research article a qfd-based mathematical model for new...
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Research ArticleA QFD-Based Mathematical Model for New ProductDevelopment Considering the Target Market Segment
Liang-Hsuan Chen and Cheng-Nien Chen
Department of Industrial and Information Management National Cheng Kung University Tainan 70101 Taiwan
Correspondence should be addressed to Liang-Hsuan Chen lhchenmailnckuedutw
Received 11 August 2014 Accepted 12 November 2014 Published 1 December 2014
Academic Editor Chong Lin
Copyright copy 2014 L-H Chen and C-N ChenThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Responding to customer needs is important for business success Quality function deployment provides systematic procedures forconverting customer needs into technical requirements to ensure maximum customer satisfaction The existing literature mainlyfocuses on the achievement of maximum customer satisfaction under a budgetary limit via mathematical models The marketgoal of the new product for the target market segment is usually ignored In this study the proposed approach thus considers thetarget customer satisfaction degree for the target market segment in the model by formulating the overall customer satisfaction asa function of the quality level In addition the proposed approach emphasizes the cost-effectiveness concept in the design stage viathe achievement of the target customer satisfaction degree using theminimal total cost A numerical example is used to demonstratethe applicability of the proposed approach and its characteristics are discussed
1 Introduction
In a fast-changing business environment business units mustinvent new products or improve the quality of productscontinually to meet customer needsThe introduction of newproducts into the market to respond to customer demands isimportant for business success From a marketing perspec-tive market segmentation is a necessary means for findingtarget customers The new products should be positioned atthe target customers during the product positioning processThe target customer satisfaction level for product qualityshould then be determined to meet the target customerrequirements To do this a systematic new product develop-ment (NPD) process is usually carried out by business units todesign an appropriate product that achieves the determinedtarget customer satisfaction level based on a limited budgetor using the minimum cost expenditure
Quality function deployment (QFD) has been widelyadopted by practitioners since the 1970s to design newproducts or improve existing ones [1] Besides productdevelopmentdesign QFD has been applied to fields suchas quality managementplanning decision-making man-ufacturing service and education [2] QFD provides a
systematic procedure for converting customer needs intotechnical requirements to ensure customer satisfaction Anumber of researchers have proposed various quantitativeapproaches for applying QFD to a variety of problemsAmong quantitative approachesmathematical programmingis usually applied to construct models to find the optimumdesign requirements for maximizing customer satisfactionunder the limits of budget time andor other resources [3ndash14]
For developing new products the quality level is usuallydetermined by the RampD team to achieve the anticipated satis-faction degree of the target customers However the existingliterature related to quantitative approaches for applyingQFDin NPD processes focuses on finding the optimal solutionsof design requirements for maximizing customer satisfactionunder a budgetary limitation not for achieving the desiredcustomer satisfaction level in terms of product quality Thusthe determined quality level of new products may not meetcustomer requirements so that the business unit may loseits competitive advantage in the market In addition therelationship between customer satisfaction and quality levelfor target customers is important for the developments ofnew products to determine the quality level in order to
Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2014 Article ID 594150 10 pageshttpdxdoiorg1011552014594150
2 Journal of Applied Mathematics
achieve the target customer satisfaction Nevertheless sucha relationship is not incorporated in existing QFD modelsBased on the above considerations how to use the minimalbudgetresources to achieve the quality level in order to meetthe desired customer satisfaction should be considered inQFD-related problems In this regard instead of consideringthe budget constraint this paper takes into account therelationship between customer satisfaction and quality levelfor the target customers in the QFD model to satisfy thedesired satisfaction level in which the minimum design costis achieved
The rest of this paper is organized as follows Section 2briefly introduces the concept of QFD and the relatednormalization formulations which are used in the pro-posed model From a marketing perspective the relationshipbetween customer satisfaction and quality level for targetcustomers is described in Section 3 In Section 4 consideringthe desired customer satisfaction and the correspondingquality level for target customers as constraints a nonlinearmathematical programming model is proposed to minimizethe total design cost Section 5 provides an illustrative exam-ple of new bike design to demonstrate the feasibility andapplicability of the proposed approachNumerical analyses ofthe design parameters in the proposedmodel are alsomade toexplore the characteristics of the model and their managerialimplications Finally conclusions are provided in the finalsection
2 Background
The basic concept of QFD is to transform customer voicesinto technical requirements to ensure customer satisfac-tion The QFD processes are performed by applying thedesign information embodied in the relation matrix calledthe house of quality (HOQ) as illustrated in Figure 1 Inpractice QFD transforms customer needs into technical(or designengineering) characteristics via the HOQ duringthe design or planning stage The interior of the HOQmatches customer requirements (CRs) with the correspond-ing design requirements (DRs) identifying the relationalintensity between each pair of CRs and DRs to ensurequality performance that can satisfy the target customers Ifnecessary the roof of the HOQ represented as a correlationmatrix is constructed to indicate the technical correlationsamong DRs Figure 1 shows a HOQ example to signify therelational intensities between CRs and DRs as well as thecorrelation degrees among DRs The importance degree ofeach CR is also displayed in the figure In general the HOQcontains the relational intensity between each pair of CRs andDRs and the technical correlation between each pair of DRsThe legend in Figure 1 shows various designated symbolsused to represent different degrees of relational intensity ortechnical correlation in the HOQ
In general the design information contained in the HOQis integrated to further determine the importance of DRsand their achievement degrees in order to optimally satisfycustomer satisfaction To do this a normalization process isusually applied by QFD researchers and practitioners In theliterature the normalization model proposed by Wasserman
Impor-tance
StrongModerateWeak
Weak negativeModerate negative
Strong negative
Relationship
CR1
CR2
CR3
CR4
d1
d2
d3
d4
DR1 DR2 DR3 DR4
Figure 1 Matrix structure of HOQ
[3] has been widely adopted (eg [6 7 9 10 13 15ndash29])Based on Lymanrsquos normalization concept [30] this modelis developed by incorporating the correlations among DRsformulated as
1198771015840
119894119895=
sum119899
119896=1119877119894119896sdot 120574119896119895
sum119899
119895=1sum119899
119896=1119877119894119896sdot 120574119896119895
(1)
from the vector space concept where 120574119896119895denotes the techni-
cal correlation between DR119896and DR
119895 In the above equation
119877119894119896indicates the relational intensity between CR
119894and DR
119896
which is measured based on a 3-point scale such as 1-3-9 or1-5-9 for describing the weak-moderate-strong relationshipAlthoughWassermanrsquos normalizationmodel has been widelyadopted it has someweaknesses For example it assumes thatcustomer requirements are mutually independent Howeverthismay not be true in practiceMore importantly thismodelmay generate a relational intensity for a pair of CRs and DRsthat does not exist in the original design information Themodel may thus produce unreasonable outcomes
Identifying such weaknesses in Wassermanrsquos normaliza-tion model L-H Chen and C-N Chen [31] proposed thefollowing modified normalization model
119877norm119894119895
=
(sum119899
119896=1120574119896119895) 119877119894119895
sum119899
119895=1(sum119899
119896=1120574119896119895) 119877119894119895
(2)
where 119877norm119894119895
denotes the normalized relationship betweenCR119894and DR
119895 Applying the above modified normalization
model to integrate design information the unreasonableoutcomes from Wassermanrsquos model can be avoided Fur-thermore considering the possibility that some CRs arecorrelated as shown in Figure 2 L-H Chen and C-N Chen[31] also proposed the following normalization model tointegrate CRs similar to that in (2) in determining thenormalized weights of CRs
119889norm119894
=(sum119898
119897=1120573119894119897) 119889119894
sum119898
119894=1(sum119898
119897=1120573119894119897) 119889119894
(3)
Journal of Applied Mathematics 3
`
Impor-tance
120574jn
CRi
CRm
DRj DRn
Rin
RmnRmj
Rijdi
dm
120573im
Figure 2 General HOQ structure
where 120573119894119897denotes the correlation between CR
119894and CR
119897and
119889119894is the importance of CR
119894 It is noted that the normalized
weight 119889norm119894
in (3) is reduced to 119889119894when CRs are mutually
independent that issum119898119897=1120573119894119897= 1
3 Satisfaction Function with Quality Level
The purpose of the development of new products or theimprovement of existing products is mainly to satisfy cus-tomer needs or enhance customer satisfaction Achievingcustomer satisfaction is always one of the main goals for thetarget market [32] Customer satisfaction is considered oneof the most important constructs for consumers [33] Hencecustomer satisfaction is important in marketing because ofits great influence on customer purchase behavior Basedon an empirical study Anderson and Sullivan [34] foundthat customer satisfaction can generally be described as afunction of perceived quality from customers consideringan adjustment amount to reflect the customer perception ofconfirmationdisconfirmation In their study the customersatisfaction function is expressed as a concave down functionof perceived quality Following the concept of Andersonand Sullivanrsquos study [34] the present study considers thatcustomer satisfaction is positively related to the design qualityof the product in terms of a concave down function assumingthat the quality designed for the product in the design stagewill be perceived by the target customers in the futuremarketthat is the design quality level has a positive relationshipwith customer perceived quality Figure 3 shows customersatisfaction (CS) as a concave down function of design quality(DQ)
For QFD applications the design quality level of aproduct can be treated as the fulfillment level of designrequirements (DRs) and therefore customer satisfaction canbe described as a function of the DRsrsquo fulfillment levels inthe QFD processes Let 119862
119895represent the cost required for
DR119895with which the technical requirement for DR
119895can be
completely attained so that customer satisfaction can be fullyachieved 119909
119895(isin [0 1]) represents the decision variable taking
the fulfillment level of the technical requirement for DR119895
Custo
mer
satis
fact
ion
Design quality1
1
CS(X)
DQ(X)
Figure 3 Functional curve for customer satisfaction (CS) anddesign quality (DQ)
denoting the quality level of DR119895required tomeet the desired
customer satisfaction For simplification suppose that thecost required to achieve the fulfillment level of DR
119895 119909119895 is
119862119895119909119895 that is a proportional relation between the required
cost and the fulfillment level The value of 119909119895= 0means that
the technical need for DR119895is only the basic requirement so
that the cost is 0 In addition the use of the whole budget 119862119895
for DR119895will achieve the full technical requirement that is
119909119895= 1 and full customer satisfaction for this DRLet X = [119909
1 1199092 119909
119899]119879 be the vector containing the
fulfillment levels of the technical requirements for all DRsFor a new product the overall DQ is defined as the averageof the fulfillment levels of all DRs as
DQ (X) = 1119899
119899
sum
119895=1
119909119895 0 le 119909
119895le 1 (4)
where 0 le DQ(X) le 1 In other words 119909119895is interpreted as
the design quality level of DR119895 In addition based on previous
studies (eg [3ndash14]) using the normalized information fromthe HOQ 119877norm
119894119895and 119889norm
119894in (2) and (3) respectively the
customer satisfaction can be formulated as
CS (X) =119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895 0 le 119909
119895le 1 (5)
where 0 le CS(X) le 1 It is obvious that DQ(X) = 1 andCS(X) = 1 when 119909
119895= 1 forall119895 = 1 2 119899 As described
above based on the concept of Anderson and Sullivanrsquos study[34] customer satisfaction is characterized as a concave downfunction of the design quality of a product for a specificmarket segment Figure 3 shows such a functionThe concavedown curve illustrates the diminishing marginal effect asdesign quality increases the marginal effect of customersatisfaction decreases This is characterized here using thefollowing simple equation
CS (X) = [DQ (X)]1119896 (6)
4 Journal of Applied Mathematics
where 119896(gt 1) is a characteristic parameter used to describethe customer preference of a specific market segment for thedesign quality level of a specific product The function in(6) characterizes features of the relationship between CS(X)and DQ(X) as described above In practice if the desiredcustomer satisfaction degree is determined as the goal ofsatisfying the target market (6) is employed to transform thedesired value CS(X) into the corresponding value DQ(X) asthe required design quality level
4 Proposed QFD Budget Planning Model
In contrast to previous QFD-related studies that maximizedcustomer satisfaction under a limited budget this paper aimsto find the minimum design budget to achieve the marketgoal in terms of the target customer satisfaction To this endsome constraints are considered in the model Based on (6)the target design quality level 120572 (0 lt 120572 le 1) correspondingto the target customer satisfaction 120575 (0 lt 120575 le 1) isdetermined by the management that is 120572 = 120575119896 119896 gt 1 Theachieved customer satisfaction formulated as (5) based onthe fulfillment level of the technical requirement that is thefulfilled design quality level for each DR should not be lessthan the target customer satisfaction 120575 similarly the fulfilledoverall design quality of (4) should not be less than thetarget design quality level 120572 More importantly the fulfilledoverall design quality should not be less than the quality levelreflected by the achieved customer satisfaction for the targetmarket in (6) that is (1119899)sum119899
119895=1119909119895ge (sum119898
119894=1119889norm119894
sum119899
119895=1119877norm119894119895
sdot
119909119895)119896 The right-hand side in the above inequality relation
can be interpreted as the product quality perceived by thetarget customers since it is derived based on the relationsbetween CRs and DRs in the HOQ Thus this constraintensures that the realized overall quality achieved from theproduct design is better than or equal to that perceived bythe target customers
In addition to the restrictions on the target design qualitylevel and customer satisfaction from the designersrsquo view-point in general there is aminimumsatisfaction level for eachcustomer requirement CR
119894The constraint ofsum119899
119895=1119877norm119894119895
sdot119909119895ge
120576119894 0 lt 120576
119894le 1 119894 = 1 119898 reflects this condition where 120576
119894
can be determined based on the normalized weights of CR119894
using the equation 120576119894= 1199051119889norm119894
1199051gt 0 to reveal each CRrsquos
importanceThe fulfilled design quality level for eachDR119895119909119895
is usually required to not be less than aminimum level say 120588119895
0 lt 120588119895le 1 where 120588
119895can be set as 120588
119895= 1199052(sum119898
119894=1119889norm119894
sdot119877norm119894119895
)1205721199052gt 0 considering the normalized importance of DR
119895and
the target design quality level 120572 Note that the parameters 1199051
and 1199052can be determined subjectively by the management
in weighing the corresponding CRs and DRs respectivelyunder the constraints of 0 lt 120576
119894le 1 and 0 lt 120588
119895le 1
A nonlinear programming model is formulated in (7) inwhich constraints (7a) to (7g) are used for the specificationsdescribed above The objective function (7) in the modelreflects the proportional relation between the required costand the fulfillment level of each DR
Proposed Nonlinear Programming Model Consider
Min119899
sum
119895=1
119862119895119909119895 (7)
subject to
119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895ge 120575 0 lt 120575 le 1 (7a)
119899
sum
119895=1
119909119895ge 119899120572 0 lt 120572 le 1 (7b)
1
119899
119899
sum
119895=1
119909119895minus (
119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895)
119896
ge 0 119896 gt 1 (7c)
119899
sum
119895=1
119877norm119894119895
sdot 119909119895ge 120576119894 0 lt 120576
119894le 1 119894 = 1 2 119898 (7d)
120576119894= 1199051119889norm119894
(7e)
120588119895le 119909119895le 1 0 lt 120588
119895le 1 119895 = 1 2 119899 (7f)
120588119895= 1199052(
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
)120572 (7g)
It is noted that constraint (7a) can be represented as
119899
sum
119895=1
(
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
) sdot 119909119895ge 120575 0 lt 120575 le 1 (8)
If the normalized importance of DR119895to the contribution of
all CRs 119908norm119895
is defined as
119908norm119895
=
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
(9)
wheresum119899119895=1119908
norm119895
= 1 then (7a) and (7g) can be respectivelyexpressed as
119899
sum
119895=1
119908norm119895
sdot 119909119895ge 120575 0 lt 120575 le 1 (10)
120588119895= 1199052119908
norm119895
120572 (11)
In (6) parameter 119896 is important as it specifies therelation between the target design quality level and the targetcustomer satisfaction and the relation between the fulfilledoverall design quality and the quality level reflected by theachieved customer satisfaction that is the perceived qualitylevel As mentioned parameter 119896 is related to the customerbehavior of a specific market segment for a specific productThe value of 119896 can be either determined subjectively by themanagement or obtained using quantitative approaches Todo this the simple regression approach is suggested in thispaper Under the consideration that customer satisfaction is
Journal of Applied Mathematics 5
a concave down function of the perceived quality level of theproduct a linearly transformed function can be expressedas ln120572 = 119896 ln 120575 Using a group of paired estimations (120572
119894 120575119894)
based on the experience and knowledge from the QFD teammembers andor managers of the marketing departmentthe simple regression function ln 120575 = (1119896) ln120572 can beconstructed to determine the 119896 value
The procedure for applying the proposed model is asfollows
Step 1 Determine the desired product to be developed orimproved for the target market segment
Step 2 Construct the corresponding HOQ to reflect therelations between CRs and DRs
Step 3 Integrate the basic design information in the HOQ toobtain the normalized values 119877norm
119894119895 119889norm119894
and 119908norm119895
usingthe normalization model in (2) (and (3) if needed)
Step 4 Considering that 120575 is a concave down function of120572 subjectively determine the value of 119896 for meeting therelationship 120572 = 120575
119896 119896 gt 1 Alternatively collect a groupof paired estimations (120572
119894 120575119894) forall120572119894 120575119894isin [0 1] for the desired
product in the target market segment Decide the parameter119896(gt 1) in ln 120575 = (1119896) ln120572 by applying a simple regressionanalysis
Step 5 Determine the target customer satisfaction 120575 for NPDbased on the targetmarket segment and then obtain the targetdesign quality level 120572 based on 120572 = 120575
119896 using the 119896 valuedetermined in Step 4
Step 6 Let management subjectively decide the values ofparameters 119905
1and 1199052
Step 7 Construct the proposed nonlinear programmingmodel using the integrated information from the HOQobtained in Step 2
Step 8 Solve the model to find the optimal design qualitylevel of each DR so that the target customer satisfaction isachieved for the target market with the minimum budget
5 Numerical Illustration
This section demonstrates the applicability of the proposedapproach using a constructed example of a manufacturerof bicycles Based on this example parameter analyses areprovided to further illustrate the proposed approach
51 Example With rising awareness of environmental pro-tection themunicipal government has encouraged citizens totakemass transportation to workThemarketing departmentof the bicycle firm has observed that an increasing number ofcitizens are willing to bike the short distance between homeand mass transportation stations Therefore the marketingdepartment plans to launch a new bike to cater to this trendFor this plan an important issue for the NPD project team
is to determine the minimum budget needed to achieve themarket goal of the NPD during the design stage
Firstly the newly developed bike is positioned as simpleand easy for biking the short distance between home andmass transportation station and aims to satisfy commutersTheNPD team selects QFD as the design platform In the sec-ond step the HOQ is constructed for specifying the relationsbetween CRs and DRs The following six basic requirementsare identified (1) ride comfort (2) ride safety (3) easyhandling (4) easy movement (5) low maintenance and (6)durability Based on consensus the team members proposenine design requirements that correspond to the six basiccustomer requirementsThe nine design requirements are (1)frame (2) suspension (3) derailleur (4) brake (5) wheels (6)handlebars (7) saddle (8) pedals and (9) total weight Thedegree of relational intensity for the relationship betweenCRsand DRs is defined by weak-moderate-strong the correlationamong CRs or amongDRs is also defined by weak-moderate-strong but allowing for negative correlations Furthermorethe NPD team identifies the CRsrsquo importance degrees for theproduct to emphasize its easy handling and ride safety Thebasic QFD design information for the product is shown inFigure 4
The main work in the third step is to integrate the designinformation into the HOQ to obtain the normalized relationstrengths or weights namely 119877norm
119894119895 119889norm119894
and 119908norm119895
forestablishing the proposed nonlinear programming modelto achieve the marketquality goal at the minimum designcost As described before L-H Chen and C-N Chenrsquosnormalization models (2) and (3) are employed To do thisthe degree of relational or correlation intensity describedas weak-moderate-strong must be numerically scaled Ascommonly used in the literature the rating scale 1-3-9 isemployed for relational intensity that is weak-moderate-strong between CRs and DRs and plusmn(01-03-09) is usedfor correlation that is weak-moderate-strong among CRsor among DRs with negative correlations allowed Figure 5shows the normalized results for the product using the basicdesign information in Figure 4
After the integrated information from the HOQ hasbeen obtained the characteristic parameter 119896 for the marketsegment of commuters should be determined to characterizethe functional curve between customer satisfaction anddesign quality level Based on the experience of themarketingexperts 119896 is set to 2 that is CS(X) = [DQ(X)]12 as shownin Figure 6 Based on the determined function the fifth stepis to set up the target design quality level 120572 From a marketcompetitive analysis the target customer satisfaction is set as120575 = 08 so the target design quality level 120572 is obtained as064 based on the function 120572 = 120575119896 119896 = 2 To formulate theproposed nonlinear programming model for the minimumcost in the sixth step the parameters 119905
1and 1199052should be
determined to specify theminimumsatisfaction level for eachcustomer requirement CR
119894and the minimum design quality
level for each DR119895 The values 119905
1= 3 and 119905
2= 3 are set by the
NPD team in this exampleBased on the settings in the previous steps the pro-
posed nonlinear programming model can be formulated for
6 Journal of Applied Mathematics
movement
Custo
mer
requ
irem
ents
Deg
ree o
f im
port
ance
Design requirements
15
20
25
15
9 points 3 points 1 point
Strong relationModerate relationWeak relationWeak negative relation
Moderate negative relationStrong negative relation
Correlation symbols and values
maintenance
Relation symbols and points
13
12
minus01
minus03
minus09
0103
09
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy
(5) Low
(6) Durability
Figure 4 Basic QFD design information for product
Custo
mer
requ
irem
ents
Design requirements
Nor
mal
ized
CR
impo
rtan
ce w
eigh
t
017
024
028
011
011
011011011011011
013 011 011 013 016
016
011 011 011
015 013 013
013013
015 019 013 004004 003
009 008 023 009
009
011 023 008 005
003 037 008 048
020 017 017 020 008 006 006006
003
003
Normalized DR importance 012 010 015 012 017 014 006 007007weight
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy movement
(5) Low maintenance
(6) Durability
Figure 5 Normalized results for product
the minimum design cost Let the decision variable 119909119895 119895 =
1 2 9 represent the technical fulfillment level of DR119895
The model aims to achieve the target customer satisfaction(120575 = 08) and the target design quality levels (120572 = 064)for the product at the minimum total design cost sum9
119895=1119862119895119909119895
1
1
Custo
mer
satis
fact
ion
Design quality
k = 2
120575
120572
CS(X)
DQ(X)
Figure 6 Functional curve of customer satisfaction for product
where 119862119895denotes the design cost of completely fulfilling the
technical level of DR119895 The nonlinear programming model is
expressed as
Min9
sum
119895=1
119862119895119909119895 (12)
Journal of Applied Mathematics 7
subject to
0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9ge 08
1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099ge 9 times 064
1
9(1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099)
minus (0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9)2
ge 0
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 051
0151199091+ 013119909
2+ 013119909
3+ 015119909
4+ 019119909
5
+ 0131199096+ 004119909
7+ 004119909
8+ 003119909
9ge 072
0091199091+ 008119909
2+ 023119909
3+ 009119909
4+ 011119909
5
+ 0231199096+ 008119909
7+ 003119909
8+ 005119909
9ge 084
0031199091+ 000119909
