tk in

influencing the determinant a through cluster dimension 5 for dependency 6)8 relationships? I kja A

is the stabilized relative importance weight for attribute enablerk in the dimension j and the

determinant a cluster for interdependency 6I8 relationships. (hese values are taken from

converged super#matrix. Moreover, ikjaS is the relative impact of alternativei on enablerk of

dimension j for determinanta? K ja is the index set of attribute enablers for dimension j of

determinanta , J is the index set of the cluster j.

"ince in the /*7 model, @igure %, taken in this paper, five determinants are considered, the

number of such desirability indices set Di 6iF/, 9 and 8 will be five. (able : shows the

desirability indices for one determinant, the scope of customization, D i(SC) . (he desirability

indices D i(SC) and the normalized desirability indices, D i(SC) , for the three alternatives 6/, 9 and

8 with respect to the scope of customization 6" 8 available in their robots are obtained using(able :A )esirability matrix for scope of customization

D"/e s"* P j(SC) D

SC kj A 6 I

S kj A 686 SC ikjS Desirability index Di(SC) .

A B C i =A I =B i =CC* ,";ur!t"**, r*:*t

PC ;.&%& ;.;22 ;.;:+ ;.+ ;. 34 ;.%3& ;.;;; ;.;;;2&& ;.;;;&&WS ;.&%& ;.; & ;.;:% ;. 3 ;.+& ;.%&+ ;.;;; + ;.;;;+%4 ;.;;;%&&


23/51

OC ;.&%& ;.%+& ;.;33 ;. %3 ;.+ : ;.%& ;.;;%%% ;.;;;33+ ;.;;;&24AC ;.&%& ;.; 4 ;.;2 ;.+ ;. 34 ;.%3& ;.;;;&4 ;.;;;+4& ;.;;;%+4RS ;.&%& ;.; ;.;32 ;. : ;.+%& ;.%:4 ;.;;; +2 ;.;;;&33 ;.;;;%32CE ;.&%& ;.;&% ;.;3 ;. +% ;.+&& ;.% 3 ;.;;;%3: ;.;;;%;: .:2 #;'A ;.&%& ;.%2 ;.;4% ;.&33 ;. & ;.%3& ;.;;;34 ;.;;% ;.;;; 4

=T ;.&%& ;.;43 ;.;43 ;.&:3 ;. +: ;.%2 ;.;;; 4& ;.;;;43 ;.;;;&22PR ;.&%& ;.;2% ;.;:3 ;.&23 ;. +4 ;.%: ;.;;;++3 ;.;;;24 ;.;;;& 2PS ;.&%& ;.%24 ;.;:% ;.%&+ ;.+& ;. 3 ;.;;;+:2 ;.;;%;+ ;.;;%4

WR ;.&%& ;.; & ;.;3+ ;.%% ;.+ 2 ;. 4.4 #; ;.;;;&34 ;.;;; +2SP ;.&%& ;.;4 ;.;:& ;.%:4 ;.+%& ;. : ;.;;;+&: ;.;;; %: ;.;;;4%2

Ele+tr"+!l ! ariation in Cariation in C


47/51

3 0.345508 0.30728 0.3472124 0.345082 0.306954 0.347963: 0.344708 0.306666 0.348626

>ariation in Cariation in C


48/51

ostD!uality / 9%D: 0.349764 0.310279 0.339957%D4 0.349434 0.310109 0.340457%D3 0.349076 0.30992 0.341004%D2 0.348691 0.30971 0.341599%D 0.348282 0.309474 0.342244N 0.347862 0.309209 0.342928%D+ 0.347475 0.308911 0.343614

0.347264 0.308577 0.344159

% 0.347907 0.308227 0.343866& 0.349864 0.308101 0.342035+ 0.351542 0.308101 0.340357

0.352897 0.308124 0.338979

0.353999 0.30815 0.337851

2 0.35491 0.308175 0.3369153 0.355673 0.308198 0.3361284 0.356322 0.308219 0.335459

: 0.35688 0.308237 0.334883

>ariation in C


49/51

4 0.344074 0.302932 0.352994: 0.343931 0.302659 0.35341

>ariation in Cariation in C


50/51

ostD!uality / 9%D: 0.34378 0.312361 0.343859%D4 0.344024 0.312543 0.343434%D3 0.344308 0.312748 0.342944%D2 0.344642 0.31298 0.342377%D 0.345042 0.313242 0.341715N 0.345531 0.313531 0.340938%D+ 0.346143 0.313828 0.340029

0.346942 0.314039 0.339019

% 0.348082 0.313652 0.338266& 0.348972 0.312164 0.338864+ 0.349417 0.310816 0.339767

0.349707 0.309705 0.340588

0.349918 0.30879 0.341292

2 0.350082 0.308027 0.3418913 0.350213 0.307384 0.3424034 0.350321 0.306835 0.342844

: 0.350412 0.306361 0.343227

>ariation in C


51/51

Documents

In Journals Format