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

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

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

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 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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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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

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

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

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

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 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