2+ 003119909
3+ 000119909
4+ 037119909
5
+ 0081199096+ 000119909
7+ 000119909
8+ 048119909
9ge 033
0201199091+ 017119909
2+ 017119909
3+ 020119909
4+ 008119909
5
+ 0061199096+ 006119909
7+ 006119909
8+ 000119909
9ge 033
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 027
023 le 1199091le 1
019 le 1199092le 1
029 le 1199093le 1
023 le 1199094le 1
033 le 1199095le 1
027 le 1199096le 1
013 le 1199097le 1
012 le 1199098le 1
013 le 1199099le 1
(13)
DRj
Cj 220 250 280 200 260 130 80 50 30
Unit $ thousand
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 7 Completely fulfilled design cost 119862119895for DR
119895
1 1 1 1 1 1
Targ
eted
CS
Fulfi
lled
DQ
k MinΣCjxj
20 080 081 023 019 086 1091
x1 x2 x3 x4 x5 x6 x8x7 x9
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 8 Optimal technical fulfillments for product
To solve the model the design cost 119862119895for DR
119895must
be determined beforehand For this example the costs areprovided by the NPD team as shown in Figure 7 Theproposed nonlinear model can be solved using commercialsoftware such as LINGO 110 Figure 8 summarizes the opti-mal technical fulfillment level 119909
119895for eachDR
119895Theminimum
total design cost for the product is $1091000 The figureindicates that the target customer satisfaction can be achievedat CS(X) = sum
9
119895=1119908
norm119895
sdot 119909119895= 08 The fulfilled design
quality level is determined as DQ(X) = (19)sum9119895=1119909119895= 081
which is greater than 120572(= 064) satisfying constraint (7b)The solutions obtained in Figure 8 satisfy the requirementsof the new product for the target customer satisfaction at theminimum total design cost
52 Parameter Analyses The proposed nonlinear program-ming model includes three design parameters namely 1198961199051 and 119905
2 that are specified by the NPD team These three
parameters affect the design quality level and thereforethe total design cost The influence of the combination ofdifferent values of 119896 119905
1 and 119905
2on the total design costwas thus
examined In the analyses the target customer satisfaction120575 was set at 06 07 and 08 respectively The results of theanalyses are summarized below
(1) The parameter 119896 characterizes the customer satisfac-tion of the design quality level The larger the valueof 119896 is the more attractive to customers the productquality level is With a larger 119896 the target customersatisfaction can be achieved using only the lowerlevel of product design quality and therefore the totaldesign cost is lower As a demonstration with 119905
1and
1199052fixed at 3 Figure 9 shows that the total design cost
8 Journal of Applied Mathematics
1093
1091
1088
1090
1088
1084
1087
1085
1083
1080
1085
1090
1095
Tota
l des
ign
cost
k = 15 k = 2 k = 3
120575 = 08
120575 = 07
120575 = 06
at (t1 t2) = (3 3)
Figure 9 Variation of total design cost with 119896 for various 120575 values
1076 1076 1076
1091
889 889897
1088
717 717
852
1085
600
900
1200
1500
Tota
l des
ign
cost
at (k t2) = (2 3)
t1 = 0 t1 = 2 t1 = 25 t1 = 3 t1 = 35
120575 = 08
120575 = 07
120575 = 06
1469
Figure 10 Variation of total design cost with 1199051for various 120575 values
decreases with increasing 119896 value regardless of thetarget customer satisfaction 120575
(2) The 1199051and 1199052values in (7e) and (7g) affect the mini-
mum satisfaction level for each customer requirementCR119894and the fulfilled minimum design quality level
for each DR119895 respectively and therefore affect the
total design cost Larger values of 1199051andor 119905
2increase
the total design cost With 119896 = 2 and 1199052= 3
Figure 10 shows the impact of the 1199051value on the total
design cost The total design cost remains unchangedin a range of 119905
1values that depends on 120575 because
the fulfilled minimum design quality level 120588119895at 1199052= 3
confines the influence of the minimum satisfactionlevel 120576
119894on the total design cost at some levels of 119905
1
regardless of the target customer satisfaction level120575 It is also noted that if the 119905
1value is sufficiently
large (1199051= 35) and 119905
2= 3 the total design cost
is the same (1469) for all three levels of the target
1079
1084
1091
1099
1108
1083
1088
10931097
10821085
1088
1093
1075
1085
1095
1105
1115
Tota
l des
ign
cost
at (k t1) = (2 3)
t2 = 0 t2 = 15 t2 = 3 t2 = 45 t2 = 6
120575 = 08
120575 = 07
120575 = 06
Figure 11 Variation of total design cost with 1199052for various 120575 values
customer satisfaction since the aggregated resultsfrom the required minimum satisfaction level foreach customer requirement CR
119894surpass each target
customer satisfaction The high required minimumsatisfaction level due to 119905
1= 35 resulted in the largest
total design cost With 119896 = 2 and 1199051= 3 the total
design cost changes with 1199052 as shown in Figure 11
(3) From a design viewpoint if theminimum satisfactionlevel for each customer requirement CR
119894and the
fulfilled minimum design quality level for each DR119895
are not required that is 1199051and 1199052are fixed at 0 the
minimal total design cost can be obtained from theproposed model (7) at each setting of the targetedcustomer satisfaction level 120575 For example with 119905
1=
1199052= 0 and 120575 = 06 07 and 08 respectively the
total design costs are 700 878 and 1063 respectivelyregardless of the 119896 valueThis indicates that to achievethe target degree of customer satisfaction for a certainmarket segment the investment amount of the totaldesign cost has the lowest bound
6 Conclusions
A mathematical model was proposed for determining thedesign quality level required to achieve the target customersatisfaction for the target market segment with the minimumtotal design cost In the proposed model the customersatisfaction is expressed as a function of the quality level con-sidering the consumer behavior of the targetmarket segmentMoreover the proposedmodel allows theNPD team to set theminimum satisfaction level for each CR andor the fulfilledminimumdesign quality level for eachDRmaking the designprocesses flexible A numerical example was provided todemonstrate the feasibility and applicability of the proposedapproach In future research the relation between customersatisfaction and quality level will be further investigated tomake the proposed model more applicable in the real world
Journal of Applied Mathematics 9
Nomenclature
CR119894 The 119894th customer requirement
DR119895 The 119895th design requirement
119877119894119895 Relational intensity between CR
119894and DR
119895
120574119896119895 Technical correlation between DR
119896and
DR119895
1198771015840
119894119895 Normalized relational intensity between
CR119894and DR
119895in Wassermanrsquos
normalization model119877norm119894119895
Normalized relational intensity betweenCR119894and DR
119895in L-H Chen and C-N
Chenrsquos normalization model119889119894 Original importance weight of CR
119894
120573119894119897 Correlation between CR
119894and CR
119897
119889norm119894
Normalized importance weight of CR119894in
L-H Chen and C-N Chenrsquos integrationmodel when CRsrsquo correlations exist
119908norm119895
Normalized importance weight of DR119895
119862119895 Required cost for DR
119895to fully achieve
customer satisfaction119909119895 Technical fulfillment level for DR
119895
X Design vector containing the fulfillmentlevels of all DRs
DQ(X) Overall design quality level by designvector X
CS(X) Fulfilled customer satisfaction by designvector X
120572 Target design quality level120575 Target customer satisfaction119896 The characteristic parameter to describe
the customer preference of a specificmarket segment for the design qualitylevel of a specific product
120576119894 Minimum required satisfaction level for
CR119894
1199051 Design parameter to determine 120576
119894
120588119895 Minimum fulfilled quality level for DR
119895
1199052 Design parameter to determine 120588
119895
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] L Cohen Quality Function Deployment How to Make QFDWork for You Addison-Wesley Reading Mass USA 1995
[2] L-K Chan and M-L Wu ldquoQuality function deployment aliterature reviewrdquoEuropean Journal of Operational Research vol143 no 3 pp 463ndash497 2002
[3] G S Wasserman ldquoOn how to prioritize design requirementsduring the QFD planning processrdquo IIE Transactions vol 25 no3 pp 59ndash65 1993
[4] K-J Kim ldquoDetermining optimal design characteristic levels inquality function deploymentrdquo Quality Engineering vol 10 no2 pp 295ndash307 1997
[5] HMoskowitz and K-J Kim ldquoQFD optimizer a novice friendlyquality function deployment decision support system for opti-mizing product designsrdquo Computers amp Industrial Engineeringvol 32 no 3 pp 641ndash655 1997
[6] T Park and K-J Kim ldquoDetermination of an optimal setof design requirements using house of qualityrdquo Journal ofOperations Management vol 16 no 5 pp 569ndash581 1998
[7] J Bode and R Y K Fung ldquoCost engineering with qualityfunction deploymentrdquo Computers and Industrial Engineeringvol 35 no 3-4 pp 587ndash590 1998
[8] R G Askin and DW Dawson ldquoMaximizing customer satisfac-tion by optimal specification of engineering characteristicsrdquo IIETransactions (Institute of Industrial Engineers) vol 32 no 1 pp9ndash20 2000
[9] R Y K Fung J Tang Y Tu and D Wang ldquoProduct designresources optimization using a non-linear fuzzy quality func-tion deployment modelrdquo International Journal of ProductionResearch vol 40 no 3 pp 585ndash599 2002
[10] L-H Chen and M-C Weng ldquoA fuzzy model for exploitingquality function deploymentrdquo Mathematical and ComputerModelling vol 38 no 5-6 pp 559ndash570 2003
[11] H Iranmanesh and V Thomson ldquoCompetitive advantage byadjusting design characteristics to satisfy cost targetsrdquo Interna-tional Journal of Production Economics vol 115 no 1 pp 64ndash712008
[12] L-H Chen andW-C Ko ldquoA fuzzy nonlinear model for qualityfunction deployment considering Kanorsquos conceptrdquo Mathemati-cal and Computer Modelling vol 48 no 3-4 pp 581ndash593 2008
[13] L-H Chen and W-C Ko ldquoFuzzy approaches to qualityfunction deployment for new product designrdquo Fuzzy Sets andSystems vol 160 no 18 pp 2620ndash2639 2009
[14] J-H Shin H-B Jun D Kiritsis and P Xirouchakis ldquoA decisionsupport method for product conceptual design consideringproduct lifecycle factors and resource constraintsrdquo InternationalJournal of Advanced Manufacturing Technology vol 52 no 9ndash12 pp 865ndash886 2011
[15] M Braglia G Fantoni andM Frosolini ldquoThe house of reliabil-ityrdquo International Journal of Quality amp Reliability Managementvol 24 no 4 pp 420ndash440 2007
[16] W-C Chiou H-W Kuo and I-Y Lu ldquoA technology orientedproductivity measurement modelrdquo International Journal ofProduction Economics vol 60 pp 69ndash77 1999
[17] P-T Chuang ldquoA QFD approach for distributionrsquos locationmodelrdquo International Journal of Quality and Reliability Manage-ment vol 19 no 8 pp 1037ndash1054 2002
[18] L-H Chen and M-C Weng ldquoAn evaluation approach to engi-neering design inQFDprocesses using fuzzy goal programmingmodelsrdquo European Journal of Operational Research vol 172 no1 pp 230ndash248 2006
[19] E K Delice and Z Gungor ldquoA new mixed integer linearprogramming model for product development using qualityfunction deploymentrdquo Computers amp Industrial Engineering vol57 no 3 pp 906ndash912 2009
[20] E K Delice and Z Gungor ldquoAmixed integer goal programmingmodel for discrete values of design requirements in QFDrdquoInternational Journal of Production Research vol 49 no 10 pp2941ndash2957 2011
[21] F Franceschini and S Rossetto ldquoQFD an interactive algorithmfor the prioritization of productrsquos technical design characteris-ticsrdquo Integrated Manufacturing Systems vol 13 no 1 pp 69ndash752002
10 Journal of Applied Mathematics
[22] C H Han J K Kim S H Choi and S H Kim ldquoDeterminationof information system development priority using quality func-tion deploymentrdquoComputers and Industrial Engineering vol 35no 1-2 pp 241ndash244 1998
[23] E E Karsak ldquoFuzzy multiple objective decision makingapproach to prioritize design requirements in quality functiondeploymentrdquo International Journal of Production Research vol42 no 18 pp 3957ndash3974 2004
[24] X Lai M Xie and K C Tan ldquoDynamic programming for QFDoptimizationrdquoQuality and Reliability Engineering Internationalvol 21 no 8 pp 769ndash780 2005
[25] S-T Liu ldquoRating design requirements in fuzzy quality functiondeployment via a mathematical programming approachrdquo Inter-national Journal of Production Research vol 43 no 3 pp 497ndash513 2005
[26] R Ramanathan and J Yunfeng ldquoIncorporating cost and envi-ronmental factors in quality function deployment using dataenvelopment analysisrdquo Omega vol 37 no 3 pp 711ndash723 2009
[27] H Raharjo M Xie and A C Brombacher ldquoA systematicmethodology to deal with the dynamics of customer needs inQuality Function Deploymentrdquo Expert Systems with Applica-tions vol 38 no 4 pp 3653ndash3662 2011
[28] Y-M Wang and K-S Chin ldquoTechnical importance ratingsin fuzzy QFD by integrating fuzzy normalization and fuzzyweighted averagerdquoComputers ampMathematics with Applicationsvol 62 no 11 pp 4207ndash4221 2011
[29] Y-M Wang ldquoA fuzzy-normalisation-based group decision-making approach for prioritising engineering design require-ments in QFD under uncertaintyrdquo International Journal ofProduction Research vol 50 no 23 pp 6963ndash6977 2012
[30] D Lyman ldquoDeployment normalizationrdquo in Proceedings of theTransactions from the 2nd Symposium on Quality FunctionDeployment pp 307ndash315 Automotive Division of the AmericanSociety for Quality Control The American Supplier Instituteand GOALQPC Dearborn Mich USA 1990
[31] L-H Chen and C-N Chen ldquoNormalisation models for pri-oritising design requirements for quality function deploymentprocessesrdquo International Journal of Production Research vol 52no 2 pp 299ndash313 2014
[32] S Erevelles and C Leavitt ldquoA comparison of current modelsof consumer satisfactiondissatisfactionrdquo Journal of ConsumerSatisfaction Dissatisfaction and Complaining Behavior vol 5pp 104ndash114 1992
[33] M J Morgan J A Attaway and M Griffin ldquoThe role ofproductservice experience in the satisfaction formation pro-cess a test of moderationrdquo Journal of Consumer SatisfactionDissatisfaction and Complaining Behavior vol 9 pp 391ndash4051996
[34] E W Anderson and M W Sullivan ldquoThe antecedents andconsequences of customer satisfaction for firmsrdquo MarketingScience vol 12 no 2 pp 125ndash143 1993
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Mathematical Problems in Engineering
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Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
2 Journal of Applied Mathematics
achieve the target customer satisfaction Nevertheless sucha relationship is not incorporated in existing QFD modelsBased on the above considerations how to use the minimalbudgetresources to achieve the quality level in order to meetthe desired customer satisfaction should be considered inQFD-related problems In this regard instead of consideringthe budget constraint this paper takes into account therelationship between customer satisfaction and quality levelfor the target customers in the QFD model to satisfy thedesired satisfaction level in which the minimum design costis achieved
The rest of this paper is organized as follows Section 2briefly introduces the concept of QFD and the relatednormalization formulations which are used in the pro-posed model From a marketing perspective the relationshipbetween customer satisfaction and quality level for targetcustomers is described in Section 3 In Section 4 consideringthe desired customer satisfaction and the correspondingquality level for target customers as constraints a nonlinearmathematical programming model is proposed to minimizethe total design cost Section 5 provides an illustrative exam-ple of new bike design to demonstrate the feasibility andapplicability of the proposed approachNumerical analyses ofthe design parameters in the proposedmodel are alsomade toexplore the characteristics of the model and their managerialimplications Finally conclusions are provided in the finalsection
2 Background
The basic concept of QFD is to transform customer voicesinto technical requirements to ensure customer satisfac-tion The QFD processes are performed by applying thedesign information embodied in the relation matrix calledthe house of quality (HOQ) as illustrated in Figure 1 Inpractice QFD transforms customer needs into technical(or designengineering) characteristics via the HOQ duringthe design or planning stage The interior of the HOQmatches customer requirements (CRs) with the correspond-ing design requirements (DRs) identifying the relationalintensity between each pair of CRs and DRs to ensurequality performance that can satisfy the target customers Ifnecessary the roof of the HOQ represented as a correlationmatrix is constructed to indicate the technical correlationsamong DRs Figure 1 shows a HOQ example to signify therelational intensities between CRs and DRs as well as thecorrelation degrees among DRs The importance degree ofeach CR is also displayed in the figure In general the HOQcontains the relational intensity between each pair of CRs andDRs and the technical correlation between each pair of DRsThe legend in Figure 1 shows various designated symbolsused to represent different degrees of relational intensity ortechnical correlation in the HOQ
In general the design information contained in the HOQis integrated to further determine the importance of DRsand their achievement degrees in order to optimally satisfycustomer satisfaction To do this a normalization process isusually applied by QFD researchers and practitioners In theliterature the normalization model proposed by Wasserman
Impor-tance
StrongModerateWeak
Weak negativeModerate negative
Strong negative
Relationship
CR1
CR2
CR3
CR4
d1
d2
d3
d4
DR1 DR2 DR3 DR4
Figure 1 Matrix structure of HOQ
[3] has been widely adopted (eg [6 7 9 10 13 15ndash29])Based on Lymanrsquos normalization concept [30] this modelis developed by incorporating the correlations among DRsformulated as
1198771015840
119894119895=
sum119899
119896=1119877119894119896sdot 120574119896119895
sum119899
119895=1sum119899
119896=1119877119894119896sdot 120574119896119895
(1)
from the vector space concept where 120574119896119895denotes the techni-
cal correlation between DR119896and DR
119895 In the above equation
119877119894119896indicates the relational intensity between CR
119894and DR
119896
which is measured based on a 3-point scale such as 1-3-9 or1-5-9 for describing the weak-moderate-strong relationshipAlthoughWassermanrsquos normalizationmodel has been widelyadopted it has someweaknesses For example it assumes thatcustomer requirements are mutually independent Howeverthismay not be true in practiceMore importantly thismodelmay generate a relational intensity for a pair of CRs and DRsthat does not exist in the original design information Themodel may thus produce unreasonable outcomes
Identifying such weaknesses in Wassermanrsquos normaliza-tion model L-H Chen and C-N Chen [31] proposed thefollowing modified normalization model
119877norm119894119895
=
(sum119899
119896=1120574119896119895) 119877119894119895
sum119899
119895=1(sum119899
119896=1120574119896119895) 119877119894119895
(2)
where 119877norm119894119895
denotes the normalized relationship betweenCR119894and DR
119895 Applying the above modified normalization
model to integrate design information the unreasonableoutcomes from Wassermanrsquos model can be avoided Fur-thermore considering the possibility that some CRs arecorrelated as shown in Figure 2 L-H Chen and C-N Chen[31] also proposed the following normalization model tointegrate CRs similar to that in (2) in determining thenormalized weights of CRs
119889norm119894
=(sum119898
119897=1120573119894119897) 119889119894
sum119898
119894=1(sum119898
119897=1120573119894119897) 119889119894
(3)
Journal of Applied Mathematics 3
`
Impor-tance
120574jn
CRi
CRm
DRj DRn
Rin
RmnRmj
Rijdi
dm
120573im
Figure 2 General HOQ structure
where 120573119894119897denotes the correlation between CR
119894and CR
119897and
119889119894is the importance of CR
119894 It is noted that the normalized
weight 119889norm119894
in (3) is reduced to 119889119894when CRs are mutually
independent that issum119898119897=1120573119894119897= 1
3 Satisfaction Function with Quality Level
The purpose of the development of new products or theimprovement of existing products is mainly to satisfy cus-tomer needs or enhance customer satisfaction Achievingcustomer satisfaction is always one of the main goals for thetarget market [32] Customer satisfaction is considered oneof the most important constructs for consumers [33] Hencecustomer satisfaction is important in marketing because ofits great influence on customer purchase behavior Basedon an empirical study Anderson and Sullivan [34] foundthat customer satisfaction can generally be described as afunction of perceived quality from customers consideringan adjustment amount to reflect the customer perception ofconfirmationdisconfirmation In their study the customersatisfaction function is expressed as a concave down functionof perceived quality Following the concept of Andersonand Sullivanrsquos study [34] the present study considers thatcustomer satisfaction is positively related to the design qualityof the product in terms of a concave down function assumingthat the quality designed for the product in the design stagewill be perceived by the target customers in the futuremarketthat is the design quality level has a positive relationshipwith customer perceived quality Figure 3 shows customersatisfaction (CS) as a concave down function of design quality(DQ)
For QFD applications the design quality level of aproduct can be treated as the fulfillment level of designrequirements (DRs) and therefore customer satisfaction canbe described as a function of the DRsrsquo fulfillment levels inthe QFD processes Let 119862
119895represent the cost required for
DR119895with which the technical requirement for DR
119895can be
completely attained so that customer satisfaction can be fullyachieved 119909
119895(isin [0 1]) represents the decision variable taking
the fulfillment level of the technical requirement for DR119895
Custo
mer
satis
fact
ion
Design quality1
1
CS(X)
DQ(X)
Figure 3 Functional curve for customer satisfaction (CS) anddesign quality (DQ)
denoting the quality level of DR119895required tomeet the desired
customer satisfaction For simplification suppose that thecost required to achieve the fulfillment level of DR
119895 119909119895 is
119862119895119909119895 that is a proportional relation between the required
cost and the fulfillment level The value of 119909119895= 0means that
the technical need for DR119895is only the basic requirement so
that the cost is 0 In addition the use of the whole budget 119862119895
for DR119895will achieve the full technical requirement that is
119909119895= 1 and full customer satisfaction for this DRLet X = [119909
1 1199092 119909
119899]119879 be the vector containing the
fulfillment levels of the technical requirements for all DRsFor a new product the overall DQ is defined as the averageof the fulfillment levels of all DRs as
DQ (X) = 1119899
119899
sum
119895=1
119909119895 0 le 119909
119895le 1 (4)
where 0 le DQ(X) le 1 In other words 119909119895is interpreted as
the design quality level of DR119895 In addition based on previous
studies (eg [3ndash14]) using the normalized information fromthe HOQ 119877norm
119894119895and 119889norm
119894in (2) and (3) respectively the
customer satisfaction can be formulated as
CS (X) =119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895 0 le 119909
119895le 1 (5)
where 0 le CS(X) le 1 It is obvious that DQ(X) = 1 andCS(X) = 1 when 119909
119895= 1 forall119895 = 1 2 119899 As described
above based on the concept of Anderson and Sullivanrsquos study[34] customer satisfaction is characterized as a concave downfunction of the design quality of a product for a specificmarket segment Figure 3 shows such a functionThe concavedown curve illustrates the diminishing marginal effect asdesign quality increases the marginal effect of customersatisfaction decreases This is characterized here using thefollowing simple equation
CS (X) = [DQ (X)]1119896 (6)
4 Journal of Applied Mathematics
where 119896(gt 1) is a characteristic parameter used to describethe customer preference of a specific market segment for thedesign quality level of a specific product The function in(6) characterizes features of the relationship between CS(X)and DQ(X) as described above In practice if the desiredcustomer satisfaction degree is determined as the goal ofsatisfying the target market (6) is employed to transform thedesired value CS(X) into the corresponding value DQ(X) asthe required design quality level
4 Proposed QFD Budget Planning Model
In contrast to previous QFD-related studies that maximizedcustomer satisfaction under a limited budget this paper aimsto find the minimum design budget to achieve the marketgoal in terms of the target customer satisfaction To this endsome constraints are considered in the model Based on (6)the target design quality level 120572 (0 lt 120572 le 1) correspondingto the target customer satisfaction 120575 (0 lt 120575 le 1) isdetermined by the management that is 120572 = 120575119896 119896 gt 1 Theachieved customer satisfaction formulated as (5) based onthe fulfillment level of the technical requirement that is thefulfilled design quality level for each DR should not be lessthan the target customer satisfaction 120575 similarly the fulfilledoverall design quality of (4) should not be less than thetarget design quality level 120572 More importantly the fulfilledoverall design quality should not be less than the quality levelreflected by the achieved customer satisfaction for the targetmarket in (6) that is (1119899)sum119899
119895=1119909119895ge (sum119898
119894=1119889norm119894
sum119899
119895=1119877norm119894119895
sdot
119909119895)119896 The right-hand side in the above inequality relation
can be interpreted as the product quality perceived by thetarget customers since it is derived based on the relationsbetween CRs and DRs in the HOQ Thus this constraintensures that the realized overall quality achieved from theproduct design is better than or equal to that perceived bythe target customers
In addition to the restrictions on the target design qualitylevel and customer satisfaction from the designersrsquo view-point in general there is aminimumsatisfaction level for eachcustomer requirement CR
119894The constraint ofsum119899
119895=1119877norm119894119895
sdot119909119895ge
120576119894 0 lt 120576
119894le 1 119894 = 1 119898 reflects this condition where 120576
119894
can be determined based on the normalized weights of CR119894
using the equation 120576119894= 1199051119889norm119894
1199051gt 0 to reveal each CRrsquos
importanceThe fulfilled design quality level for eachDR119895119909119895
is usually required to not be less than aminimum level say 120588119895
0 lt 120588119895le 1 where 120588
119895can be set as 120588
119895= 1199052(sum119898
119894=1119889norm119894
sdot119877norm119894119895
)1205721199052gt 0 considering the normalized importance of DR
119895and
the target design quality level 120572 Note that the parameters 1199051
and 1199052can be determined subjectively by the management
in weighing the corresponding CRs and DRs respectivelyunder the constraints of 0 lt 120576
119894le 1 and 0 lt 120588
119895le 1
A nonlinear programming model is formulated in (7) inwhich constraints (7a) to (7g) are used for the specificationsdescribed above The objective function (7) in the modelreflects the proportional relation between the required costand the fulfillment level of each DR
Proposed Nonlinear Programming Model Consider
Min119899
sum
119895=1
119862119895119909119895 (7)
subject to
119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895ge 120575 0 lt 120575 le 1 (7a)
119899
sum
119895=1
119909119895ge 119899120572 0 lt 120572 le 1 (7b)
1
119899
119899
sum
119895=1
119909119895minus (
119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895)
119896
ge 0 119896 gt 1 (7c)
119899
sum
119895=1
119877norm119894119895
sdot 119909119895ge 120576119894 0 lt 120576
119894le 1 119894 = 1 2 119898 (7d)
120576119894= 1199051119889norm119894
(7e)
120588119895le 119909119895le 1 0 lt 120588
119895le 1 119895 = 1 2 119899 (7f)
120588119895= 1199052(
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
)120572 (7g)
It is noted that constraint (7a) can be represented as
119899
sum
119895=1
(
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
) sdot 119909119895ge 120575 0 lt 120575 le 1 (8)
If the normalized importance of DR119895to the contribution of
all CRs 119908norm119895
is defined as
119908norm119895
=
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
(9)
wheresum119899119895=1119908
norm119895
= 1 then (7a) and (7g) can be respectivelyexpressed as
119899
sum
119895=1
119908norm119895
sdot 119909119895ge 120575 0 lt 120575 le 1 (10)
120588119895= 1199052119908
norm119895
120572 (11)
In (6) parameter 119896 is important as it specifies therelation between the target design quality level and the targetcustomer satisfaction and the relation between the fulfilledoverall design quality and the quality level reflected by theachieved customer satisfaction that is the perceived qualitylevel As mentioned parameter 119896 is related to the customerbehavior of a specific market segment for a specific productThe value of 119896 can be either determined subjectively by themanagement or obtained using quantitative approaches Todo this the simple regression approach is suggested in thispaper Under the consideration that customer satisfaction is
Journal of Applied Mathematics 5
a concave down function of the perceived quality level of theproduct a linearly transformed function can be expressedas ln120572 = 119896 ln 120575 Using a group of paired estimations (120572
119894 120575119894)
based on the experience and knowledge from the QFD teammembers andor managers of the marketing departmentthe simple regression function ln 120575 = (1119896) ln120572 can beconstructed to determine the 119896 value
The procedure for applying the proposed model is asfollows
Step 1 Determine the desired product to be developed orimproved for the target market segment
Step 2 Construct the corresponding HOQ to reflect therelations between CRs and DRs
Step 3 Integrate the basic design information in the HOQ toobtain the normalized values 119877norm
119894119895 119889norm119894
and 119908norm119895
usingthe normalization model in (2) (and (3) if needed)
Step 4 Considering that 120575 is a concave down function of120572 subjectively determine the value of 119896 for meeting therelationship 120572 = 120575
119896 119896 gt 1 Alternatively collect a groupof paired estimations (120572
119894 120575119894) forall120572119894 120575119894isin [0 1] for the desired
product in the target market segment Decide the parameter119896(gt 1) in ln 120575 = (1119896) ln120572 by applying a simple regressionanalysis
Step 5 Determine the target customer satisfaction 120575 for NPDbased on the targetmarket segment and then obtain the targetdesign quality level 120572 based on 120572 = 120575
119896 using the 119896 valuedetermined in Step 4
Step 6 Let management subjectively decide the values ofparameters 119905
1and 1199052
Step 7 Construct the proposed nonlinear programmingmodel using the integrated information from the HOQobtained in Step 2
Step 8 Solve the model to find the optimal design qualitylevel of each DR so that the target customer satisfaction isachieved for the target market with the minimum budget
5 Numerical Illustration
This section demonstrates the applicability of the proposedapproach using a constructed example of a manufacturerof bicycles Based on this example parameter analyses areprovided to further illustrate the proposed approach
51 Example With rising awareness of environmental pro-tection themunicipal government has encouraged citizens totakemass transportation to workThemarketing departmentof the bicycle firm has observed that an increasing number ofcitizens are willing to bike the short distance between homeand mass transportation stations Therefore the marketingdepartment plans to launch a new bike to cater to this trendFor this plan an important issue for the NPD project team
is to determine the minimum budget needed to achieve themarket goal of the NPD during the design stage
Firstly the newly developed bike is positioned as simpleand easy for biking the short distance between home andmass transportation station and aims to satisfy commutersTheNPD team selects QFD as the design platform In the sec-ond step the HOQ is constructed for specifying the relationsbetween CRs and DRs The following six basic requirementsare identified (1) ride comfort (2) ride safety (3) easyhandling (4) easy movement (5) low maintenance and (6)durability Based on consensus the team members proposenine design requirements that correspond to the six basiccustomer requirementsThe nine design requirements are (1)frame (2) suspension (3) derailleur (4) brake (5) wheels (6)handlebars (7) saddle (8) pedals and (9) total weight Thedegree of relational intensity for the relationship betweenCRsand DRs is defined by weak-moderate-strong the correlationamong CRs or amongDRs is also defined by weak-moderate-strong but allowing for negative correlations Furthermorethe NPD team identifies the CRsrsquo importance degrees for theproduct to emphasize its easy handling and ride safety Thebasic QFD design information for the product is shown inFigure 4
The main work in the third step is to integrate the designinformation into the HOQ to obtain the normalized relationstrengths or weights namely 119877norm
119894119895 119889norm119894
and 119908norm119895
forestablishing the proposed nonlinear programming modelto achieve the marketquality goal at the minimum designcost As described before L-H Chen and C-N Chenrsquosnormalization models (2) and (3) are employed To do thisthe degree of relational or correlation intensity describedas weak-moderate-strong must be numerically scaled Ascommonly used in the literature the rating scale 1-3-9 isemployed for relational intensity that is weak-moderate-strong between CRs and DRs and plusmn(01-03-09) is usedfor correlation that is weak-moderate-strong among CRsor among DRs with negative correlations allowed Figure 5shows the normalized results for the product using the basicdesign information in Figure 4
After the integrated information from the HOQ hasbeen obtained the characteristic parameter 119896 for the marketsegment of commuters should be determined to characterizethe functional curve between customer satisfaction anddesign quality level Based on the experience of themarketingexperts 119896 is set to 2 that is CS(X) = [DQ(X)]12 as shownin Figure 6 Based on the determined function the fifth stepis to set up the target design quality level 120572 From a marketcompetitive analysis the target customer satisfaction is set as120575 = 08 so the target design quality level 120572 is obtained as064 based on the function 120572 = 120575119896 119896 = 2 To formulate theproposed nonlinear programming model for the minimumcost in the sixth step the parameters 119905
1and 1199052should be
determined to specify theminimumsatisfaction level for eachcustomer requirement CR
119894and the minimum design quality
level for each DR119895 The values 119905
1= 3 and 119905
2= 3 are set by the
NPD team in this exampleBased on the settings in the previous steps the pro-
posed nonlinear programming model can be formulated for
6 Journal of Applied Mathematics
movement
Custo
mer
requ
irem
ents
Deg
ree o
f im
port
ance
Design requirements
15
20
25
15
9 points 3 points 1 point
Strong relationModerate relationWeak relationWeak negative relation
Moderate negative relationStrong negative relation
Correlation symbols and values
maintenance
Relation symbols and points
13
12
minus01
minus03
minus09
0103
09
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy
(5) Low
(6) Durability
Figure 4 Basic QFD design information for product
Custo
mer
requ
irem
ents
Design requirements
Nor
mal
ized
CR
impo
rtan
ce w
eigh
t
017
024
028
011
011
011011011011011
013 011 011 013 016
016
011 011 011
015 013 013
013013
015 019 013 004004 003
009 008 023 009
009
011 023 008 005
003 037 008 048
020 017 017 020 008 006 006006
003
003
Normalized DR importance 012 010 015 012 017 014 006 007007weight
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy movement
(5) Low maintenance
(6) Durability
Figure 5 Normalized results for product
the minimum design cost Let the decision variable 119909119895 119895 =
1 2 9 represent the technical fulfillment level of DR119895
The model aims to achieve the target customer satisfaction(120575 = 08) and the target design quality levels (120572 = 064)for the product at the minimum total design cost sum9
119895=1119862119895119909119895
1
1
Custo
mer
satis
fact
ion
Design quality
k = 2
120575
120572
CS(X)
DQ(X)
Figure 6 Functional curve of customer satisfaction for product
where 119862119895denotes the design cost of completely fulfilling the
technical level of DR119895 The nonlinear programming model is
expressed as
Min9
sum
119895=1
119862119895119909119895 (12)
Journal of Applied Mathematics 7
subject to
0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9ge 08
1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099ge 9 times 064
1
9(1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099)
minus (0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9)2
ge 0
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 051
0151199091+ 013119909
2+ 013119909
3+ 015119909
4+ 019119909
5
+ 0131199096+ 004119909
7+ 004119909
8+ 003119909
9ge 072
0091199091+ 008119909
2+ 023119909
3+ 009119909
4+ 011119909
5
+ 0231199096+ 008119909
7+ 003119909
8+ 005119909
9ge 084
0031199091+ 000119909
2+ 003119909
3+ 000119909
4+ 037119909
5
+ 0081199096+ 000119909
7+ 000119909
8+ 048119909
9ge 033
0201199091+ 017119909
2+ 017119909
3+ 020119909
4+ 008119909
5
+ 0061199096+ 006119909
7+ 006119909
8+ 000119909
9ge 033
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 027
023 le 1199091le 1
019 le 1199092le 1
029 le 1199093le 1
023 le 1199094le 1
033 le 1199095le 1
027 le 1199096le 1
013 le 1199097le 1
012 le 1199098le 1
013 le 1199099le 1
(13)
DRj
Cj 220 250 280 200 260 130 80 50 30
Unit $ thousand
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 7 Completely fulfilled design cost 119862119895for DR
119895
1 1 1 1 1 1
Targ
eted
CS
Fulfi
lled
DQ
k MinΣCjxj
20 080 081 023 019 086 1091
x1 x2 x3 x4 x5 x6 x8x7 x9
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 8 Optimal technical fulfillments for product
To solve the model the design cost 119862119895for DR
119895must
be determined beforehand For this example the costs areprovided by the NPD team as shown in Figure 7 Theproposed nonlinear model can be solved using commercialsoftware such as LINGO 110 Figure 8 summarizes the opti-mal technical fulfillment level 119909
119895for eachDR
119895Theminimum
total design cost for the product is $1091000 The figureindicates that the target customer satisfaction can be achievedat CS(X) = sum
9
119895=1119908
norm119895
sdot 119909119895= 08 The fulfilled design
quality level is determined as DQ(X) = (19)sum9119895=1119909119895= 081
which is greater than 120572(= 064) satisfying constraint (7b)The solutions obtained in Figure 8 satisfy the requirementsof the new product for the target customer satisfaction at theminimum total design cost
52 Parameter Analyses The proposed nonlinear program-ming model includes three design parameters namely 1198961199051 and 119905
2 that are specified by the NPD team These three
parameters affect the design quality level and thereforethe total design cost The influence of the combination ofdifferent values of 119896 119905
1 and 119905
2on the total design costwas thus
examined In the analyses the target customer satisfaction120575 was set at 06 07 and 08 respectively The results of theanalyses are summarized below
(1) The parameter 119896 characterizes the customer satisfac-tion of the design quality level The larger the valueof 119896 is the more attractive to customers the productquality level is With a larger 119896 the target customersatisfaction can be achieved using only the lowerlevel of product design quality and therefore the totaldesign cost is lower As a demonstration with 119905
1and
1199052fixed at 3 Figure 9 shows that the total design cost
8 Journal of Applied Mathematics
1093
1091
1088
1090
1088
1084
1087
1085
1083
1080
1085
1090
1095
Tota
l des
ign
cost
k = 15 k = 2 k = 3
120575 = 08
120575 = 07
120575 = 06
at (t1 t2) = (3 3)
Figure 9 Variation of total design cost with 119896 for various 120575 values
1076 1076 1076
1091
889 889897
1088
717 717
852
1085
600
900
1200
1500
Tota
l des
ign
cost
at (k t2) = (2 3)
t1 = 0 t1 = 2 t1 = 25 t1 = 3 t1 = 35
120575 = 08
120575 = 07
120575 = 06
1469
Figure 10 Variation of total design cost with 1199051for various 120575 values
decreases with increasing 119896 value regardless of thetarget customer satisfaction 120575
(2) The 1199051and 1199052values in (7e) and (7g) affect the mini-
mum satisfaction level for each customer requirementCR119894and the fulfilled minimum design quality level
for each DR119895 respectively and therefore affect the
total design cost Larger values of 1199051andor 119905
2increase
the total design cost With 119896 = 2 and 1199052= 3
Figure 10 shows the impact of the 1199051value on the total
design cost The total design cost remains unchangedin a range of 119905
1values that depends on 120575 because
the fulfilled minimum design quality level 120588119895at 1199052= 3
confines the influence of the minimum satisfactionlevel 120576
119894on the total design cost at some levels of 119905
1
regardless of the target customer satisfaction level120575 It is also noted that if the 119905
1value is sufficiently
large (1199051= 35) and 119905
2= 3 the total design cost
is the same (1469) for all three levels of the target
1079
1084
1091
1099
1108
1083
1088
10931097
10821085
1088
1093
1075
1085
1095
1105
1115
Tota
l des
ign
cost
at (k t1) = (2 3)
t2 = 0 t2 = 15 t2 = 3 t2 = 45 t2 = 6
120575 = 08
120575 = 07
120575 = 06
Figure 11 Variation of total design cost with 1199052for various 120575 values
customer satisfaction since the aggregated resultsfrom the required minimum satisfaction level foreach customer requirement CR
119894surpass each target
customer satisfaction The high required minimumsatisfaction level due to 119905
1= 35 resulted in the largest
total design cost With 119896 = 2 and 1199051= 3 the total
design cost changes with 1199052 as shown in Figure 11
(3) From a design viewpoint if theminimum satisfactionlevel for each customer requirement CR
119894and the
fulfilled minimum design quality level for each DR119895
are not required that is 1199051and 1199052are fixed at 0 the
minimal total design cost can be obtained from theproposed model (7) at each setting of the targetedcustomer satisfaction level 120575 For example with 119905
1=
1199052= 0 and 120575 = 06 07 and 08 respectively the
total design costs are 700 878 and 1063 respectivelyregardless of the 119896 valueThis indicates that to achievethe target degree of customer satisfaction for a certainmarket segment the investment amount of the totaldesign cost has the lowest bound
6 Conclusions
A mathematical model was proposed for determining thedesign quality level required to achieve the target customersatisfaction for the target market segment with the minimumtotal design cost In the proposed model the customersatisfaction is expressed as a function of the quality level con-sidering the consumer behavior of the targetmarket segmentMoreover the proposedmodel allows theNPD team to set theminimum satisfaction level for each CR andor the fulfilledminimumdesign quality level for eachDRmaking the designprocesses flexible A numerical example was provided todemonstrate the feasibility and applicability of the proposedapproach In future research the relation between customersatisfaction and quality level will be further investigated tomake the proposed model more applicable in the real world
Journal of Applied Mathematics 9
Nomenclature
CR119894 The 119894th customer requirement
DR119895 The 119895th design requirement
119877119894119895 Relational intensity between CR
119894and DR
119895
120574119896119895 Technical correlation between DR
119896and
DR119895
1198771015840
119894119895 Normalized relational intensity between
CR119894and DR
119895in Wassermanrsquos
normalization model119877norm119894119895
Normalized relational intensity betweenCR119894and DR
119895in L-H Chen and C-N
Chenrsquos normalization model119889119894 Original importance weight of CR
119894
120573119894119897 Correlation between CR
119894and CR
119897
119889norm119894
Normalized importance weight of CR119894in
L-H Chen and C-N Chenrsquos integrationmodel when CRsrsquo correlations exist
119908norm119895
Normalized importance weight of DR119895
119862119895 Required cost for DR
119895to fully achieve
customer satisfaction119909119895 Technical fulfillment level for DR
119895
X Design vector containing the fulfillmentlevels of all DRs
DQ(X) Overall design quality level by designvector X
CS(X) Fulfilled customer satisfaction by designvector X
120572 Target design quality level120575 Target customer satisfaction119896 The characteristic parameter to describe
the customer preference of a specificmarket segment for the design qualitylevel of a specific product
120576119894 Minimum required satisfaction level for
CR119894
1199051 Design parameter to determine 120576
119894
120588119895 Minimum fulfilled quality level for DR
119895
1199052 Design parameter to determine 120588
119895
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] L Cohen Quality Function Deployment How to Make QFDWork for You Addison-Wesley Reading Mass USA 1995
[2] L-K Chan and M-L Wu ldquoQuality function deployment aliterature reviewrdquoEuropean Journal of Operational Research vol143 no 3 pp 463ndash497 2002
[3] G S Wasserman ldquoOn how to prioritize design requirementsduring the QFD planning processrdquo IIE Transactions vol 25 no3 pp 59ndash65 1993
[4] K-J Kim ldquoDetermining optimal design characteristic levels inquality function deploymentrdquo Quality Engineering vol 10 no2 pp 295ndash307 1997
[5] HMoskowitz and K-J Kim ldquoQFD optimizer a novice friendlyquality function deployment decision support system for opti-mizing product designsrdquo Computers amp Industrial Engineeringvol 32 no 3 pp 641ndash655 1997
[6] T Park and K-J Kim ldquoDetermination of an optimal setof design requirements using house of qualityrdquo Journal ofOperations Management vol 16 no 5 pp 569ndash581 1998
[7] J Bode and R Y K Fung ldquoCost engineering with qualityfunction deploymentrdquo Computers and Industrial Engineeringvol 35 no 3-4 pp 587ndash590 1998
[8] R G Askin and DW Dawson ldquoMaximizing customer satisfac-tion by optimal specification of engineering characteristicsrdquo IIETransactions (Institute of Industrial Engineers) vol 32 no 1 pp9ndash20 2000
[9] R Y K Fung J Tang Y Tu and D Wang ldquoProduct designresources optimization using a non-linear fuzzy quality func-tion deployment modelrdquo International Journal of ProductionResearch vol 40 no 3 pp 585ndash599 2002
[10] L-H Chen and M-C Weng ldquoA fuzzy model for exploitingquality function deploymentrdquo Mathematical and ComputerModelling vol 38 no 5-6 pp 559ndash570 2003
[11] H Iranmanesh and V Thomson ldquoCompetitive advantage byadjusting design characteristics to satisfy cost targetsrdquo Interna-tional Journal of Production Economics vol 115 no 1 pp 64ndash712008
[12] L-H Chen andW-C Ko ldquoA fuzzy nonlinear model for qualityfunction deployment considering Kanorsquos conceptrdquo Mathemati-cal and Computer Modelling vol 48 no 3-4 pp 581ndash593 2008
[13] L-H Chen and W-C Ko ldquoFuzzy approaches to qualityfunction deployment for new product designrdquo Fuzzy Sets andSystems vol 160 no 18 pp 2620ndash2639 2009
[14] J-H Shin H-B Jun D Kiritsis and P Xirouchakis ldquoA decisionsupport method for product conceptual design consideringproduct lifecycle factors and resource constraintsrdquo InternationalJournal of Advanced Manufacturing Technology vol 52 no 9ndash12 pp 865ndash886 2011
[15] M Braglia G Fantoni andM Frosolini ldquoThe house of reliabil-ityrdquo International Journal of Quality amp Reliability Managementvol 24 no 4 pp 420ndash440 2007
[16] W-C Chiou H-W Kuo and I-Y Lu ldquoA technology orientedproductivity measurement modelrdquo International Journal ofProduction Economics vol 60 pp 69ndash77 1999
[17] P-T Chuang ldquoA QFD approach for distributionrsquos locationmodelrdquo International Journal of Quality and Reliability Manage-ment vol 19 no 8 pp 1037ndash1054 2002
[18] L-H Chen and M-C Weng ldquoAn evaluation approach to engi-neering design inQFDprocesses using fuzzy goal programmingmodelsrdquo European Journal of Operational Research vol 172 no1 pp 230ndash248 2006
[19] E K Delice and Z Gungor ldquoA new mixed integer linearprogramming model for product development using qualityfunction deploymentrdquo Computers amp Industrial Engineering vol57 no 3 pp 906ndash912 2009
[20] E K Delice and Z Gungor ldquoAmixed integer goal programmingmodel for discrete values of design requirements in QFDrdquoInternational Journal of Production Research vol 49 no 10 pp2941ndash2957 2011
[21] F Franceschini and S Rossetto ldquoQFD an interactive algorithmfor the prioritization of productrsquos technical design characteris-ticsrdquo Integrated Manufacturing Systems vol 13 no 1 pp 69ndash752002
10 Journal of Applied Mathematics
[22] C H Han J K Kim S H Choi and S H Kim ldquoDeterminationof information system development priority using quality func-tion deploymentrdquoComputers and Industrial Engineering vol 35no 1-2 pp 241ndash244 1998
[23] E E Karsak ldquoFuzzy multiple objective decision makingapproach to prioritize design requirements in quality functiondeploymentrdquo International Journal of Production Research vol42 no 18 pp 3957ndash3974 2004
[24] X Lai M Xie and K C Tan ldquoDynamic programming for QFDoptimizationrdquoQuality and Reliability Engineering Internationalvol 21 no 8 pp 769ndash780 2005
[25] S-T Liu ldquoRating design requirements in fuzzy quality functiondeployment via a mathematical programming approachrdquo Inter-national Journal of Production Research vol 43 no 3 pp 497ndash513 2005
[26] R Ramanathan and J Yunfeng ldquoIncorporating cost and envi-ronmental factors in quality function deployment using dataenvelopment analysisrdquo Omega vol 37 no 3 pp 711ndash723 2009
[27] H Raharjo M Xie and A C Brombacher ldquoA systematicmethodology to deal with the dynamics of customer needs inQuality Function Deploymentrdquo Expert Systems with Applica-tions vol 38 no 4 pp 3653ndash3662 2011
[28] Y-M Wang and K-S Chin ldquoTechnical importance ratingsin fuzzy QFD by integrating fuzzy normalization and fuzzyweighted averagerdquoComputers ampMathematics with Applicationsvol 62 no 11 pp 4207ndash4221 2011
[29] Y-M Wang ldquoA fuzzy-normalisation-based group decision-making approach for prioritising engineering design require-ments in QFD under uncertaintyrdquo International Journal ofProduction Research vol 50 no 23 pp 6963ndash6977 2012
[30] D Lyman ldquoDeployment normalizationrdquo in Proceedings of theTransactions from the 2nd Symposium on Quality FunctionDeployment pp 307ndash315 Automotive Division of the AmericanSociety for Quality Control The American Supplier Instituteand GOALQPC Dearborn Mich USA 1990
[31] L-H Chen and C-N Chen ldquoNormalisation models for pri-oritising design requirements for quality function deploymentprocessesrdquo International Journal of Production Research vol 52no 2 pp 299ndash313 2014
[32] S Erevelles and C Leavitt ldquoA comparison of current modelsof consumer satisfactiondissatisfactionrdquo Journal of ConsumerSatisfaction Dissatisfaction and Complaining Behavior vol 5pp 104ndash114 1992
[33] M J Morgan J A Attaway and M Griffin ldquoThe role ofproductservice experience in the satisfaction formation pro-cess a test of moderationrdquo Journal of Consumer SatisfactionDissatisfaction and Complaining Behavior vol 9 pp 391ndash4051996
[34] E W Anderson and M W Sullivan ldquoThe antecedents andconsequences of customer satisfaction for firmsrdquo MarketingScience vol 12 no 2 pp 125ndash143 1993
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Mathematical Problems in Engineering
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Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Journal of Applied Mathematics 3
`
Impor-tance
120574jn
CRi
CRm
DRj DRn
Rin
RmnRmj
Rijdi
dm
120573im
Figure 2 General HOQ structure
where 120573119894119897denotes the correlation between CR
119894and CR
119897and
119889119894is the importance of CR
119894 It is noted that the normalized
weight 119889norm119894
in (3) is reduced to 119889119894when CRs are mutually
independent that issum119898119897=1120573119894119897= 1
3 Satisfaction Function with Quality Level
The purpose of the development of new products or theimprovement of existing products is mainly to satisfy cus-tomer needs or enhance customer satisfaction Achievingcustomer satisfaction is always one of the main goals for thetarget market [32] Customer satisfaction is considered oneof the most important constructs for consumers [33] Hencecustomer satisfaction is important in marketing because ofits great influence on customer purchase behavior Basedon an empirical study Anderson and Sullivan [34] foundthat customer satisfaction can generally be described as afunction of perceived quality from customers consideringan adjustment amount to reflect the customer perception ofconfirmationdisconfirmation In their study the customersatisfaction function is expressed as a concave down functionof perceived quality Following the concept of Andersonand Sullivanrsquos study [34] the present study considers thatcustomer satisfaction is positively related to the design qualityof the product in terms of a concave down function assumingthat the quality designed for the product in the design stagewill be perceived by the target customers in the futuremarketthat is the design quality level has a positive relationshipwith customer perceived quality Figure 3 shows customersatisfaction (CS) as a concave down function of design quality(DQ)
For QFD applications the design quality level of aproduct can be treated as the fulfillment level of designrequirements (DRs) and therefore customer satisfaction canbe described as a function of the DRsrsquo fulfillment levels inthe QFD processes Let 119862
119895represent the cost required for
DR119895with which the technical requirement for DR
119895can be
completely attained so that customer satisfaction can be fullyachieved 119909
119895(isin [0 1]) represents the decision variable taking
the fulfillment level of the technical requirement for DR119895
Custo
mer
satis
fact
ion
Design quality1
1
CS(X)
DQ(X)
Figure 3 Functional curve for customer satisfaction (CS) anddesign quality (DQ)
denoting the quality level of DR119895required tomeet the desired
customer satisfaction For simplification suppose that thecost required to achieve the fulfillment level of DR
119895 119909119895 is
119862119895119909119895 that is a proportional relation between the required
cost and the fulfillment level The value of 119909119895= 0means that
the technical need for DR119895is only the basic requirement so
that the cost is 0 In addition the use of the whole budget 119862119895
for DR119895will achieve the full technical requirement that is
119909119895= 1 and full customer satisfaction for this DRLet X = [119909
1 1199092 119909
119899]119879 be the vector containing the
fulfillment levels of the technical requirements for all DRsFor a new product the overall DQ is defined as the averageof the fulfillment levels of all DRs as
DQ (X) = 1119899
119899
sum
119895=1
119909119895 0 le 119909
119895le 1 (4)
where 0 le DQ(X) le 1 In other words 119909119895is interpreted as
the design quality level of DR119895 In addition based on previous
studies (eg [3ndash14]) using the normalized information fromthe HOQ 119877norm
119894119895and 119889norm
119894in (2) and (3) respectively the
customer satisfaction can be formulated as
CS (X) =119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895 0 le 119909
119895le 1 (5)
where 0 le CS(X) le 1 It is obvious that DQ(X) = 1 andCS(X) = 1 when 119909
119895= 1 forall119895 = 1 2 119899 As described
above based on the concept of Anderson and Sullivanrsquos study[34] customer satisfaction is characterized as a concave downfunction of the design quality of a product for a specificmarket segment Figure 3 shows such a functionThe concavedown curve illustrates the diminishing marginal effect asdesign quality increases the marginal effect of customersatisfaction decreases This is characterized here using thefollowing simple equation
CS (X) = [DQ (X)]1119896 (6)
4 Journal of Applied Mathematics
where 119896(gt 1) is a characteristic parameter used to describethe customer preference of a specific market segment for thedesign quality level of a specific product The function in(6) characterizes features of the relationship between CS(X)and DQ(X) as described above In practice if the desiredcustomer satisfaction degree is determined as the goal ofsatisfying the target market (6) is employed to transform thedesired value CS(X) into the corresponding value DQ(X) asthe required design quality level
4 Proposed QFD Budget Planning Model
In contrast to previous QFD-related studies that maximizedcustomer satisfaction under a limited budget this paper aimsto find the minimum design budget to achieve the marketgoal in terms of the target customer satisfaction To this endsome constraints are considered in the model Based on (6)the target design quality level 120572 (0 lt 120572 le 1) correspondingto the target customer satisfaction 120575 (0 lt 120575 le 1) isdetermined by the management that is 120572 = 120575119896 119896 gt 1 Theachieved customer satisfaction formulated as (5) based onthe fulfillment level of the technical requirement that is thefulfilled design quality level for each DR should not be lessthan the target customer satisfaction 120575 similarly the fulfilledoverall design quality of (4) should not be less than thetarget design quality level 120572 More importantly the fulfilledoverall design quality should not be less than the quality levelreflected by the achieved customer satisfaction for the targetmarket in (6) that is (1119899)sum119899
119895=1119909119895ge (sum119898
119894=1119889norm119894
sum119899
119895=1119877norm119894119895
sdot
119909119895)119896 The right-hand side in the above inequality relation
can be interpreted as the product quality perceived by thetarget customers since it is derived based on the relationsbetween CRs and DRs in the HOQ Thus this constraintensures that the realized overall quality achieved from theproduct design is better than or equal to that perceived bythe target customers
In addition to the restrictions on the target design qualitylevel and customer satisfaction from the designersrsquo view-point in general there is aminimumsatisfaction level for eachcustomer requirement CR
119894The constraint ofsum119899
119895=1119877norm119894119895
sdot119909119895ge
120576119894 0 lt 120576
119894le 1 119894 = 1 119898 reflects this condition where 120576
119894
can be determined based on the normalized weights of CR119894
using the equation 120576119894= 1199051119889norm119894
1199051gt 0 to reveal each CRrsquos
importanceThe fulfilled design quality level for eachDR119895119909119895
is usually required to not be less than aminimum level say 120588119895
0 lt 120588119895le 1 where 120588
119895can be set as 120588
119895= 1199052(sum119898
119894=1119889norm119894
sdot119877norm119894119895
)1205721199052gt 0 considering the normalized importance of DR
119895and
the target design quality level 120572 Note that the parameters 1199051
and 1199052can be determined subjectively by the management
in weighing the corresponding CRs and DRs respectivelyunder the constraints of 0 lt 120576
119894le 1 and 0 lt 120588
119895le 1
A nonlinear programming model is formulated in (7) inwhich constraints (7a) to (7g) are used for the specificationsdescribed above The objective function (7) in the modelreflects the proportional relation between the required costand the fulfillment level of each DR
Proposed Nonlinear Programming Model Consider
Min119899
sum
119895=1
119862119895119909119895 (7)
subject to
119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895ge 120575 0 lt 120575 le 1 (7a)
119899
sum
119895=1
119909119895ge 119899120572 0 lt 120572 le 1 (7b)
1
119899
119899
sum
119895=1
119909119895minus (
119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895)
119896
ge 0 119896 gt 1 (7c)
119899
sum
119895=1
119877norm119894119895
sdot 119909119895ge 120576119894 0 lt 120576
119894le 1 119894 = 1 2 119898 (7d)
120576119894= 1199051119889norm119894
(7e)
120588119895le 119909119895le 1 0 lt 120588
119895le 1 119895 = 1 2 119899 (7f)
120588119895= 1199052(
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
)120572 (7g)
It is noted that constraint (7a) can be represented as
119899
sum
119895=1
(
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
) sdot 119909119895ge 120575 0 lt 120575 le 1 (8)
If the normalized importance of DR119895to the contribution of
all CRs 119908norm119895
is defined as
119908norm119895
=
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
(9)
wheresum119899119895=1119908
norm119895
= 1 then (7a) and (7g) can be respectivelyexpressed as
119899
sum
119895=1
119908norm119895
sdot 119909119895ge 120575 0 lt 120575 le 1 (10)
120588119895= 1199052119908
norm119895
120572 (11)
In (6) parameter 119896 is important as it specifies therelation between the target design quality level and the targetcustomer satisfaction and the relation between the fulfilledoverall design quality and the quality level reflected by theachieved customer satisfaction that is the perceived qualitylevel As mentioned parameter 119896 is related to the customerbehavior of a specific market segment for a specific productThe value of 119896 can be either determined subjectively by themanagement or obtained using quantitative approaches Todo this the simple regression approach is suggested in thispaper Under the consideration that customer satisfaction is
Journal of Applied Mathematics 5
a concave down function of the perceived quality level of theproduct a linearly transformed function can be expressedas ln120572 = 119896 ln 120575 Using a group of paired estimations (120572
119894 120575119894)
based on the experience and knowledge from the QFD teammembers andor managers of the marketing departmentthe simple regression function ln 120575 = (1119896) ln120572 can beconstructed to determine the 119896 value
The procedure for applying the proposed model is asfollows
Step 1 Determine the desired product to be developed orimproved for the target market segment
Step 2 Construct the corresponding HOQ to reflect therelations between CRs and DRs
Step 3 Integrate the basic design information in the HOQ toobtain the normalized values 119877norm
119894119895 119889norm119894
and 119908norm119895
usingthe normalization model in (2) (and (3) if needed)
Step 4 Considering that 120575 is a concave down function of120572 subjectively determine the value of 119896 for meeting therelationship 120572 = 120575
119896 119896 gt 1 Alternatively collect a groupof paired estimations (120572
119894 120575119894) forall120572119894 120575119894isin [0 1] for the desired
product in the target market segment Decide the parameter119896(gt 1) in ln 120575 = (1119896) ln120572 by applying a simple regressionanalysis
Step 5 Determine the target customer satisfaction 120575 for NPDbased on the targetmarket segment and then obtain the targetdesign quality level 120572 based on 120572 = 120575
119896 using the 119896 valuedetermined in Step 4
Step 6 Let management subjectively decide the values ofparameters 119905
1and 1199052
Step 7 Construct the proposed nonlinear programmingmodel using the integrated information from the HOQobtained in Step 2
Step 8 Solve the model to find the optimal design qualitylevel of each DR so that the target customer satisfaction isachieved for the target market with the minimum budget
5 Numerical Illustration
This section demonstrates the applicability of the proposedapproach using a constructed example of a manufacturerof bicycles Based on this example parameter analyses areprovided to further illustrate the proposed approach
51 Example With rising awareness of environmental pro-tection themunicipal government has encouraged citizens totakemass transportation to workThemarketing departmentof the bicycle firm has observed that an increasing number ofcitizens are willing to bike the short distance between homeand mass transportation stations Therefore the marketingdepartment plans to launch a new bike to cater to this trendFor this plan an important issue for the NPD project team
is to determine the minimum budget needed to achieve themarket goal of the NPD during the design stage
Firstly the newly developed bike is positioned as simpleand easy for biking the short distance between home andmass transportation station and aims to satisfy commutersTheNPD team selects QFD as the design platform In the sec-ond step the HOQ is constructed for specifying the relationsbetween CRs and DRs The following six basic requirementsare identified (1) ride comfort (2) ride safety (3) easyhandling (4) easy movement (5) low maintenance and (6)durability Based on consensus the team members proposenine design requirements that correspond to the six basiccustomer requirementsThe nine design requirements are (1)frame (2) suspension (3) derailleur (4) brake (5) wheels (6)handlebars (7) saddle (8) pedals and (9) total weight Thedegree of relational intensity for the relationship betweenCRsand DRs is defined by weak-moderate-strong the correlationamong CRs or amongDRs is also defined by weak-moderate-strong but allowing for negative correlations Furthermorethe NPD team identifies the CRsrsquo importance degrees for theproduct to emphasize its easy handling and ride safety Thebasic QFD design information for the product is shown inFigure 4
The main work in the third step is to integrate the designinformation into the HOQ to obtain the normalized relationstrengths or weights namely 119877norm
119894119895 119889norm119894
and 119908norm119895
forestablishing the proposed nonlinear programming modelto achieve the marketquality goal at the minimum designcost As described before L-H Chen and C-N Chenrsquosnormalization models (2) and (3) are employed To do thisthe degree of relational or correlation intensity describedas weak-moderate-strong must be numerically scaled Ascommonly used in the literature the rating scale 1-3-9 isemployed for relational intensity that is weak-moderate-strong between CRs and DRs and plusmn(01-03-09) is usedfor correlation that is weak-moderate-strong among CRsor among DRs with negative correlations allowed Figure 5shows the normalized results for the product using the basicdesign information in Figure 4
After the integrated information from the HOQ hasbeen obtained the characteristic parameter 119896 for the marketsegment of commuters should be determined to characterizethe functional curve between customer satisfaction anddesign quality level Based on the experience of themarketingexperts 119896 is set to 2 that is CS(X) = [DQ(X)]12 as shownin Figure 6 Based on the determined function the fifth stepis to set up the target design quality level 120572 From a marketcompetitive analysis the target customer satisfaction is set as120575 = 08 so the target design quality level 120572 is obtained as064 based on the function 120572 = 120575119896 119896 = 2 To formulate theproposed nonlinear programming model for the minimumcost in the sixth step the parameters 119905
1and 1199052should be
determined to specify theminimumsatisfaction level for eachcustomer requirement CR
119894and the minimum design quality
level for each DR119895 The values 119905
1= 3 and 119905
2= 3 are set by the
NPD team in this exampleBased on the settings in the previous steps the pro-
posed nonlinear programming model can be formulated for
6 Journal of Applied Mathematics
movement
Custo
mer
requ
irem
ents
Deg
ree o
f im
port
ance
Design requirements
15
20
25
15
9 points 3 points 1 point
Strong relationModerate relationWeak relationWeak negative relation
Moderate negative relationStrong negative relation
Correlation symbols and values
maintenance
Relation symbols and points
13
12
minus01
minus03
minus09
0103
09
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy
(5) Low
(6) Durability
Figure 4 Basic QFD design information for product
Custo
mer
requ
irem
ents
Design requirements
Nor
mal
ized
CR
impo
rtan
ce w
eigh
t
017
024
028
011
011
011011011011011
013 011 011 013 016
016
011 011 011
015 013 013
013013
015 019 013 004004 003
009 008 023 009
009
011 023 008 005
003 037 008 048
020 017 017 020 008 006 006006
003
003
Normalized DR importance 012 010 015 012 017 014 006 007007weight
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy movement
(5) Low maintenance
(6) Durability
Figure 5 Normalized results for product
the minimum design cost Let the decision variable 119909119895 119895 =
1 2 9 represent the technical fulfillment level of DR119895
The model aims to achieve the target customer satisfaction(120575 = 08) and the target design quality levels (120572 = 064)for the product at the minimum total design cost sum9
119895=1119862119895119909119895
1
1
Custo
mer
satis
fact
ion
Design quality
k = 2
120575
120572
CS(X)
DQ(X)
Figure 6 Functional curve of customer satisfaction for product
where 119862119895denotes the design cost of completely fulfilling the
technical level of DR119895 The nonlinear programming model is
expressed as
Min9
sum
119895=1
119862119895119909119895 (12)
Journal of Applied Mathematics 7
subject to
0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9ge 08
1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099ge 9 times 064
1
9(1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099)
minus (0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9)2
ge 0
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 051
0151199091+ 013119909
2+ 013119909
3+ 015119909
4+ 019119909
5
+ 0131199096+ 004119909
7+ 004119909
8+ 003119909
9ge 072
0091199091+ 008119909
2+ 023119909
3+ 009119909
4+ 011119909
5
+ 0231199096+ 008119909
7+ 003119909
8+ 005119909
9ge 084
0031199091+ 000119909
2+ 003119909
3+ 000119909
4+ 037119909
5
+ 0081199096+ 000119909
7+ 000119909
8+ 048119909
9ge 033
0201199091+ 017119909
2+ 017119909
3+ 020119909
4+ 008119909
5
+ 0061199096+ 006119909
7+ 006119909
8+ 000119909
9ge 033
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 027
023 le 1199091le 1
019 le 1199092le 1
029 le 1199093le 1
023 le 1199094le 1
033 le 1199095le 1
027 le 1199096le 1
013 le 1199097le 1
012 le 1199098le 1
013 le 1199099le 1
(13)
DRj
Cj 220 250 280 200 260 130 80 50 30
Unit $ thousand
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 7 Completely fulfilled design cost 119862119895for DR
119895
1 1 1 1 1 1
Targ
eted
CS
Fulfi
lled
DQ
k MinΣCjxj
20 080 081 023 019 086 1091
x1 x2 x3 x4 x5 x6 x8x7 x9
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 8 Optimal technical fulfillments for product
To solve the model the design cost 119862119895for DR
119895must
be determined beforehand For this example the costs areprovided by the NPD team as shown in Figure 7 Theproposed nonlinear model can be solved using commercialsoftware such as LINGO 110 Figure 8 summarizes the opti-mal technical fulfillment level 119909
119895for eachDR
119895Theminimum
total design cost for the product is $1091000 The figureindicates that the target customer satisfaction can be achievedat CS(X) = sum
9
119895=1119908
norm119895
sdot 119909119895= 08 The fulfilled design
quality level is determined as DQ(X) = (19)sum9119895=1119909119895= 081
which is greater than 120572(= 064) satisfying constraint (7b)The solutions obtained in Figure 8 satisfy the requirementsof the new product for the target customer satisfaction at theminimum total design cost
52 Parameter Analyses The proposed nonlinear program-ming model includes three design parameters namely 1198961199051 and 119905
2 that are specified by the NPD team These three
parameters affect the design quality level and thereforethe total design cost The influence of the combination ofdifferent values of 119896 119905
1 and 119905
2on the total design costwas thus
examined In the analyses the target customer satisfaction120575 was set at 06 07 and 08 respectively The results of theanalyses are summarized below
(1) The parameter 119896 characterizes the customer satisfac-tion of the design quality level The larger the valueof 119896 is the more attractive to customers the productquality level is With a larger 119896 the target customersatisfaction can be achieved using only the lowerlevel of product design quality and therefore the totaldesign cost is lower As a demonstration with 119905
1and
1199052fixed at 3 Figure 9 shows that the total design cost
8 Journal of Applied Mathematics
1093
1091
1088
1090
1088
1084
1087
1085
1083
1080
1085
1090
1095
Tota
l des
ign
cost
k = 15 k = 2 k = 3
120575 = 08
120575 = 07
120575 = 06
at (t1 t2) = (3 3)
Figure 9 Variation of total design cost with 119896 for various 120575 values
1076 1076 1076
1091
889 889897
1088
717 717
852
1085
600
900
1200
1500
Tota
l des
ign
cost
at (k t2) = (2 3)
t1 = 0 t1 = 2 t1 = 25 t1 = 3 t1 = 35
120575 = 08
120575 = 07
120575 = 06
1469
Figure 10 Variation of total design cost with 1199051for various 120575 values
decreases with increasing 119896 value regardless of thetarget customer satisfaction 120575
(2) The 1199051and 1199052values in (7e) and (7g) affect the mini-
mum satisfaction level for each customer requirementCR119894and the fulfilled minimum design quality level
for each DR119895 respectively and therefore affect the
total design cost Larger values of 1199051andor 119905
2increase
the total design cost With 119896 = 2 and 1199052= 3
Figure 10 shows the impact of the 1199051value on the total
design cost The total design cost remains unchangedin a range of 119905
1values that depends on 120575 because
the fulfilled minimum design quality level 120588119895at 1199052= 3
confines the influence of the minimum satisfactionlevel 120576
119894on the total design cost at some levels of 119905
1
regardless of the target customer satisfaction level120575 It is also noted that if the 119905
1value is sufficiently
large (1199051= 35) and 119905
2= 3 the total design cost
is the same (1469) for all three levels of the target
1079
1084
1091
1099
1108
1083
1088
10931097
10821085
1088
1093
1075
1085
1095
1105
1115
Tota
l des
ign
cost
at (k t1) = (2 3)
t2 = 0 t2 = 15 t2 = 3 t2 = 45 t2 = 6
120575 = 08
120575 = 07
120575 = 06
Figure 11 Variation of total design cost with 1199052for various 120575 values
customer satisfaction since the aggregated resultsfrom the required minimum satisfaction level foreach customer requirement CR
119894surpass each target
customer satisfaction The high required minimumsatisfaction level due to 119905
1= 35 resulted in the largest
total design cost With 119896 = 2 and 1199051= 3 the total
design cost changes with 1199052 as shown in Figure 11
(3) From a design viewpoint if theminimum satisfactionlevel for each customer requirement CR
119894and the
fulfilled minimum design quality level for each DR119895
are not required that is 1199051and 1199052are fixed at 0 the
minimal total design cost can be obtained from theproposed model (7) at each setting of the targetedcustomer satisfaction level 120575 For example with 119905
1=
1199052= 0 and 120575 = 06 07 and 08 respectively the
total design costs are 700 878 and 1063 respectivelyregardless of the 119896 valueThis indicates that to achievethe target degree of customer satisfaction for a certainmarket segment the investment amount of the totaldesign cost has the lowest bound
6 Conclusions
A mathematical model was proposed for determining thedesign quality level required to achieve the target customersatisfaction for the target market segment with the minimumtotal design cost In the proposed model the customersatisfaction is expressed as a function of the quality level con-sidering the consumer behavior of the targetmarket segmentMoreover the proposedmodel allows theNPD team to set theminimum satisfaction level for each CR andor the fulfilledminimumdesign quality level for eachDRmaking the designprocesses flexible A numerical example was provided todemonstrate the feasibility and applicability of the proposedapproach In future research the relation between customersatisfaction and quality level will be further investigated tomake the proposed model more applicable in the real world
Journal of Applied Mathematics 9
Nomenclature
CR119894 The 119894th customer requirement
DR119895 The 119895th design requirement
119877119894119895 Relational intensity between CR
119894and DR
119895
120574119896119895 Technical correlation between DR
119896and
DR119895
1198771015840
119894119895 Normalized relational intensity between
CR119894and DR
119895in Wassermanrsquos
normalization model119877norm119894119895
Normalized relational intensity betweenCR119894and DR
119895in L-H Chen and C-N
Chenrsquos normalization model119889119894 Original importance weight of CR
119894
120573119894119897 Correlation between CR
119894and CR
119897
119889norm119894
Normalized importance weight of CR119894in
L-H Chen and C-N Chenrsquos integrationmodel when CRsrsquo correlations exist
119908norm119895
Normalized importance weight of DR119895
119862119895 Required cost for DR
119895to fully achieve
customer satisfaction119909119895 Technical fulfillment level for DR
119895
X Design vector containing the fulfillmentlevels of all DRs
DQ(X) Overall design quality level by designvector X
CS(X) Fulfilled customer satisfaction by designvector X
120572 Target design quality level120575 Target customer satisfaction119896 The characteristic parameter to describe
the customer preference of a specificmarket segment for the design qualitylevel of a specific product
120576119894 Minimum required satisfaction level for
CR119894
1199051 Design parameter to determine 120576
119894
120588119895 Minimum fulfilled quality level for DR
119895
1199052 Design parameter to determine 120588
119895
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] L Cohen Quality Function Deployment How to Make QFDWork for You Addison-Wesley Reading Mass USA 1995
[2] L-K Chan and M-L Wu ldquoQuality function deployment aliterature reviewrdquoEuropean Journal of Operational Research vol143 no 3 pp 463ndash497 2002
[3] G S Wasserman ldquoOn how to prioritize design requirementsduring the QFD planning processrdquo IIE Transactions vol 25 no3 pp 59ndash65 1993
[4] K-J Kim ldquoDetermining optimal design characteristic levels inquality function deploymentrdquo Quality Engineering vol 10 no2 pp 295ndash307 1997
[5] HMoskowitz and K-J Kim ldquoQFD optimizer a novice friendlyquality function deployment decision support system for opti-mizing product designsrdquo Computers amp Industrial Engineeringvol 32 no 3 pp 641ndash655 1997
[6] T Park and K-J Kim ldquoDetermination of an optimal setof design requirements using house of qualityrdquo Journal ofOperations Management vol 16 no 5 pp 569ndash581 1998
[7] J Bode and R Y K Fung ldquoCost engineering with qualityfunction deploymentrdquo Computers and Industrial Engineeringvol 35 no 3-4 pp 587ndash590 1998
[8] R G Askin and DW Dawson ldquoMaximizing customer satisfac-tion by optimal specification of engineering characteristicsrdquo IIETransactions (Institute of Industrial Engineers) vol 32 no 1 pp9ndash20 2000
[9] R Y K Fung J Tang Y Tu and D Wang ldquoProduct designresources optimization using a non-linear fuzzy quality func-tion deployment modelrdquo International Journal of ProductionResearch vol 40 no 3 pp 585ndash599 2002
[10] L-H Chen and M-C Weng ldquoA fuzzy model for exploitingquality function deploymentrdquo Mathematical and ComputerModelling vol 38 no 5-6 pp 559ndash570 2003
[11] H Iranmanesh and V Thomson ldquoCompetitive advantage byadjusting design characteristics to satisfy cost targetsrdquo Interna-tional Journal of Production Economics vol 115 no 1 pp 64ndash712008
[12] L-H Chen andW-C Ko ldquoA fuzzy nonlinear model for qualityfunction deployment considering Kanorsquos conceptrdquo Mathemati-cal and Computer Modelling vol 48 no 3-4 pp 581ndash593 2008
[13] L-H Chen and W-C Ko ldquoFuzzy approaches to qualityfunction deployment for new product designrdquo Fuzzy Sets andSystems vol 160 no 18 pp 2620ndash2639 2009
[14] J-H Shin H-B Jun D Kiritsis and P Xirouchakis ldquoA decisionsupport method for product conceptual design consideringproduct lifecycle factors and resource constraintsrdquo InternationalJournal of Advanced Manufacturing Technology vol 52 no 9ndash12 pp 865ndash886 2011
[15] M Braglia G Fantoni andM Frosolini ldquoThe house of reliabil-ityrdquo International Journal of Quality amp Reliability Managementvol 24 no 4 pp 420ndash440 2007
[16] W-C Chiou H-W Kuo and I-Y Lu ldquoA technology orientedproductivity measurement modelrdquo International Journal ofProduction Economics vol 60 pp 69ndash77 1999
[17] P-T Chuang ldquoA QFD approach for distributionrsquos locationmodelrdquo International Journal of Quality and Reliability Manage-ment vol 19 no 8 pp 1037ndash1054 2002
[18] L-H Chen and M-C Weng ldquoAn evaluation approach to engi-neering design inQFDprocesses using fuzzy goal programmingmodelsrdquo European Journal of Operational Research vol 172 no1 pp 230ndash248 2006
[19] E K Delice and Z Gungor ldquoA new mixed integer linearprogramming model for product development using qualityfunction deploymentrdquo Computers amp Industrial Engineering vol57 no 3 pp 906ndash912 2009
[20] E K Delice and Z Gungor ldquoAmixed integer goal programmingmodel for discrete values of design requirements in QFDrdquoInternational Journal of Production Research vol 49 no 10 pp2941ndash2957 2011
[21] F Franceschini and S Rossetto ldquoQFD an interactive algorithmfor the prioritization of productrsquos technical design characteris-ticsrdquo Integrated Manufacturing Systems vol 13 no 1 pp 69ndash752002
10 Journal of Applied Mathematics
[22] C H Han J K Kim S H Choi and S H Kim ldquoDeterminationof information system development priority using quality func-tion deploymentrdquoComputers and Industrial Engineering vol 35no 1-2 pp 241ndash244 1998
[23] E E Karsak ldquoFuzzy multiple objective decision makingapproach to prioritize design requirements in quality functiondeploymentrdquo International Journal of Production Research vol42 no 18 pp 3957ndash3974 2004
[24] X Lai M Xie and K C Tan ldquoDynamic programming for QFDoptimizationrdquoQuality and Reliability Engineering Internationalvol 21 no 8 pp 769ndash780 2005
[25] S-T Liu ldquoRating design requirements in fuzzy quality functiondeployment via a mathematical programming approachrdquo Inter-national Journal of Production Research vol 43 no 3 pp 497ndash513 2005
[26] R Ramanathan and J Yunfeng ldquoIncorporating cost and envi-ronmental factors in quality function deployment using dataenvelopment analysisrdquo Omega vol 37 no 3 pp 711ndash723 2009
[27] H Raharjo M Xie and A C Brombacher ldquoA systematicmethodology to deal with the dynamics of customer needs inQuality Function Deploymentrdquo Expert Systems with Applica-tions vol 38 no 4 pp 3653ndash3662 2011
[28] Y-M Wang and K-S Chin ldquoTechnical importance ratingsin fuzzy QFD by integrating fuzzy normalization and fuzzyweighted averagerdquoComputers ampMathematics with Applicationsvol 62 no 11 pp 4207ndash4221 2011
[29] Y-M Wang ldquoA fuzzy-normalisation-based group decision-making approach for prioritising engineering design require-ments in QFD under uncertaintyrdquo International Journal ofProduction Research vol 50 no 23 pp 6963ndash6977 2012
[30] D Lyman ldquoDeployment normalizationrdquo in Proceedings of theTransactions from the 2nd Symposium on Quality FunctionDeployment pp 307ndash315 Automotive Division of the AmericanSociety for Quality Control The American Supplier Instituteand GOALQPC Dearborn Mich USA 1990
[31] L-H Chen and C-N Chen ldquoNormalisation models for pri-oritising design requirements for quality function deploymentprocessesrdquo International Journal of Production Research vol 52no 2 pp 299ndash313 2014
[32] S Erevelles and C Leavitt ldquoA comparison of current modelsof consumer satisfactiondissatisfactionrdquo Journal of ConsumerSatisfaction Dissatisfaction and Complaining Behavior vol 5pp 104ndash114 1992
[33] M J Morgan J A Attaway and M Griffin ldquoThe role ofproductservice experience in the satisfaction formation pro-cess a test of moderationrdquo Journal of Consumer SatisfactionDissatisfaction and Complaining Behavior vol 9 pp 391ndash4051996
[34] E W Anderson and M W Sullivan ldquoThe antecedents andconsequences of customer satisfaction for firmsrdquo MarketingScience vol 12 no 2 pp 125ndash143 1993
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Differential EquationsInternational Journal of
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
4 Journal of Applied Mathematics
where 119896(gt 1) is a characteristic parameter used to describethe customer preference of a specific market segment for thedesign quality level of a specific product The function in(6) characterizes features of the relationship between CS(X)and DQ(X) as described above In practice if the desiredcustomer satisfaction degree is determined as the goal ofsatisfying the target market (6) is employed to transform thedesired value CS(X) into the corresponding value DQ(X) asthe required design quality level
4 Proposed QFD Budget Planning Model
In contrast to previous QFD-related studies that maximizedcustomer satisfaction under a limited budget this paper aimsto find the minimum design budget to achieve the marketgoal in terms of the target customer satisfaction To this endsome constraints are considered in the model Based on (6)the target design quality level 120572 (0 lt 120572 le 1) correspondingto the target customer satisfaction 120575 (0 lt 120575 le 1) isdetermined by the management that is 120572 = 120575119896 119896 gt 1 Theachieved customer satisfaction formulated as (5) based onthe fulfillment level of the technical requirement that is thefulfilled design quality level for each DR should not be lessthan the target customer satisfaction 120575 similarly the fulfilledoverall design quality of (4) should not be less than thetarget design quality level 120572 More importantly the fulfilledoverall design quality should not be less than the quality levelreflected by the achieved customer satisfaction for the targetmarket in (6) that is (1119899)sum119899
119895=1119909119895ge (sum119898
119894=1119889norm119894
sum119899
119895=1119877norm119894119895
sdot
119909119895)119896 The right-hand side in the above inequality relation
can be interpreted as the product quality perceived by thetarget customers since it is derived based on the relationsbetween CRs and DRs in the HOQ Thus this constraintensures that the realized overall quality achieved from theproduct design is better than or equal to that perceived bythe target customers
In addition to the restrictions on the target design qualitylevel and customer satisfaction from the designersrsquo view-point in general there is aminimumsatisfaction level for eachcustomer requirement CR
119894The constraint ofsum119899
119895=1119877norm119894119895
sdot119909119895ge
120576119894 0 lt 120576
119894le 1 119894 = 1 119898 reflects this condition where 120576
119894
can be determined based on the normalized weights of CR119894
using the equation 120576119894= 1199051119889norm119894
1199051gt 0 to reveal each CRrsquos
importanceThe fulfilled design quality level for eachDR119895119909119895
is usually required to not be less than aminimum level say 120588119895
0 lt 120588119895le 1 where 120588
119895can be set as 120588
119895= 1199052(sum119898
119894=1119889norm119894
sdot119877norm119894119895
)1205721199052gt 0 considering the normalized importance of DR
119895and
the target design quality level 120572 Note that the parameters 1199051
and 1199052can be determined subjectively by the management
in weighing the corresponding CRs and DRs respectivelyunder the constraints of 0 lt 120576
119894le 1 and 0 lt 120588
119895le 1
A nonlinear programming model is formulated in (7) inwhich constraints (7a) to (7g) are used for the specificationsdescribed above The objective function (7) in the modelreflects the proportional relation between the required costand the fulfillment level of each DR
Proposed Nonlinear Programming Model Consider
Min119899
sum
119895=1
119862119895119909119895 (7)
subject to
119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895ge 120575 0 lt 120575 le 1 (7a)
119899
sum
119895=1
119909119895ge 119899120572 0 lt 120572 le 1 (7b)
1
119899
119899
sum
119895=1
119909119895minus (
119898
sum
119894=1
119889norm119894
119899
sum
119895=1
119877norm119894119895
sdot 119909119895)
119896
ge 0 119896 gt 1 (7c)
119899
sum
119895=1
119877norm119894119895
sdot 119909119895ge 120576119894 0 lt 120576
119894le 1 119894 = 1 2 119898 (7d)
120576119894= 1199051119889norm119894
(7e)
120588119895le 119909119895le 1 0 lt 120588
119895le 1 119895 = 1 2 119899 (7f)
120588119895= 1199052(
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
)120572 (7g)
It is noted that constraint (7a) can be represented as
119899
sum
119895=1
(
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
) sdot 119909119895ge 120575 0 lt 120575 le 1 (8)
If the normalized importance of DR119895to the contribution of
all CRs 119908norm119895
is defined as
119908norm119895
=
119898
sum
119894=1
119889norm119894
sdot 119877norm119894119895
(9)
wheresum119899119895=1119908
norm119895
= 1 then (7a) and (7g) can be respectivelyexpressed as
119899
sum
119895=1
119908norm119895
sdot 119909119895ge 120575 0 lt 120575 le 1 (10)
120588119895= 1199052119908
norm119895
120572 (11)
In (6) parameter 119896 is important as it specifies therelation between the target design quality level and the targetcustomer satisfaction and the relation between the fulfilledoverall design quality and the quality level reflected by theachieved customer satisfaction that is the perceived qualitylevel As mentioned parameter 119896 is related to the customerbehavior of a specific market segment for a specific productThe value of 119896 can be either determined subjectively by themanagement or obtained using quantitative approaches Todo this the simple regression approach is suggested in thispaper Under the consideration that customer satisfaction is
Journal of Applied Mathematics 5
a concave down function of the perceived quality level of theproduct a linearly transformed function can be expressedas ln120572 = 119896 ln 120575 Using a group of paired estimations (120572
119894 120575119894)
based on the experience and knowledge from the QFD teammembers andor managers of the marketing departmentthe simple regression function ln 120575 = (1119896) ln120572 can beconstructed to determine the 119896 value
The procedure for applying the proposed model is asfollows
Step 1 Determine the desired product to be developed orimproved for the target market segment
Step 2 Construct the corresponding HOQ to reflect therelations between CRs and DRs
Step 3 Integrate the basic design information in the HOQ toobtain the normalized values 119877norm
119894119895 119889norm119894
and 119908norm119895
usingthe normalization model in (2) (and (3) if needed)
Step 4 Considering that 120575 is a concave down function of120572 subjectively determine the value of 119896 for meeting therelationship 120572 = 120575
119896 119896 gt 1 Alternatively collect a groupof paired estimations (120572
119894 120575119894) forall120572119894 120575119894isin [0 1] for the desired
product in the target market segment Decide the parameter119896(gt 1) in ln 120575 = (1119896) ln120572 by applying a simple regressionanalysis
Step 5 Determine the target customer satisfaction 120575 for NPDbased on the targetmarket segment and then obtain the targetdesign quality level 120572 based on 120572 = 120575
119896 using the 119896 valuedetermined in Step 4
Step 6 Let management subjectively decide the values ofparameters 119905
1and 1199052
Step 7 Construct the proposed nonlinear programmingmodel using the integrated information from the HOQobtained in Step 2
Step 8 Solve the model to find the optimal design qualitylevel of each DR so that the target customer satisfaction isachieved for the target market with the minimum budget
5 Numerical Illustration
This section demonstrates the applicability of the proposedapproach using a constructed example of a manufacturerof bicycles Based on this example parameter analyses areprovided to further illustrate the proposed approach
51 Example With rising awareness of environmental pro-tection themunicipal government has encouraged citizens totakemass transportation to workThemarketing departmentof the bicycle firm has observed that an increasing number ofcitizens are willing to bike the short distance between homeand mass transportation stations Therefore the marketingdepartment plans to launch a new bike to cater to this trendFor this plan an important issue for the NPD project team
is to determine the minimum budget needed to achieve themarket goal of the NPD during the design stage
Firstly the newly developed bike is positioned as simpleand easy for biking the short distance between home andmass transportation station and aims to satisfy commutersTheNPD team selects QFD as the design platform In the sec-ond step the HOQ is constructed for specifying the relationsbetween CRs and DRs The following six basic requirementsare identified (1) ride comfort (2) ride safety (3) easyhandling (4) easy movement (5) low maintenance and (6)durability Based on consensus the team members proposenine design requirements that correspond to the six basiccustomer requirementsThe nine design requirements are (1)frame (2) suspension (3) derailleur (4) brake (5) wheels (6)handlebars (7) saddle (8) pedals and (9) total weight Thedegree of relational intensity for the relationship betweenCRsand DRs is defined by weak-moderate-strong the correlationamong CRs or amongDRs is also defined by weak-moderate-strong but allowing for negative correlations Furthermorethe NPD team identifies the CRsrsquo importance degrees for theproduct to emphasize its easy handling and ride safety Thebasic QFD design information for the product is shown inFigure 4
The main work in the third step is to integrate the designinformation into the HOQ to obtain the normalized relationstrengths or weights namely 119877norm
119894119895 119889norm119894
and 119908norm119895
forestablishing the proposed nonlinear programming modelto achieve the marketquality goal at the minimum designcost As described before L-H Chen and C-N Chenrsquosnormalization models (2) and (3) are employed To do thisthe degree of relational or correlation intensity describedas weak-moderate-strong must be numerically scaled Ascommonly used in the literature the rating scale 1-3-9 isemployed for relational intensity that is weak-moderate-strong between CRs and DRs and plusmn(01-03-09) is usedfor correlation that is weak-moderate-strong among CRsor among DRs with negative correlations allowed Figure 5shows the normalized results for the product using the basicdesign information in Figure 4
After the integrated information from the HOQ hasbeen obtained the characteristic parameter 119896 for the marketsegment of commuters should be determined to characterizethe functional curve between customer satisfaction anddesign quality level Based on the experience of themarketingexperts 119896 is set to 2 that is CS(X) = [DQ(X)]12 as shownin Figure 6 Based on the determined function the fifth stepis to set up the target design quality level 120572 From a marketcompetitive analysis the target customer satisfaction is set as120575 = 08 so the target design quality level 120572 is obtained as064 based on the function 120572 = 120575119896 119896 = 2 To formulate theproposed nonlinear programming model for the minimumcost in the sixth step the parameters 119905
1and 1199052should be
determined to specify theminimumsatisfaction level for eachcustomer requirement CR
119894and the minimum design quality
level for each DR119895 The values 119905
1= 3 and 119905
2= 3 are set by the
NPD team in this exampleBased on the settings in the previous steps the pro-
posed nonlinear programming model can be formulated for
6 Journal of Applied Mathematics
movement
Custo
mer
requ
irem
ents
Deg
ree o
f im
port
ance
Design requirements
15
20
25
15
9 points 3 points 1 point
Strong relationModerate relationWeak relationWeak negative relation
Moderate negative relationStrong negative relation
Correlation symbols and values
maintenance
Relation symbols and points
13
12
minus01
minus03
minus09
0103
09
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy
(5) Low
(6) Durability
Figure 4 Basic QFD design information for product
Custo
mer
requ
irem
ents
Design requirements
Nor
mal
ized
CR
impo
rtan
ce w
eigh
t
017
024
028
011
011
011011011011011
013 011 011 013 016
016
011 011 011
015 013 013
013013
015 019 013 004004 003
009 008 023 009
009
011 023 008 005
003 037 008 048
020 017 017 020 008 006 006006
003
003
Normalized DR importance 012 010 015 012 017 014 006 007007weight
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy movement
(5) Low maintenance
(6) Durability
Figure 5 Normalized results for product
the minimum design cost Let the decision variable 119909119895 119895 =
1 2 9 represent the technical fulfillment level of DR119895
The model aims to achieve the target customer satisfaction(120575 = 08) and the target design quality levels (120572 = 064)for the product at the minimum total design cost sum9
119895=1119862119895119909119895
1
1
Custo
mer
satis
fact
ion
Design quality
k = 2
120575
120572
CS(X)
DQ(X)
Figure 6 Functional curve of customer satisfaction for product
where 119862119895denotes the design cost of completely fulfilling the
technical level of DR119895 The nonlinear programming model is
expressed as
Min9
sum
119895=1
119862119895119909119895 (12)
Journal of Applied Mathematics 7
subject to
0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9ge 08
1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099ge 9 times 064
1
9(1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099)
minus (0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9)2
ge 0
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 051
0151199091+ 013119909
2+ 013119909
3+ 015119909
4+ 019119909
5
+ 0131199096+ 004119909
7+ 004119909
8+ 003119909
9ge 072
0091199091+ 008119909
2+ 023119909
3+ 009119909
4+ 011119909
5
+ 0231199096+ 008119909
7+ 003119909
8+ 005119909
9ge 084
0031199091+ 000119909
2+ 003119909
3+ 000119909
4+ 037119909
5
+ 0081199096+ 000119909
7+ 000119909
8+ 048119909
9ge 033
0201199091+ 017119909
2+ 017119909
3+ 020119909
4+ 008119909
5
+ 0061199096+ 006119909
7+ 006119909
8+ 000119909
9ge 033
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 027
023 le 1199091le 1
019 le 1199092le 1
029 le 1199093le 1
023 le 1199094le 1
033 le 1199095le 1
027 le 1199096le 1
013 le 1199097le 1
012 le 1199098le 1
013 le 1199099le 1
(13)
DRj
Cj 220 250 280 200 260 130 80 50 30
Unit $ thousand
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 7 Completely fulfilled design cost 119862119895for DR
119895
1 1 1 1 1 1
Targ
eted
CS
Fulfi
lled
DQ
k MinΣCjxj
20 080 081 023 019 086 1091
x1 x2 x3 x4 x5 x6 x8x7 x9
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 8 Optimal technical fulfillments for product
To solve the model the design cost 119862119895for DR
119895must
be determined beforehand For this example the costs areprovided by the NPD team as shown in Figure 7 Theproposed nonlinear model can be solved using commercialsoftware such as LINGO 110 Figure 8 summarizes the opti-mal technical fulfillment level 119909
119895for eachDR
119895Theminimum
total design cost for the product is $1091000 The figureindicates that the target customer satisfaction can be achievedat CS(X) = sum
9
119895=1119908
norm119895
sdot 119909119895= 08 The fulfilled design
quality level is determined as DQ(X) = (19)sum9119895=1119909119895= 081
which is greater than 120572(= 064) satisfying constraint (7b)The solutions obtained in Figure 8 satisfy the requirementsof the new product for the target customer satisfaction at theminimum total design cost
52 Parameter Analyses The proposed nonlinear program-ming model includes three design parameters namely 1198961199051 and 119905
2 that are specified by the NPD team These three
parameters affect the design quality level and thereforethe total design cost The influence of the combination ofdifferent values of 119896 119905
1 and 119905
2on the total design costwas thus
examined In the analyses the target customer satisfaction120575 was set at 06 07 and 08 respectively The results of theanalyses are summarized below
(1) The parameter 119896 characterizes the customer satisfac-tion of the design quality level The larger the valueof 119896 is the more attractive to customers the productquality level is With a larger 119896 the target customersatisfaction can be achieved using only the lowerlevel of product design quality and therefore the totaldesign cost is lower As a demonstration with 119905
1and
1199052fixed at 3 Figure 9 shows that the total design cost
8 Journal of Applied Mathematics
1093
1091
1088
1090
1088
1084
1087
1085
1083
1080
1085
1090
1095
Tota
l des
ign
cost
k = 15 k = 2 k = 3
120575 = 08
120575 = 07
120575 = 06
at (t1 t2) = (3 3)
Figure 9 Variation of total design cost with 119896 for various 120575 values
1076 1076 1076
1091
889 889897
1088
717 717
852
1085
600
900
1200
1500
Tota
l des
ign
cost
at (k t2) = (2 3)
t1 = 0 t1 = 2 t1 = 25 t1 = 3 t1 = 35
120575 = 08
120575 = 07
120575 = 06
1469
Figure 10 Variation of total design cost with 1199051for various 120575 values
decreases with increasing 119896 value regardless of thetarget customer satisfaction 120575
(2) The 1199051and 1199052values in (7e) and (7g) affect the mini-
mum satisfaction level for each customer requirementCR119894and the fulfilled minimum design quality level
for each DR119895 respectively and therefore affect the
total design cost Larger values of 1199051andor 119905
2increase
the total design cost With 119896 = 2 and 1199052= 3
Figure 10 shows the impact of the 1199051value on the total
design cost The total design cost remains unchangedin a range of 119905
1values that depends on 120575 because
the fulfilled minimum design quality level 120588119895at 1199052= 3
confines the influence of the minimum satisfactionlevel 120576
119894on the total design cost at some levels of 119905
1
regardless of the target customer satisfaction level120575 It is also noted that if the 119905
1value is sufficiently
large (1199051= 35) and 119905
2= 3 the total design cost
is the same (1469) for all three levels of the target
1079
1084
1091
1099
1108
1083
1088
10931097
10821085
1088
1093
1075
1085
1095
1105
1115
Tota
l des
ign
cost
at (k t1) = (2 3)
t2 = 0 t2 = 15 t2 = 3 t2 = 45 t2 = 6
120575 = 08
120575 = 07
120575 = 06
Figure 11 Variation of total design cost with 1199052for various 120575 values
customer satisfaction since the aggregated resultsfrom the required minimum satisfaction level foreach customer requirement CR
119894surpass each target
customer satisfaction The high required minimumsatisfaction level due to 119905
1= 35 resulted in the largest
total design cost With 119896 = 2 and 1199051= 3 the total
design cost changes with 1199052 as shown in Figure 11
(3) From a design viewpoint if theminimum satisfactionlevel for each customer requirement CR
119894and the
fulfilled minimum design quality level for each DR119895
are not required that is 1199051and 1199052are fixed at 0 the
minimal total design cost can be obtained from theproposed model (7) at each setting of the targetedcustomer satisfaction level 120575 For example with 119905
1=
1199052= 0 and 120575 = 06 07 and 08 respectively the
total design costs are 700 878 and 1063 respectivelyregardless of the 119896 valueThis indicates that to achievethe target degree of customer satisfaction for a certainmarket segment the investment amount of the totaldesign cost has the lowest bound
6 Conclusions
A mathematical model was proposed for determining thedesign quality level required to achieve the target customersatisfaction for the target market segment with the minimumtotal design cost In the proposed model the customersatisfaction is expressed as a function of the quality level con-sidering the consumer behavior of the targetmarket segmentMoreover the proposedmodel allows theNPD team to set theminimum satisfaction level for each CR andor the fulfilledminimumdesign quality level for eachDRmaking the designprocesses flexible A numerical example was provided todemonstrate the feasibility and applicability of the proposedapproach In future research the relation between customersatisfaction and quality level will be further investigated tomake the proposed model more applicable in the real world
Journal of Applied Mathematics 9
Nomenclature
CR119894 The 119894th customer requirement
DR119895 The 119895th design requirement
119877119894119895 Relational intensity between CR
119894and DR
119895
120574119896119895 Technical correlation between DR
119896and
DR119895
1198771015840
119894119895 Normalized relational intensity between
CR119894and DR
119895in Wassermanrsquos
normalization model119877norm119894119895
Normalized relational intensity betweenCR119894and DR
119895in L-H Chen and C-N
Chenrsquos normalization model119889119894 Original importance weight of CR
119894
120573119894119897 Correlation between CR
119894and CR
119897
119889norm119894
Normalized importance weight of CR119894in
L-H Chen and C-N Chenrsquos integrationmodel when CRsrsquo correlations exist
119908norm119895
Normalized importance weight of DR119895
119862119895 Required cost for DR
119895to fully achieve
customer satisfaction119909119895 Technical fulfillment level for DR
119895
X Design vector containing the fulfillmentlevels of all DRs
DQ(X) Overall design quality level by designvector X
CS(X) Fulfilled customer satisfaction by designvector X
120572 Target design quality level120575 Target customer satisfaction119896 The characteristic parameter to describe
the customer preference of a specificmarket segment for the design qualitylevel of a specific product
120576119894 Minimum required satisfaction level for
CR119894
1199051 Design parameter to determine 120576
119894
120588119895 Minimum fulfilled quality level for DR
119895
1199052 Design parameter to determine 120588
119895
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] L Cohen Quality Function Deployment How to Make QFDWork for You Addison-Wesley Reading Mass USA 1995
[2] L-K Chan and M-L Wu ldquoQuality function deployment aliterature reviewrdquoEuropean Journal of Operational Research vol143 no 3 pp 463ndash497 2002
[3] G S Wasserman ldquoOn how to prioritize design requirementsduring the QFD planning processrdquo IIE Transactions vol 25 no3 pp 59ndash65 1993
[4] K-J Kim ldquoDetermining optimal design characteristic levels inquality function deploymentrdquo Quality Engineering vol 10 no2 pp 295ndash307 1997
[5] HMoskowitz and K-J Kim ldquoQFD optimizer a novice friendlyquality function deployment decision support system for opti-mizing product designsrdquo Computers amp Industrial Engineeringvol 32 no 3 pp 641ndash655 1997
[6] T Park and K-J Kim ldquoDetermination of an optimal setof design requirements using house of qualityrdquo Journal ofOperations Management vol 16 no 5 pp 569ndash581 1998
[7] J Bode and R Y K Fung ldquoCost engineering with qualityfunction deploymentrdquo Computers and Industrial Engineeringvol 35 no 3-4 pp 587ndash590 1998
[8] R G Askin and DW Dawson ldquoMaximizing customer satisfac-tion by optimal specification of engineering characteristicsrdquo IIETransactions (Institute of Industrial Engineers) vol 32 no 1 pp9ndash20 2000
[9] R Y K Fung J Tang Y Tu and D Wang ldquoProduct designresources optimization using a non-linear fuzzy quality func-tion deployment modelrdquo International Journal of ProductionResearch vol 40 no 3 pp 585ndash599 2002
[10] L-H Chen and M-C Weng ldquoA fuzzy model for exploitingquality function deploymentrdquo Mathematical and ComputerModelling vol 38 no 5-6 pp 559ndash570 2003
[11] H Iranmanesh and V Thomson ldquoCompetitive advantage byadjusting design characteristics to satisfy cost targetsrdquo Interna-tional Journal of Production Economics vol 115 no 1 pp 64ndash712008
[12] L-H Chen andW-C Ko ldquoA fuzzy nonlinear model for qualityfunction deployment considering Kanorsquos conceptrdquo Mathemati-cal and Computer Modelling vol 48 no 3-4 pp 581ndash593 2008
[13] L-H Chen and W-C Ko ldquoFuzzy approaches to qualityfunction deployment for new product designrdquo Fuzzy Sets andSystems vol 160 no 18 pp 2620ndash2639 2009
[14] J-H Shin H-B Jun D Kiritsis and P Xirouchakis ldquoA decisionsupport method for product conceptual design consideringproduct lifecycle factors and resource constraintsrdquo InternationalJournal of Advanced Manufacturing Technology vol 52 no 9ndash12 pp 865ndash886 2011
[15] M Braglia G Fantoni andM Frosolini ldquoThe house of reliabil-ityrdquo International Journal of Quality amp Reliability Managementvol 24 no 4 pp 420ndash440 2007
[16] W-C Chiou H-W Kuo and I-Y Lu ldquoA technology orientedproductivity measurement modelrdquo International Journal ofProduction Economics vol 60 pp 69ndash77 1999
[17] P-T Chuang ldquoA QFD approach for distributionrsquos locationmodelrdquo International Journal of Quality and Reliability Manage-ment vol 19 no 8 pp 1037ndash1054 2002
[18] L-H Chen and M-C Weng ldquoAn evaluation approach to engi-neering design inQFDprocesses using fuzzy goal programmingmodelsrdquo European Journal of Operational Research vol 172 no1 pp 230ndash248 2006
[19] E K Delice and Z Gungor ldquoA new mixed integer linearprogramming model for product development using qualityfunction deploymentrdquo Computers amp Industrial Engineering vol57 no 3 pp 906ndash912 2009
[20] E K Delice and Z Gungor ldquoAmixed integer goal programmingmodel for discrete values of design requirements in QFDrdquoInternational Journal of Production Research vol 49 no 10 pp2941ndash2957 2011
[21] F Franceschini and S Rossetto ldquoQFD an interactive algorithmfor the prioritization of productrsquos technical design characteris-ticsrdquo Integrated Manufacturing Systems vol 13 no 1 pp 69ndash752002
10 Journal of Applied Mathematics
[22] C H Han J K Kim S H Choi and S H Kim ldquoDeterminationof information system development priority using quality func-tion deploymentrdquoComputers and Industrial Engineering vol 35no 1-2 pp 241ndash244 1998
[23] E E Karsak ldquoFuzzy multiple objective decision makingapproach to prioritize design requirements in quality functiondeploymentrdquo International Journal of Production Research vol42 no 18 pp 3957ndash3974 2004
[24] X Lai M Xie and K C Tan ldquoDynamic programming for QFDoptimizationrdquoQuality and Reliability Engineering Internationalvol 21 no 8 pp 769ndash780 2005
[25] S-T Liu ldquoRating design requirements in fuzzy quality functiondeployment via a mathematical programming approachrdquo Inter-national Journal of Production Research vol 43 no 3 pp 497ndash513 2005
[26] R Ramanathan and J Yunfeng ldquoIncorporating cost and envi-ronmental factors in quality function deployment using dataenvelopment analysisrdquo Omega vol 37 no 3 pp 711ndash723 2009
[27] H Raharjo M Xie and A C Brombacher ldquoA systematicmethodology to deal with the dynamics of customer needs inQuality Function Deploymentrdquo Expert Systems with Applica-tions vol 38 no 4 pp 3653ndash3662 2011
[28] Y-M Wang and K-S Chin ldquoTechnical importance ratingsin fuzzy QFD by integrating fuzzy normalization and fuzzyweighted averagerdquoComputers ampMathematics with Applicationsvol 62 no 11 pp 4207ndash4221 2011
[29] Y-M Wang ldquoA fuzzy-normalisation-based group decision-making approach for prioritising engineering design require-ments in QFD under uncertaintyrdquo International Journal ofProduction Research vol 50 no 23 pp 6963ndash6977 2012
[30] D Lyman ldquoDeployment normalizationrdquo in Proceedings of theTransactions from the 2nd Symposium on Quality FunctionDeployment pp 307ndash315 Automotive Division of the AmericanSociety for Quality Control The American Supplier Instituteand GOALQPC Dearborn Mich USA 1990
[31] L-H Chen and C-N Chen ldquoNormalisation models for pri-oritising design requirements for quality function deploymentprocessesrdquo International Journal of Production Research vol 52no 2 pp 299ndash313 2014
[32] S Erevelles and C Leavitt ldquoA comparison of current modelsof consumer satisfactiondissatisfactionrdquo Journal of ConsumerSatisfaction Dissatisfaction and Complaining Behavior vol 5pp 104ndash114 1992
[33] M J Morgan J A Attaway and M Griffin ldquoThe role ofproductservice experience in the satisfaction formation pro-cess a test of moderationrdquo Journal of Consumer SatisfactionDissatisfaction and Complaining Behavior vol 9 pp 391ndash4051996
[34] E W Anderson and M W Sullivan ldquoThe antecedents andconsequences of customer satisfaction for firmsrdquo MarketingScience vol 12 no 2 pp 125ndash143 1993
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Journal of Applied Mathematics 5
a concave down function of the perceived quality level of theproduct a linearly transformed function can be expressedas ln120572 = 119896 ln 120575 Using a group of paired estimations (120572
119894 120575119894)
based on the experience and knowledge from the QFD teammembers andor managers of the marketing departmentthe simple regression function ln 120575 = (1119896) ln120572 can beconstructed to determine the 119896 value
The procedure for applying the proposed model is asfollows
Step 1 Determine the desired product to be developed orimproved for the target market segment
Step 2 Construct the corresponding HOQ to reflect therelations between CRs and DRs
Step 3 Integrate the basic design information in the HOQ toobtain the normalized values 119877norm
119894119895 119889norm119894
and 119908norm119895
usingthe normalization model in (2) (and (3) if needed)
Step 4 Considering that 120575 is a concave down function of120572 subjectively determine the value of 119896 for meeting therelationship 120572 = 120575
119896 119896 gt 1 Alternatively collect a groupof paired estimations (120572
119894 120575119894) forall120572119894 120575119894isin [0 1] for the desired
product in the target market segment Decide the parameter119896(gt 1) in ln 120575 = (1119896) ln120572 by applying a simple regressionanalysis
Step 5 Determine the target customer satisfaction 120575 for NPDbased on the targetmarket segment and then obtain the targetdesign quality level 120572 based on 120572 = 120575
119896 using the 119896 valuedetermined in Step 4
Step 6 Let management subjectively decide the values ofparameters 119905
1and 1199052
Step 7 Construct the proposed nonlinear programmingmodel using the integrated information from the HOQobtained in Step 2
Step 8 Solve the model to find the optimal design qualitylevel of each DR so that the target customer satisfaction isachieved for the target market with the minimum budget
5 Numerical Illustration
This section demonstrates the applicability of the proposedapproach using a constructed example of a manufacturerof bicycles Based on this example parameter analyses areprovided to further illustrate the proposed approach
51 Example With rising awareness of environmental pro-tection themunicipal government has encouraged citizens totakemass transportation to workThemarketing departmentof the bicycle firm has observed that an increasing number ofcitizens are willing to bike the short distance between homeand mass transportation stations Therefore the marketingdepartment plans to launch a new bike to cater to this trendFor this plan an important issue for the NPD project team
is to determine the minimum budget needed to achieve themarket goal of the NPD during the design stage
Firstly the newly developed bike is positioned as simpleand easy for biking the short distance between home andmass transportation station and aims to satisfy commutersTheNPD team selects QFD as the design platform In the sec-ond step the HOQ is constructed for specifying the relationsbetween CRs and DRs The following six basic requirementsare identified (1) ride comfort (2) ride safety (3) easyhandling (4) easy movement (5) low maintenance and (6)durability Based on consensus the team members proposenine design requirements that correspond to the six basiccustomer requirementsThe nine design requirements are (1)frame (2) suspension (3) derailleur (4) brake (5) wheels (6)handlebars (7) saddle (8) pedals and (9) total weight Thedegree of relational intensity for the relationship betweenCRsand DRs is defined by weak-moderate-strong the correlationamong CRs or amongDRs is also defined by weak-moderate-strong but allowing for negative correlations Furthermorethe NPD team identifies the CRsrsquo importance degrees for theproduct to emphasize its easy handling and ride safety Thebasic QFD design information for the product is shown inFigure 4
The main work in the third step is to integrate the designinformation into the HOQ to obtain the normalized relationstrengths or weights namely 119877norm
119894119895 119889norm119894
and 119908norm119895
forestablishing the proposed nonlinear programming modelto achieve the marketquality goal at the minimum designcost As described before L-H Chen and C-N Chenrsquosnormalization models (2) and (3) are employed To do thisthe degree of relational or correlation intensity describedas weak-moderate-strong must be numerically scaled Ascommonly used in the literature the rating scale 1-3-9 isemployed for relational intensity that is weak-moderate-strong between CRs and DRs and plusmn(01-03-09) is usedfor correlation that is weak-moderate-strong among CRsor among DRs with negative correlations allowed Figure 5shows the normalized results for the product using the basicdesign information in Figure 4
After the integrated information from the HOQ hasbeen obtained the characteristic parameter 119896 for the marketsegment of commuters should be determined to characterizethe functional curve between customer satisfaction anddesign quality level Based on the experience of themarketingexperts 119896 is set to 2 that is CS(X) = [DQ(X)]12 as shownin Figure 6 Based on the determined function the fifth stepis to set up the target design quality level 120572 From a marketcompetitive analysis the target customer satisfaction is set as120575 = 08 so the target design quality level 120572 is obtained as064 based on the function 120572 = 120575119896 119896 = 2 To formulate theproposed nonlinear programming model for the minimumcost in the sixth step the parameters 119905
1and 1199052should be
determined to specify theminimumsatisfaction level for eachcustomer requirement CR
119894and the minimum design quality
level for each DR119895 The values 119905
1= 3 and 119905
2= 3 are set by the
NPD team in this exampleBased on the settings in the previous steps the pro-
posed nonlinear programming model can be formulated for
6 Journal of Applied Mathematics
movement
Custo
mer
requ
irem
ents
Deg
ree o
f im
port
ance
Design requirements
15
20
25
15
9 points 3 points 1 point
Strong relationModerate relationWeak relationWeak negative relation
Moderate negative relationStrong negative relation
Correlation symbols and values
maintenance
Relation symbols and points
13
12
minus01
minus03
minus09
0103
09
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy
(5) Low
(6) Durability
Figure 4 Basic QFD design information for product
Custo
mer
requ
irem
ents
Design requirements
Nor
mal
ized
CR
impo
rtan
ce w
eigh
t
017
024
028
011
011
011011011011011
013 011 011 013 016
016
011 011 011
015 013 013
013013
015 019 013 004004 003
009 008 023 009
009
011 023 008 005
003 037 008 048
020 017 017 020 008 006 006006
003
003
Normalized DR importance 012 010 015 012 017 014 006 007007weight
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy movement
(5) Low maintenance
(6) Durability
Figure 5 Normalized results for product
the minimum design cost Let the decision variable 119909119895 119895 =
1 2 9 represent the technical fulfillment level of DR119895
The model aims to achieve the target customer satisfaction(120575 = 08) and the target design quality levels (120572 = 064)for the product at the minimum total design cost sum9
119895=1119862119895119909119895
1
1
Custo
mer
satis
fact
ion
Design quality
k = 2
120575
120572
CS(X)
DQ(X)
Figure 6 Functional curve of customer satisfaction for product
where 119862119895denotes the design cost of completely fulfilling the
technical level of DR119895 The nonlinear programming model is
expressed as
Min9
sum
119895=1
119862119895119909119895 (12)
Journal of Applied Mathematics 7
subject to
0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9ge 08
1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099ge 9 times 064
1
9(1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099)
minus (0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9)2
ge 0
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 051
0151199091+ 013119909
2+ 013119909
3+ 015119909
4+ 019119909
5
+ 0131199096+ 004119909
7+ 004119909
8+ 003119909
9ge 072
0091199091+ 008119909
2+ 023119909
3+ 009119909
4+ 011119909
5
+ 0231199096+ 008119909
7+ 003119909
8+ 005119909
9ge 084
0031199091+ 000119909
2+ 003119909
3+ 000119909
4+ 037119909
5
+ 0081199096+ 000119909
7+ 000119909
8+ 048119909
9ge 033
0201199091+ 017119909
2+ 017119909
3+ 020119909
4+ 008119909
5
+ 0061199096+ 006119909
7+ 006119909
8+ 000119909
9ge 033
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 027
023 le 1199091le 1
019 le 1199092le 1
029 le 1199093le 1
023 le 1199094le 1
033 le 1199095le 1
027 le 1199096le 1
013 le 1199097le 1
012 le 1199098le 1
013 le 1199099le 1
(13)
DRj
Cj 220 250 280 200 260 130 80 50 30
Unit $ thousand
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 7 Completely fulfilled design cost 119862119895for DR
119895
1 1 1 1 1 1
Targ
eted
CS
Fulfi
lled
DQ
k MinΣCjxj
20 080 081 023 019 086 1091
x1 x2 x3 x4 x5 x6 x8x7 x9
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 8 Optimal technical fulfillments for product
To solve the model the design cost 119862119895for DR
119895must
be determined beforehand For this example the costs areprovided by the NPD team as shown in Figure 7 Theproposed nonlinear model can be solved using commercialsoftware such as LINGO 110 Figure 8 summarizes the opti-mal technical fulfillment level 119909
119895for eachDR
119895Theminimum
total design cost for the product is $1091000 The figureindicates that the target customer satisfaction can be achievedat CS(X) = sum
9
119895=1119908
norm119895
sdot 119909119895= 08 The fulfilled design
quality level is determined as DQ(X) = (19)sum9119895=1119909119895= 081
which is greater than 120572(= 064) satisfying constraint (7b)The solutions obtained in Figure 8 satisfy the requirementsof the new product for the target customer satisfaction at theminimum total design cost
52 Parameter Analyses The proposed nonlinear program-ming model includes three design parameters namely 1198961199051 and 119905
2 that are specified by the NPD team These three
parameters affect the design quality level and thereforethe total design cost The influence of the combination ofdifferent values of 119896 119905
1 and 119905
2on the total design costwas thus
examined In the analyses the target customer satisfaction120575 was set at 06 07 and 08 respectively The results of theanalyses are summarized below
(1) The parameter 119896 characterizes the customer satisfac-tion of the design quality level The larger the valueof 119896 is the more attractive to customers the productquality level is With a larger 119896 the target customersatisfaction can be achieved using only the lowerlevel of product design quality and therefore the totaldesign cost is lower As a demonstration with 119905
1and
1199052fixed at 3 Figure 9 shows that the total design cost
8 Journal of Applied Mathematics
1093
1091
1088
1090
1088
1084
1087
1085
1083
1080
1085
1090
1095
Tota
l des
ign
cost
k = 15 k = 2 k = 3
120575 = 08
120575 = 07
120575 = 06
at (t1 t2) = (3 3)
Figure 9 Variation of total design cost with 119896 for various 120575 values
1076 1076 1076
1091
889 889897
1088
717 717
852
1085
600
900
1200
1500
Tota
l des
ign
cost
at (k t2) = (2 3)
t1 = 0 t1 = 2 t1 = 25 t1 = 3 t1 = 35
120575 = 08
120575 = 07
120575 = 06
1469
Figure 10 Variation of total design cost with 1199051for various 120575 values
decreases with increasing 119896 value regardless of thetarget customer satisfaction 120575
(2) The 1199051and 1199052values in (7e) and (7g) affect the mini-
mum satisfaction level for each customer requirementCR119894and the fulfilled minimum design quality level
for each DR119895 respectively and therefore affect the
total design cost Larger values of 1199051andor 119905
2increase
the total design cost With 119896 = 2 and 1199052= 3
Figure 10 shows the impact of the 1199051value on the total
design cost The total design cost remains unchangedin a range of 119905
1values that depends on 120575 because
the fulfilled minimum design quality level 120588119895at 1199052= 3
confines the influence of the minimum satisfactionlevel 120576
119894on the total design cost at some levels of 119905
1
regardless of the target customer satisfaction level120575 It is also noted that if the 119905
1value is sufficiently
large (1199051= 35) and 119905
2= 3 the total design cost
is the same (1469) for all three levels of the target
1079
1084
1091
1099
1108
1083
1088
10931097
10821085
1088
1093
1075
1085
1095
1105
1115
Tota
l des
ign
cost
at (k t1) = (2 3)
t2 = 0 t2 = 15 t2 = 3 t2 = 45 t2 = 6
120575 = 08
120575 = 07
120575 = 06
Figure 11 Variation of total design cost with 1199052for various 120575 values
customer satisfaction since the aggregated resultsfrom the required minimum satisfaction level foreach customer requirement CR
119894surpass each target
customer satisfaction The high required minimumsatisfaction level due to 119905
1= 35 resulted in the largest
total design cost With 119896 = 2 and 1199051= 3 the total
design cost changes with 1199052 as shown in Figure 11
(3) From a design viewpoint if theminimum satisfactionlevel for each customer requirement CR
119894and the
fulfilled minimum design quality level for each DR119895
are not required that is 1199051and 1199052are fixed at 0 the
minimal total design cost can be obtained from theproposed model (7) at each setting of the targetedcustomer satisfaction level 120575 For example with 119905
1=
1199052= 0 and 120575 = 06 07 and 08 respectively the
total design costs are 700 878 and 1063 respectivelyregardless of the 119896 valueThis indicates that to achievethe target degree of customer satisfaction for a certainmarket segment the investment amount of the totaldesign cost has the lowest bound
6 Conclusions
A mathematical model was proposed for determining thedesign quality level required to achieve the target customersatisfaction for the target market segment with the minimumtotal design cost In the proposed model the customersatisfaction is expressed as a function of the quality level con-sidering the consumer behavior of the targetmarket segmentMoreover the proposedmodel allows theNPD team to set theminimum satisfaction level for each CR andor the fulfilledminimumdesign quality level for eachDRmaking the designprocesses flexible A numerical example was provided todemonstrate the feasibility and applicability of the proposedapproach In future research the relation between customersatisfaction and quality level will be further investigated tomake the proposed model more applicable in the real world
Journal of Applied Mathematics 9
Nomenclature
CR119894 The 119894th customer requirement
DR119895 The 119895th design requirement
119877119894119895 Relational intensity between CR
119894and DR
119895
120574119896119895 Technical correlation between DR
119896and
DR119895
1198771015840
119894119895 Normalized relational intensity between
CR119894and DR
119895in Wassermanrsquos
normalization model119877norm119894119895
Normalized relational intensity betweenCR119894and DR
119895in L-H Chen and C-N
Chenrsquos normalization model119889119894 Original importance weight of CR
119894
120573119894119897 Correlation between CR
119894and CR
119897
119889norm119894
Normalized importance weight of CR119894in
L-H Chen and C-N Chenrsquos integrationmodel when CRsrsquo correlations exist
119908norm119895
Normalized importance weight of DR119895
119862119895 Required cost for DR
119895to fully achieve
customer satisfaction119909119895 Technical fulfillment level for DR
119895
X Design vector containing the fulfillmentlevels of all DRs
DQ(X) Overall design quality level by designvector X
CS(X) Fulfilled customer satisfaction by designvector X
120572 Target design quality level120575 Target customer satisfaction119896 The characteristic parameter to describe
the customer preference of a specificmarket segment for the design qualitylevel of a specific product
120576119894 Minimum required satisfaction level for
CR119894
1199051 Design parameter to determine 120576
119894
120588119895 Minimum fulfilled quality level for DR
119895
1199052 Design parameter to determine 120588
119895
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] L Cohen Quality Function Deployment How to Make QFDWork for You Addison-Wesley Reading Mass USA 1995
[2] L-K Chan and M-L Wu ldquoQuality function deployment aliterature reviewrdquoEuropean Journal of Operational Research vol143 no 3 pp 463ndash497 2002
[3] G S Wasserman ldquoOn how to prioritize design requirementsduring the QFD planning processrdquo IIE Transactions vol 25 no3 pp 59ndash65 1993
[4] K-J Kim ldquoDetermining optimal design characteristic levels inquality function deploymentrdquo Quality Engineering vol 10 no2 pp 295ndash307 1997
[5] HMoskowitz and K-J Kim ldquoQFD optimizer a novice friendlyquality function deployment decision support system for opti-mizing product designsrdquo Computers amp Industrial Engineeringvol 32 no 3 pp 641ndash655 1997
[6] T Park and K-J Kim ldquoDetermination of an optimal setof design requirements using house of qualityrdquo Journal ofOperations Management vol 16 no 5 pp 569ndash581 1998
[7] J Bode and R Y K Fung ldquoCost engineering with qualityfunction deploymentrdquo Computers and Industrial Engineeringvol 35 no 3-4 pp 587ndash590 1998
[8] R G Askin and DW Dawson ldquoMaximizing customer satisfac-tion by optimal specification of engineering characteristicsrdquo IIETransactions (Institute of Industrial Engineers) vol 32 no 1 pp9ndash20 2000
[9] R Y K Fung J Tang Y Tu and D Wang ldquoProduct designresources optimization using a non-linear fuzzy quality func-tion deployment modelrdquo International Journal of ProductionResearch vol 40 no 3 pp 585ndash599 2002
[10] L-H Chen and M-C Weng ldquoA fuzzy model for exploitingquality function deploymentrdquo Mathematical and ComputerModelling vol 38 no 5-6 pp 559ndash570 2003
[11] H Iranmanesh and V Thomson ldquoCompetitive advantage byadjusting design characteristics to satisfy cost targetsrdquo Interna-tional Journal of Production Economics vol 115 no 1 pp 64ndash712008
[12] L-H Chen andW-C Ko ldquoA fuzzy nonlinear model for qualityfunction deployment considering Kanorsquos conceptrdquo Mathemati-cal and Computer Modelling vol 48 no 3-4 pp 581ndash593 2008
[13] L-H Chen and W-C Ko ldquoFuzzy approaches to qualityfunction deployment for new product designrdquo Fuzzy Sets andSystems vol 160 no 18 pp 2620ndash2639 2009
[14] J-H Shin H-B Jun D Kiritsis and P Xirouchakis ldquoA decisionsupport method for product conceptual design consideringproduct lifecycle factors and resource constraintsrdquo InternationalJournal of Advanced Manufacturing Technology vol 52 no 9ndash12 pp 865ndash886 2011
[15] M Braglia G Fantoni andM Frosolini ldquoThe house of reliabil-ityrdquo International Journal of Quality amp Reliability Managementvol 24 no 4 pp 420ndash440 2007
[16] W-C Chiou H-W Kuo and I-Y Lu ldquoA technology orientedproductivity measurement modelrdquo International Journal ofProduction Economics vol 60 pp 69ndash77 1999
[17] P-T Chuang ldquoA QFD approach for distributionrsquos locationmodelrdquo International Journal of Quality and Reliability Manage-ment vol 19 no 8 pp 1037ndash1054 2002
[18] L-H Chen and M-C Weng ldquoAn evaluation approach to engi-neering design inQFDprocesses using fuzzy goal programmingmodelsrdquo European Journal of Operational Research vol 172 no1 pp 230ndash248 2006
[19] E K Delice and Z Gungor ldquoA new mixed integer linearprogramming model for product development using qualityfunction deploymentrdquo Computers amp Industrial Engineering vol57 no 3 pp 906ndash912 2009
[20] E K Delice and Z Gungor ldquoAmixed integer goal programmingmodel for discrete values of design requirements in QFDrdquoInternational Journal of Production Research vol 49 no 10 pp2941ndash2957 2011
[21] F Franceschini and S Rossetto ldquoQFD an interactive algorithmfor the prioritization of productrsquos technical design characteris-ticsrdquo Integrated Manufacturing Systems vol 13 no 1 pp 69ndash752002
10 Journal of Applied Mathematics
[22] C H Han J K Kim S H Choi and S H Kim ldquoDeterminationof information system development priority using quality func-tion deploymentrdquoComputers and Industrial Engineering vol 35no 1-2 pp 241ndash244 1998
[23] E E Karsak ldquoFuzzy multiple objective decision makingapproach to prioritize design requirements in quality functiondeploymentrdquo International Journal of Production Research vol42 no 18 pp 3957ndash3974 2004
[24] X Lai M Xie and K C Tan ldquoDynamic programming for QFDoptimizationrdquoQuality and Reliability Engineering Internationalvol 21 no 8 pp 769ndash780 2005
[25] S-T Liu ldquoRating design requirements in fuzzy quality functiondeployment via a mathematical programming approachrdquo Inter-national Journal of Production Research vol 43 no 3 pp 497ndash513 2005
[26] R Ramanathan and J Yunfeng ldquoIncorporating cost and envi-ronmental factors in quality function deployment using dataenvelopment analysisrdquo Omega vol 37 no 3 pp 711ndash723 2009
[27] H Raharjo M Xie and A C Brombacher ldquoA systematicmethodology to deal with the dynamics of customer needs inQuality Function Deploymentrdquo Expert Systems with Applica-tions vol 38 no 4 pp 3653ndash3662 2011
[28] Y-M Wang and K-S Chin ldquoTechnical importance ratingsin fuzzy QFD by integrating fuzzy normalization and fuzzyweighted averagerdquoComputers ampMathematics with Applicationsvol 62 no 11 pp 4207ndash4221 2011
[29] Y-M Wang ldquoA fuzzy-normalisation-based group decision-making approach for prioritising engineering design require-ments in QFD under uncertaintyrdquo International Journal ofProduction Research vol 50 no 23 pp 6963ndash6977 2012
[30] D Lyman ldquoDeployment normalizationrdquo in Proceedings of theTransactions from the 2nd Symposium on Quality FunctionDeployment pp 307ndash315 Automotive Division of the AmericanSociety for Quality Control The American Supplier Instituteand GOALQPC Dearborn Mich USA 1990
[31] L-H Chen and C-N Chen ldquoNormalisation models for pri-oritising design requirements for quality function deploymentprocessesrdquo International Journal of Production Research vol 52no 2 pp 299ndash313 2014
[32] S Erevelles and C Leavitt ldquoA comparison of current modelsof consumer satisfactiondissatisfactionrdquo Journal of ConsumerSatisfaction Dissatisfaction and Complaining Behavior vol 5pp 104ndash114 1992
[33] M J Morgan J A Attaway and M Griffin ldquoThe role ofproductservice experience in the satisfaction formation pro-cess a test of moderationrdquo Journal of Consumer SatisfactionDissatisfaction and Complaining Behavior vol 9 pp 391ndash4051996
[34] E W Anderson and M W Sullivan ldquoThe antecedents andconsequences of customer satisfaction for firmsrdquo MarketingScience vol 12 no 2 pp 125ndash143 1993
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
6 Journal of Applied Mathematics
movement
Custo
mer
requ
irem
ents
Deg
ree o
f im
port
ance
Design requirements
15
20
25
15
9 points 3 points 1 point
Strong relationModerate relationWeak relationWeak negative relation
Moderate negative relationStrong negative relation
Correlation symbols and values
maintenance
Relation symbols and points
13
12
minus01
minus03
minus09
0103
09
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy
(5) Low
(6) Durability
Figure 4 Basic QFD design information for product
Custo
mer
requ
irem
ents
Design requirements
Nor
mal
ized
CR
impo
rtan
ce w
eigh
t
017
024
028
011
011
011011011011011
013 011 011 013 016
016
011 011 011
015 013 013
013013
015 019 013 004004 003
009 008 023 009
009
011 023 008 005
003 037 008 048
020 017 017 020 008 006 006006
003
003
Normalized DR importance 012 010 015 012 017 014 006 007007weight
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
(1) Ride comfort
(2) Ride safety
(3) Easy handling
(4) Easy movement
(5) Low maintenance
(6) Durability
Figure 5 Normalized results for product
the minimum design cost Let the decision variable 119909119895 119895 =
1 2 9 represent the technical fulfillment level of DR119895
The model aims to achieve the target customer satisfaction(120575 = 08) and the target design quality levels (120572 = 064)for the product at the minimum total design cost sum9
119895=1119862119895119909119895
1
1
Custo
mer
satis
fact
ion
Design quality
k = 2
120575
120572
CS(X)
DQ(X)
Figure 6 Functional curve of customer satisfaction for product
where 119862119895denotes the design cost of completely fulfilling the
technical level of DR119895 The nonlinear programming model is
expressed as
Min9
sum
119895=1
119862119895119909119895 (12)
Journal of Applied Mathematics 7
subject to
0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9ge 08
1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099ge 9 times 064
1
9(1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099)
minus (0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9)2
ge 0
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 051
0151199091+ 013119909
2+ 013119909
3+ 015119909
4+ 019119909
5
+ 0131199096+ 004119909
7+ 004119909
8+ 003119909
9ge 072
0091199091+ 008119909
2+ 023119909
3+ 009119909
4+ 011119909
5
+ 0231199096+ 008119909
7+ 003119909
8+ 005119909
9ge 084
0031199091+ 000119909
2+ 003119909
3+ 000119909
4+ 037119909
5
+ 0081199096+ 000119909
7+ 000119909
8+ 048119909
9ge 033
0201199091+ 017119909
2+ 017119909
3+ 020119909
4+ 008119909
5
+ 0061199096+ 006119909
7+ 006119909
8+ 000119909
9ge 033
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 027
023 le 1199091le 1
019 le 1199092le 1
029 le 1199093le 1
023 le 1199094le 1
033 le 1199095le 1
027 le 1199096le 1
013 le 1199097le 1
012 le 1199098le 1
013 le 1199099le 1
(13)
DRj
Cj 220 250 280 200 260 130 80 50 30
Unit $ thousand
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 7 Completely fulfilled design cost 119862119895for DR
119895
1 1 1 1 1 1
Targ
eted
CS
Fulfi
lled
DQ
k MinΣCjxj
20 080 081 023 019 086 1091
x1 x2 x3 x4 x5 x6 x8x7 x9
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 8 Optimal technical fulfillments for product
To solve the model the design cost 119862119895for DR
119895must
be determined beforehand For this example the costs areprovided by the NPD team as shown in Figure 7 Theproposed nonlinear model can be solved using commercialsoftware such as LINGO 110 Figure 8 summarizes the opti-mal technical fulfillment level 119909
119895for eachDR
119895Theminimum
total design cost for the product is $1091000 The figureindicates that the target customer satisfaction can be achievedat CS(X) = sum
9
119895=1119908
norm119895
sdot 119909119895= 08 The fulfilled design
quality level is determined as DQ(X) = (19)sum9119895=1119909119895= 081
which is greater than 120572(= 064) satisfying constraint (7b)The solutions obtained in Figure 8 satisfy the requirementsof the new product for the target customer satisfaction at theminimum total design cost
52 Parameter Analyses The proposed nonlinear program-ming model includes three design parameters namely 1198961199051 and 119905
2 that are specified by the NPD team These three
parameters affect the design quality level and thereforethe total design cost The influence of the combination ofdifferent values of 119896 119905
1 and 119905
2on the total design costwas thus
examined In the analyses the target customer satisfaction120575 was set at 06 07 and 08 respectively The results of theanalyses are summarized below
(1) The parameter 119896 characterizes the customer satisfac-tion of the design quality level The larger the valueof 119896 is the more attractive to customers the productquality level is With a larger 119896 the target customersatisfaction can be achieved using only the lowerlevel of product design quality and therefore the totaldesign cost is lower As a demonstration with 119905
1and
1199052fixed at 3 Figure 9 shows that the total design cost
8 Journal of Applied Mathematics
1093
1091
1088
1090
1088
1084
1087
1085
1083
1080
1085
1090
1095
Tota
l des
ign
cost
k = 15 k = 2 k = 3
120575 = 08
120575 = 07
120575 = 06
at (t1 t2) = (3 3)
Figure 9 Variation of total design cost with 119896 for various 120575 values
1076 1076 1076
1091
889 889897
1088
717 717
852
1085
600
900
1200
1500
Tota
l des
ign
cost
at (k t2) = (2 3)
t1 = 0 t1 = 2 t1 = 25 t1 = 3 t1 = 35
120575 = 08
120575 = 07
120575 = 06
1469
Figure 10 Variation of total design cost with 1199051for various 120575 values
decreases with increasing 119896 value regardless of thetarget customer satisfaction 120575
(2) The 1199051and 1199052values in (7e) and (7g) affect the mini-
mum satisfaction level for each customer requirementCR119894and the fulfilled minimum design quality level
for each DR119895 respectively and therefore affect the
total design cost Larger values of 1199051andor 119905
2increase
the total design cost With 119896 = 2 and 1199052= 3
Figure 10 shows the impact of the 1199051value on the total
design cost The total design cost remains unchangedin a range of 119905
1values that depends on 120575 because
the fulfilled minimum design quality level 120588119895at 1199052= 3
confines the influence of the minimum satisfactionlevel 120576
119894on the total design cost at some levels of 119905
1
regardless of the target customer satisfaction level120575 It is also noted that if the 119905
1value is sufficiently
large (1199051= 35) and 119905
2= 3 the total design cost
is the same (1469) for all three levels of the target
1079
1084
1091
1099
1108
1083
1088
10931097
10821085
1088
1093
1075
1085
1095
1105
1115
Tota
l des
ign
cost
at (k t1) = (2 3)
t2 = 0 t2 = 15 t2 = 3 t2 = 45 t2 = 6
120575 = 08
120575 = 07
120575 = 06
Figure 11 Variation of total design cost with 1199052for various 120575 values
customer satisfaction since the aggregated resultsfrom the required minimum satisfaction level foreach customer requirement CR
119894surpass each target
customer satisfaction The high required minimumsatisfaction level due to 119905
1= 35 resulted in the largest
total design cost With 119896 = 2 and 1199051= 3 the total
design cost changes with 1199052 as shown in Figure 11
(3) From a design viewpoint if theminimum satisfactionlevel for each customer requirement CR
119894and the
fulfilled minimum design quality level for each DR119895
are not required that is 1199051and 1199052are fixed at 0 the
minimal total design cost can be obtained from theproposed model (7) at each setting of the targetedcustomer satisfaction level 120575 For example with 119905
1=
1199052= 0 and 120575 = 06 07 and 08 respectively the
total design costs are 700 878 and 1063 respectivelyregardless of the 119896 valueThis indicates that to achievethe target degree of customer satisfaction for a certainmarket segment the investment amount of the totaldesign cost has the lowest bound
6 Conclusions
A mathematical model was proposed for determining thedesign quality level required to achieve the target customersatisfaction for the target market segment with the minimumtotal design cost In the proposed model the customersatisfaction is expressed as a function of the quality level con-sidering the consumer behavior of the targetmarket segmentMoreover the proposedmodel allows theNPD team to set theminimum satisfaction level for each CR andor the fulfilledminimumdesign quality level for eachDRmaking the designprocesses flexible A numerical example was provided todemonstrate the feasibility and applicability of the proposedapproach In future research the relation between customersatisfaction and quality level will be further investigated tomake the proposed model more applicable in the real world
Journal of Applied Mathematics 9
Nomenclature
CR119894 The 119894th customer requirement
DR119895 The 119895th design requirement
119877119894119895 Relational intensity between CR
119894and DR
119895
120574119896119895 Technical correlation between DR
119896and
DR119895
1198771015840
119894119895 Normalized relational intensity between
CR119894and DR
119895in Wassermanrsquos
normalization model119877norm119894119895
Normalized relational intensity betweenCR119894and DR
119895in L-H Chen and C-N
Chenrsquos normalization model119889119894 Original importance weight of CR
119894
120573119894119897 Correlation between CR
119894and CR
119897
119889norm119894
Normalized importance weight of CR119894in
L-H Chen and C-N Chenrsquos integrationmodel when CRsrsquo correlations exist
119908norm119895
Normalized importance weight of DR119895
119862119895 Required cost for DR
119895to fully achieve
customer satisfaction119909119895 Technical fulfillment level for DR
119895
X Design vector containing the fulfillmentlevels of all DRs
DQ(X) Overall design quality level by designvector X
CS(X) Fulfilled customer satisfaction by designvector X
120572 Target design quality level120575 Target customer satisfaction119896 The characteristic parameter to describe
the customer preference of a specificmarket segment for the design qualitylevel of a specific product
120576119894 Minimum required satisfaction level for
CR119894
1199051 Design parameter to determine 120576
119894
120588119895 Minimum fulfilled quality level for DR
119895
1199052 Design parameter to determine 120588
119895
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] L Cohen Quality Function Deployment How to Make QFDWork for You Addison-Wesley Reading Mass USA 1995
[2] L-K Chan and M-L Wu ldquoQuality function deployment aliterature reviewrdquoEuropean Journal of Operational Research vol143 no 3 pp 463ndash497 2002
[3] G S Wasserman ldquoOn how to prioritize design requirementsduring the QFD planning processrdquo IIE Transactions vol 25 no3 pp 59ndash65 1993
[4] K-J Kim ldquoDetermining optimal design characteristic levels inquality function deploymentrdquo Quality Engineering vol 10 no2 pp 295ndash307 1997
[5] HMoskowitz and K-J Kim ldquoQFD optimizer a novice friendlyquality function deployment decision support system for opti-mizing product designsrdquo Computers amp Industrial Engineeringvol 32 no 3 pp 641ndash655 1997
[6] T Park and K-J Kim ldquoDetermination of an optimal setof design requirements using house of qualityrdquo Journal ofOperations Management vol 16 no 5 pp 569ndash581 1998
[7] J Bode and R Y K Fung ldquoCost engineering with qualityfunction deploymentrdquo Computers and Industrial Engineeringvol 35 no 3-4 pp 587ndash590 1998
[8] R G Askin and DW Dawson ldquoMaximizing customer satisfac-tion by optimal specification of engineering characteristicsrdquo IIETransactions (Institute of Industrial Engineers) vol 32 no 1 pp9ndash20 2000
[9] R Y K Fung J Tang Y Tu and D Wang ldquoProduct designresources optimization using a non-linear fuzzy quality func-tion deployment modelrdquo International Journal of ProductionResearch vol 40 no 3 pp 585ndash599 2002
[10] L-H Chen and M-C Weng ldquoA fuzzy model for exploitingquality function deploymentrdquo Mathematical and ComputerModelling vol 38 no 5-6 pp 559ndash570 2003
[11] H Iranmanesh and V Thomson ldquoCompetitive advantage byadjusting design characteristics to satisfy cost targetsrdquo Interna-tional Journal of Production Economics vol 115 no 1 pp 64ndash712008
[12] L-H Chen andW-C Ko ldquoA fuzzy nonlinear model for qualityfunction deployment considering Kanorsquos conceptrdquo Mathemati-cal and Computer Modelling vol 48 no 3-4 pp 581ndash593 2008
[13] L-H Chen and W-C Ko ldquoFuzzy approaches to qualityfunction deployment for new product designrdquo Fuzzy Sets andSystems vol 160 no 18 pp 2620ndash2639 2009
[14] J-H Shin H-B Jun D Kiritsis and P Xirouchakis ldquoA decisionsupport method for product conceptual design consideringproduct lifecycle factors and resource constraintsrdquo InternationalJournal of Advanced Manufacturing Technology vol 52 no 9ndash12 pp 865ndash886 2011
[15] M Braglia G Fantoni andM Frosolini ldquoThe house of reliabil-ityrdquo International Journal of Quality amp Reliability Managementvol 24 no 4 pp 420ndash440 2007
[16] W-C Chiou H-W Kuo and I-Y Lu ldquoA technology orientedproductivity measurement modelrdquo International Journal ofProduction Economics vol 60 pp 69ndash77 1999
[17] P-T Chuang ldquoA QFD approach for distributionrsquos locationmodelrdquo International Journal of Quality and Reliability Manage-ment vol 19 no 8 pp 1037ndash1054 2002
[18] L-H Chen and M-C Weng ldquoAn evaluation approach to engi-neering design inQFDprocesses using fuzzy goal programmingmodelsrdquo European Journal of Operational Research vol 172 no1 pp 230ndash248 2006
[19] E K Delice and Z Gungor ldquoA new mixed integer linearprogramming model for product development using qualityfunction deploymentrdquo Computers amp Industrial Engineering vol57 no 3 pp 906ndash912 2009
[20] E K Delice and Z Gungor ldquoAmixed integer goal programmingmodel for discrete values of design requirements in QFDrdquoInternational Journal of Production Research vol 49 no 10 pp2941ndash2957 2011
[21] F Franceschini and S Rossetto ldquoQFD an interactive algorithmfor the prioritization of productrsquos technical design characteris-ticsrdquo Integrated Manufacturing Systems vol 13 no 1 pp 69ndash752002
10 Journal of Applied Mathematics
[22] C H Han J K Kim S H Choi and S H Kim ldquoDeterminationof information system development priority using quality func-tion deploymentrdquoComputers and Industrial Engineering vol 35no 1-2 pp 241ndash244 1998
[23] E E Karsak ldquoFuzzy multiple objective decision makingapproach to prioritize design requirements in quality functiondeploymentrdquo International Journal of Production Research vol42 no 18 pp 3957ndash3974 2004
[24] X Lai M Xie and K C Tan ldquoDynamic programming for QFDoptimizationrdquoQuality and Reliability Engineering Internationalvol 21 no 8 pp 769ndash780 2005
[25] S-T Liu ldquoRating design requirements in fuzzy quality functiondeployment via a mathematical programming approachrdquo Inter-national Journal of Production Research vol 43 no 3 pp 497ndash513 2005
[26] R Ramanathan and J Yunfeng ldquoIncorporating cost and envi-ronmental factors in quality function deployment using dataenvelopment analysisrdquo Omega vol 37 no 3 pp 711ndash723 2009
[27] H Raharjo M Xie and A C Brombacher ldquoA systematicmethodology to deal with the dynamics of customer needs inQuality Function Deploymentrdquo Expert Systems with Applica-tions vol 38 no 4 pp 3653ndash3662 2011
[28] Y-M Wang and K-S Chin ldquoTechnical importance ratingsin fuzzy QFD by integrating fuzzy normalization and fuzzyweighted averagerdquoComputers ampMathematics with Applicationsvol 62 no 11 pp 4207ndash4221 2011
[29] Y-M Wang ldquoA fuzzy-normalisation-based group decision-making approach for prioritising engineering design require-ments in QFD under uncertaintyrdquo International Journal ofProduction Research vol 50 no 23 pp 6963ndash6977 2012
[30] D Lyman ldquoDeployment normalizationrdquo in Proceedings of theTransactions from the 2nd Symposium on Quality FunctionDeployment pp 307ndash315 Automotive Division of the AmericanSociety for Quality Control The American Supplier Instituteand GOALQPC Dearborn Mich USA 1990
[31] L-H Chen and C-N Chen ldquoNormalisation models for pri-oritising design requirements for quality function deploymentprocessesrdquo International Journal of Production Research vol 52no 2 pp 299ndash313 2014
[32] S Erevelles and C Leavitt ldquoA comparison of current modelsof consumer satisfactiondissatisfactionrdquo Journal of ConsumerSatisfaction Dissatisfaction and Complaining Behavior vol 5pp 104ndash114 1992
[33] M J Morgan J A Attaway and M Griffin ldquoThe role ofproductservice experience in the satisfaction formation pro-cess a test of moderationrdquo Journal of Consumer SatisfactionDissatisfaction and Complaining Behavior vol 9 pp 391ndash4051996
[34] E W Anderson and M W Sullivan ldquoThe antecedents andconsequences of customer satisfaction for firmsrdquo MarketingScience vol 12 no 2 pp 125ndash143 1993
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Journal of Applied Mathematics 7
subject to
0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9ge 08
1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099ge 9 times 064
1
9(1199091+ 1199092+ 1199093+ 1199094+ 1199095+ 1199096+ 1199097+ 1199098+ 1199099)
minus (0121199091+ 010119909
2+ 015119909
3+ 012119909
4+ 017119909
5
+ 0141199096+ 007119909
7+ 006119909
8+ 007119909
9)2
ge 0
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 051
0151199091+ 013119909
2+ 013119909
3+ 015119909
4+ 019119909
5
+ 0131199096+ 004119909
7+ 004119909
8+ 003119909
9ge 072
0091199091+ 008119909
2+ 023119909
3+ 009119909
4+ 011119909
5
+ 0231199096+ 008119909
7+ 003119909
8+ 005119909
9ge 084
0031199091+ 000119909
2+ 003119909
3+ 000119909
4+ 037119909
5
+ 0081199096+ 000119909
7+ 000119909
8+ 048119909
9ge 033
0201199091+ 017119909
2+ 017119909
3+ 020119909
4+ 008119909
5
+ 0061199096+ 006119909
7+ 006119909
8+ 000119909
9ge 033
0131199091+ 011119909
2+ 011119909
3+ 013119909
4+ 016119909
5
+ 0111199096+ 011119909
7+ 011119909
8+ 000119909
9ge 027
023 le 1199091le 1
019 le 1199092le 1
029 le 1199093le 1
023 le 1199094le 1
033 le 1199095le 1
027 le 1199096le 1
013 le 1199097le 1
012 le 1199098le 1
013 le 1199099le 1
(13)
DRj
Cj 220 250 280 200 260 130 80 50 30
Unit $ thousand
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 7 Completely fulfilled design cost 119862119895for DR
119895
1 1 1 1 1 1
Targ
eted
CS
Fulfi
lled
DQ
k MinΣCjxj
20 080 081 023 019 086 1091
x1 x2 x3 x4 x5 x6 x8x7 x9
(1) F
ram
e
(2) S
uspe
nsio
n
(3) D
erai
lleur
(4) B
rake
(5) W
heel
s
(6) H
andl
ebar
s
(7) S
addl
e
(8) P
edal
s
(9) T
otal
wei
ght
Figure 8 Optimal technical fulfillments for product
To solve the model the design cost 119862119895for DR
119895must
be determined beforehand For this example the costs areprovided by the NPD team as shown in Figure 7 Theproposed nonlinear model can be solved using commercialsoftware such as LINGO 110 Figure 8 summarizes the opti-mal technical fulfillment level 119909
119895for eachDR
119895Theminimum
total design cost for the product is $1091000 The figureindicates that the target customer satisfaction can be achievedat CS(X) = sum
9
119895=1119908
norm119895
sdot 119909119895= 08 The fulfilled design
quality level is determined as DQ(X) = (19)sum9119895=1119909119895= 081
which is greater than 120572(= 064) satisfying constraint (7b)The solutions obtained in Figure 8 satisfy the requirementsof the new product for the target customer satisfaction at theminimum total design cost
52 Parameter Analyses The proposed nonlinear program-ming model includes three design parameters namely 1198961199051 and 119905
2 that are specified by the NPD team These three
parameters affect the design quality level and thereforethe total design cost The influence of the combination ofdifferent values of 119896 119905
1 and 119905
2on the total design costwas thus
examined In the analyses the target customer satisfaction120575 was set at 06 07 and 08 respectively The results of theanalyses are summarized below
(1) The parameter 119896 characterizes the customer satisfac-tion of the design quality level The larger the valueof 119896 is the more attractive to customers the productquality level is With a larger 119896 the target customersatisfaction can be achieved using only the lowerlevel of product design quality and therefore the totaldesign cost is lower As a demonstration with 119905
1and
1199052fixed at 3 Figure 9 shows that the total design cost
8 Journal of Applied Mathematics
1093
1091
1088
1090
1088
1084
1087
1085
1083
1080
1085
1090
1095
Tota
l des
ign
cost
k = 15 k = 2 k = 3
120575 = 08
120575 = 07
120575 = 06
at (t1 t2) = (3 3)
Figure 9 Variation of total design cost with 119896 for various 120575 values
1076 1076 1076
1091
889 889897
1088
717 717
852
1085
600
900
1200
1500
Tota
l des
ign
cost
at (k t2) = (2 3)
t1 = 0 t1 = 2 t1 = 25 t1 = 3 t1 = 35
120575 = 08
120575 = 07
120575 = 06
1469
Figure 10 Variation of total design cost with 1199051for various 120575 values
decreases with increasing 119896 value regardless of thetarget customer satisfaction 120575
(2) The 1199051and 1199052values in (7e) and (7g) affect the mini-
mum satisfaction level for each customer requirementCR119894and the fulfilled minimum design quality level
for each DR119895 respectively and therefore affect the
total design cost Larger values of 1199051andor 119905
2increase
the total design cost With 119896 = 2 and 1199052= 3
Figure 10 shows the impact of the 1199051value on the total
design cost The total design cost remains unchangedin a range of 119905
1values that depends on 120575 because
the fulfilled minimum design quality level 120588119895at 1199052= 3
confines the influence of the minimum satisfactionlevel 120576
119894on the total design cost at some levels of 119905
1
regardless of the target customer satisfaction level120575 It is also noted that if the 119905
1value is sufficiently
large (1199051= 35) and 119905
2= 3 the total design cost
is the same (1469) for all three levels of the target
1079
1084
1091
1099
1108
1083
1088
10931097
10821085
1088
1093
1075
1085
1095
1105
1115
Tota
l des
ign
cost
at (k t1) = (2 3)
t2 = 0 t2 = 15 t2 = 3 t2 = 45 t2 = 6
120575 = 08
120575 = 07
120575 = 06
Figure 11 Variation of total design cost with 1199052for various 120575 values
customer satisfaction since the aggregated resultsfrom the required minimum satisfaction level foreach customer requirement CR
119894surpass each target
customer satisfaction The high required minimumsatisfaction level due to 119905
1= 35 resulted in the largest
total design cost With 119896 = 2 and 1199051= 3 the total
design cost changes with 1199052 as shown in Figure 11
(3) From a design viewpoint if theminimum satisfactionlevel for each customer requirement CR
119894and the
fulfilled minimum design quality level for each DR119895
are not required that is 1199051and 1199052are fixed at 0 the
minimal total design cost can be obtained from theproposed model (7) at each setting of the targetedcustomer satisfaction level 120575 For example with 119905
1=
1199052= 0 and 120575 = 06 07 and 08 respectively the
total design costs are 700 878 and 1063 respectivelyregardless of the 119896 valueThis indicates that to achievethe target degree of customer satisfaction for a certainmarket segment the investment amount of the totaldesign cost has the lowest bound
6 Conclusions
A mathematical model was proposed for determining thedesign quality level required to achieve the target customersatisfaction for the target market segment with the minimumtotal design cost In the proposed model the customersatisfaction is expressed as a function of the quality level con-sidering the consumer behavior of the targetmarket segmentMoreover the proposedmodel allows theNPD team to set theminimum satisfaction level for each CR andor the fulfilledminimumdesign quality level for eachDRmaking the designprocesses flexible A numerical example was provided todemonstrate the feasibility and applicability of the proposedapproach In future research the relation between customersatisfaction and quality level will be further investigated tomake the proposed model more applicable in the real world
Journal of Applied Mathematics 9
Nomenclature
CR119894 The 119894th customer requirement
DR119895 The 119895th design requirement
119877119894119895 Relational intensity between CR
119894and DR
119895
120574119896119895 Technical correlation between DR
119896and
DR119895
1198771015840
119894119895 Normalized relational intensity between
CR119894and DR
119895in Wassermanrsquos
normalization model119877norm119894119895
Normalized relational intensity betweenCR119894and DR
119895in L-H Chen and C-N
Chenrsquos normalization model119889119894 Original importance weight of CR
119894
120573119894119897 Correlation between CR
119894and CR
119897
119889norm119894
Normalized importance weight of CR119894in
L-H Chen and C-N Chenrsquos integrationmodel when CRsrsquo correlations exist
119908norm119895
Normalized importance weight of DR119895
119862119895 Required cost for DR
119895to fully achieve
customer satisfaction119909119895 Technical fulfillment level for DR
119895
X Design vector containing the fulfillmentlevels of all DRs
DQ(X) Overall design quality level by designvector X
CS(X) Fulfilled customer satisfaction by designvector X
120572 Target design quality level120575 Target customer satisfaction119896 The characteristic parameter to describe
the customer preference of a specificmarket segment for the design qualitylevel of a specific product
120576119894 Minimum required satisfaction level for
CR119894
1199051 Design parameter to determine 120576
119894
120588119895 Minimum fulfilled quality level for DR
119895
1199052 Design parameter to determine 120588
119895
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] L Cohen Quality Function Deployment How to Make QFDWork for You Addison-Wesley Reading Mass USA 1995
[2] L-K Chan and M-L Wu ldquoQuality function deployment aliterature reviewrdquoEuropean Journal of Operational Research vol143 no 3 pp 463ndash497 2002
[3] G S Wasserman ldquoOn how to prioritize design requirementsduring the QFD planning processrdquo IIE Transactions vol 25 no3 pp 59ndash65 1993
[4] K-J Kim ldquoDetermining optimal design characteristic levels inquality function deploymentrdquo Quality Engineering vol 10 no2 pp 295ndash307 1997
[5] HMoskowitz and K-J Kim ldquoQFD optimizer a novice friendlyquality function deployment decision support system for opti-mizing product designsrdquo Computers amp Industrial Engineeringvol 32 no 3 pp 641ndash655 1997
[6] T Park and K-J Kim ldquoDetermination of an optimal setof design requirements using house of qualityrdquo Journal ofOperations Management vol 16 no 5 pp 569ndash581 1998
[7] J Bode and R Y K Fung ldquoCost engineering with qualityfunction deploymentrdquo Computers and Industrial Engineeringvol 35 no 3-4 pp 587ndash590 1998
[8] R G Askin and DW Dawson ldquoMaximizing customer satisfac-tion by optimal specification of engineering characteristicsrdquo IIETransactions (Institute of Industrial Engineers) vol 32 no 1 pp9ndash20 2000
[9] R Y K Fung J Tang Y Tu and D Wang ldquoProduct designresources optimization using a non-linear fuzzy quality func-tion deployment modelrdquo International Journal of ProductionResearch vol 40 no 3 pp 585ndash599 2002
[10] L-H Chen and M-C Weng ldquoA fuzzy model for exploitingquality function deploymentrdquo Mathematical and ComputerModelling vol 38 no 5-6 pp 559ndash570 2003
[11] H Iranmanesh and V Thomson ldquoCompetitive advantage byadjusting design characteristics to satisfy cost targetsrdquo Interna-tional Journal of Production Economics vol 115 no 1 pp 64ndash712008
[12] L-H Chen andW-C Ko ldquoA fuzzy nonlinear model for qualityfunction deployment considering Kanorsquos conceptrdquo Mathemati-cal and Computer Modelling vol 48 no 3-4 pp 581ndash593 2008
[13] L-H Chen and W-C Ko ldquoFuzzy approaches to qualityfunction deployment for new product designrdquo Fuzzy Sets andSystems vol 160 no 18 pp 2620ndash2639 2009
[14] J-H Shin H-B Jun D Kiritsis and P Xirouchakis ldquoA decisionsupport method for product conceptual design consideringproduct lifecycle factors and resource constraintsrdquo InternationalJournal of Advanced Manufacturing Technology vol 52 no 9ndash12 pp 865ndash886 2011
[15] M Braglia G Fantoni andM Frosolini ldquoThe house of reliabil-ityrdquo International Journal of Quality amp Reliability Managementvol 24 no 4 pp 420ndash440 2007
[16] W-C Chiou H-W Kuo and I-Y Lu ldquoA technology orientedproductivity measurement modelrdquo International Journal ofProduction Economics vol 60 pp 69ndash77 1999
[17] P-T Chuang ldquoA QFD approach for distributionrsquos locationmodelrdquo International Journal of Quality and Reliability Manage-ment vol 19 no 8 pp 1037ndash1054 2002
[18] L-H Chen and M-C Weng ldquoAn evaluation approach to engi-neering design inQFDprocesses using fuzzy goal programmingmodelsrdquo European Journal of Operational Research vol 172 no1 pp 230ndash248 2006
[19] E K Delice and Z Gungor ldquoA new mixed integer linearprogramming model for product development using qualityfunction deploymentrdquo Computers amp Industrial Engineering vol57 no 3 pp 906ndash912 2009
[20] E K Delice and Z Gungor ldquoAmixed integer goal programmingmodel for discrete values of design requirements in QFDrdquoInternational Journal of Production Research vol 49 no 10 pp2941ndash2957 2011
[21] F Franceschini and S Rossetto ldquoQFD an interactive algorithmfor the prioritization of productrsquos technical design characteris-ticsrdquo Integrated Manufacturing Systems vol 13 no 1 pp 69ndash752002
10 Journal of Applied Mathematics
[22] C H Han J K Kim S H Choi and S H Kim ldquoDeterminationof information system development priority using quality func-tion deploymentrdquoComputers and Industrial Engineering vol 35no 1-2 pp 241ndash244 1998
[23] E E Karsak ldquoFuzzy multiple objective decision makingapproach to prioritize design requirements in quality functiondeploymentrdquo International Journal of Production Research vol42 no 18 pp 3957ndash3974 2004
[24] X Lai M Xie and K C Tan ldquoDynamic programming for QFDoptimizationrdquoQuality and Reliability Engineering Internationalvol 21 no 8 pp 769ndash780 2005
[25] S-T Liu ldquoRating design requirements in fuzzy quality functiondeployment via a mathematical programming approachrdquo Inter-national Journal of Production Research vol 43 no 3 pp 497ndash513 2005
[26] R Ramanathan and J Yunfeng ldquoIncorporating cost and envi-ronmental factors in quality function deployment using dataenvelopment analysisrdquo Omega vol 37 no 3 pp 711ndash723 2009
[27] H Raharjo M Xie and A C Brombacher ldquoA systematicmethodology to deal with the dynamics of customer needs inQuality Function Deploymentrdquo Expert Systems with Applica-tions vol 38 no 4 pp 3653ndash3662 2011
[28] Y-M Wang and K-S Chin ldquoTechnical importance ratingsin fuzzy QFD by integrating fuzzy normalization and fuzzyweighted averagerdquoComputers ampMathematics with Applicationsvol 62 no 11 pp 4207ndash4221 2011
[29] Y-M Wang ldquoA fuzzy-normalisation-based group decision-making approach for prioritising engineering design require-ments in QFD under uncertaintyrdquo International Journal ofProduction Research vol 50 no 23 pp 6963ndash6977 2012
[30] D Lyman ldquoDeployment normalizationrdquo in Proceedings of theTransactions from the 2nd Symposium on Quality FunctionDeployment pp 307ndash315 Automotive Division of the AmericanSociety for Quality Control The American Supplier Instituteand GOALQPC Dearborn Mich USA 1990
[31] L-H Chen and C-N Chen ldquoNormalisation models for pri-oritising design requirements for quality function deploymentprocessesrdquo International Journal of Production Research vol 52no 2 pp 299ndash313 2014
[32] S Erevelles and C Leavitt ldquoA comparison of current modelsof consumer satisfactiondissatisfactionrdquo Journal of ConsumerSatisfaction Dissatisfaction and Complaining Behavior vol 5pp 104ndash114 1992
[33] M J Morgan J A Attaway and M Griffin ldquoThe role ofproductservice experience in the satisfaction formation pro-cess a test of moderationrdquo Journal of Consumer SatisfactionDissatisfaction and Complaining Behavior vol 9 pp 391ndash4051996
[34] E W Anderson and M W Sullivan ldquoThe antecedents andconsequences of customer satisfaction for firmsrdquo MarketingScience vol 12 no 2 pp 125ndash143 1993
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
8 Journal of Applied Mathematics
1093
1091
1088
1090
1088
1084
1087
1085
1083
1080
1085
1090
1095
Tota
l des
ign
cost
k = 15 k = 2 k = 3
120575 = 08
120575 = 07
120575 = 06
at (t1 t2) = (3 3)
Figure 9 Variation of total design cost with 119896 for various 120575 values
1076 1076 1076
1091
889 889897
1088
717 717
852
1085
600
900
1200
1500
Tota
l des
ign
cost
at (k t2) = (2 3)
t1 = 0 t1 = 2 t1 = 25 t1 = 3 t1 = 35
120575 = 08
120575 = 07
120575 = 06
1469
Figure 10 Variation of total design cost with 1199051for various 120575 values
decreases with increasing 119896 value regardless of thetarget customer satisfaction 120575
(2) The 1199051and 1199052values in (7e) and (7g) affect the mini-
mum satisfaction level for each customer requirementCR119894and the fulfilled minimum design quality level
for each DR119895 respectively and therefore affect the
total design cost Larger values of 1199051andor 119905
2increase
the total design cost With 119896 = 2 and 1199052= 3
Figure 10 shows the impact of the 1199051value on the total
design cost The total design cost remains unchangedin a range of 119905
1values that depends on 120575 because
the fulfilled minimum design quality level 120588119895at 1199052= 3
confines the influence of the minimum satisfactionlevel 120576
119894on the total design cost at some levels of 119905
1
regardless of the target customer satisfaction level120575 It is also noted that if the 119905
1value is sufficiently
large (1199051= 35) and 119905
2= 3 the total design cost
is the same (1469) for all three levels of the target
1079
1084
1091
1099
1108
1083
1088
10931097
10821085
1088
1093
1075
1085
1095
1105
1115
Tota
l des
ign
cost
at (k t1) = (2 3)
t2 = 0 t2 = 15 t2 = 3 t2 = 45 t2 = 6
120575 = 08
120575 = 07
120575 = 06
Figure 11 Variation of total design cost with 1199052for various 120575 values
customer satisfaction since the aggregated resultsfrom the required minimum satisfaction level foreach customer requirement CR
119894surpass each target
customer satisfaction The high required minimumsatisfaction level due to 119905
1= 35 resulted in the largest
total design cost With 119896 = 2 and 1199051= 3 the total
design cost changes with 1199052 as shown in Figure 11
(3) From a design viewpoint if theminimum satisfactionlevel for each customer requirement CR
119894and the
fulfilled minimum design quality level for each DR119895
are not required that is 1199051and 1199052are fixed at 0 the
minimal total design cost can be obtained from theproposed model (7) at each setting of the targetedcustomer satisfaction level 120575 For example with 119905
1=
1199052= 0 and 120575 = 06 07 and 08 respectively the
total design costs are 700 878 and 1063 respectivelyregardless of the 119896 valueThis indicates that to achievethe target degree of customer satisfaction for a certainmarket segment the investment amount of the totaldesign cost has the lowest bound
6 Conclusions
A mathematical model was proposed for determining thedesign quality level required to achieve the target customersatisfaction for the target market segment with the minimumtotal design cost In the proposed model the customersatisfaction is expressed as a function of the quality level con-sidering the consumer behavior of the targetmarket segmentMoreover the proposedmodel allows theNPD team to set theminimum satisfaction level for each CR andor the fulfilledminimumdesign quality level for eachDRmaking the designprocesses flexible A numerical example was provided todemonstrate the feasibility and applicability of the proposedapproach In future research the relation between customersatisfaction and quality level will be further investigated tomake the proposed model more applicable in the real world
Journal of Applied Mathematics 9
Nomenclature
CR119894 The 119894th customer requirement
DR119895 The 119895th design requirement
119877119894119895 Relational intensity between CR
119894and DR
119895
120574119896119895 Technical correlation between DR
119896and
DR119895
1198771015840
119894119895 Normalized relational intensity between
CR119894and DR
119895in Wassermanrsquos
normalization model119877norm119894119895
Normalized relational intensity betweenCR119894and DR
119895in L-H Chen and C-N
Chenrsquos normalization model119889119894 Original importance weight of CR
119894
120573119894119897 Correlation between CR
119894and CR
119897
119889norm119894
Normalized importance weight of CR119894in
L-H Chen and C-N Chenrsquos integrationmodel when CRsrsquo correlations exist
119908norm119895
Normalized importance weight of DR119895
119862119895 Required cost for DR
119895to fully achieve
customer satisfaction119909119895 Technical fulfillment level for DR
119895
X Design vector containing the fulfillmentlevels of all DRs
DQ(X) Overall design quality level by designvector X
CS(X) Fulfilled customer satisfaction by designvector X
120572 Target design quality level120575 Target customer satisfaction119896 The characteristic parameter to describe
the customer preference of a specificmarket segment for the design qualitylevel of a specific product
120576119894 Minimum required satisfaction level for
CR119894
1199051 Design parameter to determine 120576
119894
120588119895 Minimum fulfilled quality level for DR
119895
1199052 Design parameter to determine 120588
119895
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] L Cohen Quality Function Deployment How to Make QFDWork for You Addison-Wesley Reading Mass USA 1995
[2] L-K Chan and M-L Wu ldquoQuality function deployment aliterature reviewrdquoEuropean Journal of Operational Research vol143 no 3 pp 463ndash497 2002
[3] G S Wasserman ldquoOn how to prioritize design requirementsduring the QFD planning processrdquo IIE Transactions vol 25 no3 pp 59ndash65 1993
[4] K-J Kim ldquoDetermining optimal design characteristic levels inquality function deploymentrdquo Quality Engineering vol 10 no2 pp 295ndash307 1997
[5] HMoskowitz and K-J Kim ldquoQFD optimizer a novice friendlyquality function deployment decision support system for opti-mizing product designsrdquo Computers amp Industrial Engineeringvol 32 no 3 pp 641ndash655 1997
[6] T Park and K-J Kim ldquoDetermination of an optimal setof design requirements using house of qualityrdquo Journal ofOperations Management vol 16 no 5 pp 569ndash581 1998
[7] J Bode and R Y K Fung ldquoCost engineering with qualityfunction deploymentrdquo Computers and Industrial Engineeringvol 35 no 3-4 pp 587ndash590 1998
[8] R G Askin and DW Dawson ldquoMaximizing customer satisfac-tion by optimal specification of engineering characteristicsrdquo IIETransactions (Institute of Industrial Engineers) vol 32 no 1 pp9ndash20 2000
[9] R Y K Fung J Tang Y Tu and D Wang ldquoProduct designresources optimization using a non-linear fuzzy quality func-tion deployment modelrdquo International Journal of ProductionResearch vol 40 no 3 pp 585ndash599 2002
[10] L-H Chen and M-C Weng ldquoA fuzzy model for exploitingquality function deploymentrdquo Mathematical and ComputerModelling vol 38 no 5-6 pp 559ndash570 2003
[11] H Iranmanesh and V Thomson ldquoCompetitive advantage byadjusting design characteristics to satisfy cost targetsrdquo Interna-tional Journal of Production Economics vol 115 no 1 pp 64ndash712008
[12] L-H Chen andW-C Ko ldquoA fuzzy nonlinear model for qualityfunction deployment considering Kanorsquos conceptrdquo Mathemati-cal and Computer Modelling vol 48 no 3-4 pp 581ndash593 2008
[13] L-H Chen and W-C Ko ldquoFuzzy approaches to qualityfunction deployment for new product designrdquo Fuzzy Sets andSystems vol 160 no 18 pp 2620ndash2639 2009
[14] J-H Shin H-B Jun D Kiritsis and P Xirouchakis ldquoA decisionsupport method for product conceptual design consideringproduct lifecycle factors and resource constraintsrdquo InternationalJournal of Advanced Manufacturing Technology vol 52 no 9ndash12 pp 865ndash886 2011
[15] M Braglia G Fantoni andM Frosolini ldquoThe house of reliabil-ityrdquo International Journal of Quality amp Reliability Managementvol 24 no 4 pp 420ndash440 2007
[16] W-C Chiou H-W Kuo and I-Y Lu ldquoA technology orientedproductivity measurement modelrdquo International Journal ofProduction Economics vol 60 pp 69ndash77 1999
[17] P-T Chuang ldquoA QFD approach for distributionrsquos locationmodelrdquo International Journal of Quality and Reliability Manage-ment vol 19 no 8 pp 1037ndash1054 2002
[18] L-H Chen and M-C Weng ldquoAn evaluation approach to engi-neering design inQFDprocesses using fuzzy goal programmingmodelsrdquo European Journal of Operational Research vol 172 no1 pp 230ndash248 2006
[19] E K Delice and Z Gungor ldquoA new mixed integer linearprogramming model for product development using qualityfunction deploymentrdquo Computers amp Industrial Engineering vol57 no 3 pp 906ndash912 2009
[20] E K Delice and Z Gungor ldquoAmixed integer goal programmingmodel for discrete values of design requirements in QFDrdquoInternational Journal of Production Research vol 49 no 10 pp2941ndash2957 2011
[21] F Franceschini and S Rossetto ldquoQFD an interactive algorithmfor the prioritization of productrsquos technical design characteris-ticsrdquo Integrated Manufacturing Systems vol 13 no 1 pp 69ndash752002
10 Journal of Applied Mathematics
[22] C H Han J K Kim S H Choi and S H Kim ldquoDeterminationof information system development priority using quality func-tion deploymentrdquoComputers and Industrial Engineering vol 35no 1-2 pp 241ndash244 1998
[23] E E Karsak ldquoFuzzy multiple objective decision makingapproach to prioritize design requirements in quality functiondeploymentrdquo International Journal of Production Research vol42 no 18 pp 3957ndash3974 2004
[24] X Lai M Xie and K C Tan ldquoDynamic programming for QFDoptimizationrdquoQuality and Reliability Engineering Internationalvol 21 no 8 pp 769ndash780 2005
[25] S-T Liu ldquoRating design requirements in fuzzy quality functiondeployment via a mathematical programming approachrdquo Inter-national Journal of Production Research vol 43 no 3 pp 497ndash513 2005
[26] R Ramanathan and J Yunfeng ldquoIncorporating cost and envi-ronmental factors in quality function deployment using dataenvelopment analysisrdquo Omega vol 37 no 3 pp 711ndash723 2009
[27] H Raharjo M Xie and A C Brombacher ldquoA systematicmethodology to deal with the dynamics of customer needs inQuality Function Deploymentrdquo Expert Systems with Applica-tions vol 38 no 4 pp 3653ndash3662 2011
[28] Y-M Wang and K-S Chin ldquoTechnical importance ratingsin fuzzy QFD by integrating fuzzy normalization and fuzzyweighted averagerdquoComputers ampMathematics with Applicationsvol 62 no 11 pp 4207ndash4221 2011
[29] Y-M Wang ldquoA fuzzy-normalisation-based group decision-making approach for prioritising engineering design require-ments in QFD under uncertaintyrdquo International Journal ofProduction Research vol 50 no 23 pp 6963ndash6977 2012
[30] D Lyman ldquoDeployment normalizationrdquo in Proceedings of theTransactions from the 2nd Symposium on Quality FunctionDeployment pp 307ndash315 Automotive Division of the AmericanSociety for Quality Control The American Supplier Instituteand GOALQPC Dearborn Mich USA 1990
[31] L-H Chen and C-N Chen ldquoNormalisation models for pri-oritising design requirements for quality function deploymentprocessesrdquo International Journal of Production Research vol 52no 2 pp 299ndash313 2014
[32] S Erevelles and C Leavitt ldquoA comparison of current modelsof consumer satisfactiondissatisfactionrdquo Journal of ConsumerSatisfaction Dissatisfaction and Complaining Behavior vol 5pp 104ndash114 1992
[33] M J Morgan J A Attaway and M Griffin ldquoThe role ofproductservice experience in the satisfaction formation pro-cess a test of moderationrdquo Journal of Consumer SatisfactionDissatisfaction and Complaining Behavior vol 9 pp 391ndash4051996
[34] E W Anderson and M W Sullivan ldquoThe antecedents andconsequences of customer satisfaction for firmsrdquo MarketingScience vol 12 no 2 pp 125ndash143 1993
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Journal of Applied Mathematics 9
Nomenclature
CR119894 The 119894th customer requirement
DR119895 The 119895th design requirement
119877119894119895 Relational intensity between CR
119894and DR
119895
120574119896119895 Technical correlation between DR
119896and
DR119895
1198771015840
119894119895 Normalized relational intensity between
CR119894and DR
119895in Wassermanrsquos
normalization model119877norm119894119895
Normalized relational intensity betweenCR119894and DR
119895in L-H Chen and C-N
Chenrsquos normalization model119889119894 Original importance weight of CR
119894
120573119894119897 Correlation between CR
119894and CR
119897
119889norm119894
Normalized importance weight of CR119894in
L-H Chen and C-N Chenrsquos integrationmodel when CRsrsquo correlations exist
119908norm119895
Normalized importance weight of DR119895
119862119895 Required cost for DR
119895to fully achieve
customer satisfaction119909119895 Technical fulfillment level for DR
119895
X Design vector containing the fulfillmentlevels of all DRs
DQ(X) Overall design quality level by designvector X
CS(X) Fulfilled customer satisfaction by designvector X
120572 Target design quality level120575 Target customer satisfaction119896 The characteristic parameter to describe
the customer preference of a specificmarket segment for the design qualitylevel of a specific product
120576119894 Minimum required satisfaction level for
CR119894
1199051 Design parameter to determine 120576
119894
120588119895 Minimum fulfilled quality level for DR
119895
1199052 Design parameter to determine 120588
119895
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] L Cohen Quality Function Deployment How to Make QFDWork for You Addison-Wesley Reading Mass USA 1995
[2] L-K Chan and M-L Wu ldquoQuality function deployment aliterature reviewrdquoEuropean Journal of Operational Research vol143 no 3 pp 463ndash497 2002
[3] G S Wasserman ldquoOn how to prioritize design requirementsduring the QFD planning processrdquo IIE Transactions vol 25 no3 pp 59ndash65 1993
[4] K-J Kim ldquoDetermining optimal design characteristic levels inquality function deploymentrdquo Quality Engineering vol 10 no2 pp 295ndash307 1997
[5] HMoskowitz and K-J Kim ldquoQFD optimizer a novice friendlyquality function deployment decision support system for opti-mizing product designsrdquo Computers amp Industrial Engineeringvol 32 no 3 pp 641ndash655 1997
[6] T Park and K-J Kim ldquoDetermination of an optimal setof design requirements using house of qualityrdquo Journal ofOperations Management vol 16 no 5 pp 569ndash581 1998
[7] J Bode and R Y K Fung ldquoCost engineering with qualityfunction deploymentrdquo Computers and Industrial Engineeringvol 35 no 3-4 pp 587ndash590 1998
[8] R G Askin and DW Dawson ldquoMaximizing customer satisfac-tion by optimal specification of engineering characteristicsrdquo IIETransactions (Institute of Industrial Engineers) vol 32 no 1 pp9ndash20 2000
[9] R Y K Fung J Tang Y Tu and D Wang ldquoProduct designresources optimization using a non-linear fuzzy quality func-tion deployment modelrdquo International Journal of ProductionResearch vol 40 no 3 pp 585ndash599 2002
[10] L-H Chen and M-C Weng ldquoA fuzzy model for exploitingquality function deploymentrdquo Mathematical and ComputerModelling vol 38 no 5-6 pp 559ndash570 2003
[11] H Iranmanesh and V Thomson ldquoCompetitive advantage byadjusting design characteristics to satisfy cost targetsrdquo Interna-tional Journal of Production Economics vol 115 no 1 pp 64ndash712008
[12] L-H Chen andW-C Ko ldquoA fuzzy nonlinear model for qualityfunction deployment considering Kanorsquos conceptrdquo Mathemati-cal and Computer Modelling vol 48 no 3-4 pp 581ndash593 2008
[13] L-H Chen and W-C Ko ldquoFuzzy approaches to qualityfunction deployment for new product designrdquo Fuzzy Sets andSystems vol 160 no 18 pp 2620ndash2639 2009
[14] J-H Shin H-B Jun D Kiritsis and P Xirouchakis ldquoA decisionsupport method for product conceptual design consideringproduct lifecycle factors and resource constraintsrdquo InternationalJournal of Advanced Manufacturing Technology vol 52 no 9ndash12 pp 865ndash886 2011
[15] M Braglia G Fantoni andM Frosolini ldquoThe house of reliabil-ityrdquo International Journal of Quality amp Reliability Managementvol 24 no 4 pp 420ndash440 2007
[16] W-C Chiou H-W Kuo and I-Y Lu ldquoA technology orientedproductivity measurement modelrdquo International Journal ofProduction Economics vol 60 pp 69ndash77 1999
[17] P-T Chuang ldquoA QFD approach for distributionrsquos locationmodelrdquo International Journal of Quality and Reliability Manage-ment vol 19 no 8 pp 1037ndash1054 2002
[18] L-H Chen and M-C Weng ldquoAn evaluation approach to engi-neering design inQFDprocesses using fuzzy goal programmingmodelsrdquo European Journal of Operational Research vol 172 no1 pp 230ndash248 2006
[19] E K Delice and Z Gungor ldquoA new mixed integer linearprogramming model for product development using qualityfunction deploymentrdquo Computers amp Industrial Engineering vol57 no 3 pp 906ndash912 2009
[20] E K Delice and Z Gungor ldquoAmixed integer goal programmingmodel for discrete values of design requirements in QFDrdquoInternational Journal of Production Research vol 49 no 10 pp2941ndash2957 2011
[21] F Franceschini and S Rossetto ldquoQFD an interactive algorithmfor the prioritization of productrsquos technical design characteris-ticsrdquo Integrated Manufacturing Systems vol 13 no 1 pp 69ndash752002
10 Journal of Applied Mathematics
[22] C H Han J K Kim S H Choi and S H Kim ldquoDeterminationof information system development priority using quality func-tion deploymentrdquoComputers and Industrial Engineering vol 35no 1-2 pp 241ndash244 1998
[23] E E Karsak ldquoFuzzy multiple objective decision makingapproach to prioritize design requirements in quality functiondeploymentrdquo International Journal of Production Research vol42 no 18 pp 3957ndash3974 2004
[24] X Lai M Xie and K C Tan ldquoDynamic programming for QFDoptimizationrdquoQuality and Reliability Engineering Internationalvol 21 no 8 pp 769ndash780 2005
[25] S-T Liu ldquoRating design requirements in fuzzy quality functiondeployment via a mathematical programming approachrdquo Inter-national Journal of Production Research vol 43 no 3 pp 497ndash513 2005
[26] R Ramanathan and J Yunfeng ldquoIncorporating cost and envi-ronmental factors in quality function deployment using dataenvelopment analysisrdquo Omega vol 37 no 3 pp 711ndash723 2009
[27] H Raharjo M Xie and A C Brombacher ldquoA systematicmethodology to deal with the dynamics of customer needs inQuality Function Deploymentrdquo Expert Systems with Applica-tions vol 38 no 4 pp 3653ndash3662 2011
[28] Y-M Wang and K-S Chin ldquoTechnical importance ratingsin fuzzy QFD by integrating fuzzy normalization and fuzzyweighted averagerdquoComputers ampMathematics with Applicationsvol 62 no 11 pp 4207ndash4221 2011
[29] Y-M Wang ldquoA fuzzy-normalisation-based group decision-making approach for prioritising engineering design require-ments in QFD under uncertaintyrdquo International Journal ofProduction Research vol 50 no 23 pp 6963ndash6977 2012
[30] D Lyman ldquoDeployment normalizationrdquo in Proceedings of theTransactions from the 2nd Symposium on Quality FunctionDeployment pp 307ndash315 Automotive Division of the AmericanSociety for Quality Control The American Supplier Instituteand GOALQPC Dearborn Mich USA 1990
[31] L-H Chen and C-N Chen ldquoNormalisation models for pri-oritising design requirements for quality function deploymentprocessesrdquo International Journal of Production Research vol 52no 2 pp 299ndash313 2014
[32] S Erevelles and C Leavitt ldquoA comparison of current modelsof consumer satisfactiondissatisfactionrdquo Journal of ConsumerSatisfaction Dissatisfaction and Complaining Behavior vol 5pp 104ndash114 1992
[33] M J Morgan J A Attaway and M Griffin ldquoThe role ofproductservice experience in the satisfaction formation pro-cess a test of moderationrdquo Journal of Consumer SatisfactionDissatisfaction and Complaining Behavior vol 9 pp 391ndash4051996
[34] E W Anderson and M W Sullivan ldquoThe antecedents andconsequences of customer satisfaction for firmsrdquo MarketingScience vol 12 no 2 pp 125ndash143 1993
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
10 Journal of Applied Mathematics
[22] C H Han J K Kim S H Choi and S H Kim ldquoDeterminationof information system development priority using quality func-tion deploymentrdquoComputers and Industrial Engineering vol 35no 1-2 pp 241ndash244 1998
[23] E E Karsak ldquoFuzzy multiple objective decision makingapproach to prioritize design requirements in quality functiondeploymentrdquo International Journal of Production Research vol42 no 18 pp 3957ndash3974 2004
[24] X Lai M Xie and K C Tan ldquoDynamic programming for QFDoptimizationrdquoQuality and Reliability Engineering Internationalvol 21 no 8 pp 769ndash780 2005
[25] S-T Liu ldquoRating design requirements in fuzzy quality functiondeployment via a mathematical programming approachrdquo Inter-national Journal of Production Research vol 43 no 3 pp 497ndash513 2005
[26] R Ramanathan and J Yunfeng ldquoIncorporating cost and envi-ronmental factors in quality function deployment using dataenvelopment analysisrdquo Omega vol 37 no 3 pp 711ndash723 2009
[27] H Raharjo M Xie and A C Brombacher ldquoA systematicmethodology to deal with the dynamics of customer needs inQuality Function Deploymentrdquo Expert Systems with Applica-tions vol 38 no 4 pp 3653ndash3662 2011
[28] Y-M Wang and K-S Chin ldquoTechnical importance ratingsin fuzzy QFD by integrating fuzzy normalization and fuzzyweighted averagerdquoComputers ampMathematics with Applicationsvol 62 no 11 pp 4207ndash4221 2011
[29] Y-M Wang ldquoA fuzzy-normalisation-based group decision-making approach for prioritising engineering design require-ments in QFD under uncertaintyrdquo International Journal ofProduction Research vol 50 no 23 pp 6963ndash6977 2012
[30] D Lyman ldquoDeployment normalizationrdquo in Proceedings of theTransactions from the 2nd Symposium on Quality FunctionDeployment pp 307ndash315 Automotive Division of the AmericanSociety for Quality Control The American Supplier Instituteand GOALQPC Dearborn Mich USA 1990
[31] L-H Chen and C-N Chen ldquoNormalisation models for pri-oritising design requirements for quality function deploymentprocessesrdquo International Journal of Production Research vol 52no 2 pp 299ndash313 2014
[32] S Erevelles and C Leavitt ldquoA comparison of current modelsof consumer satisfactiondissatisfactionrdquo Journal of ConsumerSatisfaction Dissatisfaction and Complaining Behavior vol 5pp 104ndash114 1992
[33] M J Morgan J A Attaway and M Griffin ldquoThe role ofproductservice experience in the satisfaction formation pro-cess a test of moderationrdquo Journal of Consumer SatisfactionDissatisfaction and Complaining Behavior vol 9 pp 391ndash4051996
[34] E W Anderson and M W Sullivan ldquoThe antecedents andconsequences of customer satisfaction for firmsrdquo MarketingScience vol 12 no 2 pp 125ndash143 1993
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of