Intl. Trans. in Op. Res. 17 (2010) 85–102 DOI: 10.1111/j.1475-3995.2009.00718.x

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH

Integrating customer’s preferences in the QFD planning process using a combined benchmarking and imprecise goal programming model
Mohamed Sadok Cherif a, Habib Chabchoubb and Belaı¨ d Aounic a Institut Supe´rieur d’Informatique et de Mathe´matiques, Universite´ de Monastir, B.P. 223, C.P. 5000, Monastir, Tunisia, b Institut Supe´rieur de Gestion Industrielle, Universite´ de Sfax, B.P. 954, C.P. 3018, Sfax, Tunisia, c Decision Aid Research Group, School of Commerce and Administration, Faculty of Management, Laurentian University, Sudbury, Ontario, Canada P3E2C6 E-mail: baouni@laurentian.ca Received 15 October 2008; received in revised form 29 March 2009; accepted 9 April 2009

Abstract Quality function deployment (QFD) is a customer-oriented design tool for developing new or improved products to achieve higher customer satisfaction by integrating various functions of an organization. The engineering characteristics (ECs) affecting the product performances are designed to match the customer attributes (CAs). However, from the viewpoint of the QFD team, product design processes are performed in imprecise environments, and more than one factor must be taken into account in determining the target levels of ECs, especially the limited resources and increased market competition. This paper presents an imprecise goal programming (GP) approach to determine the optimum target levels of ECs in QFD for maximizing customer satisfaction under resource limitation and considerations of market competition. Based on benchmarking data of CAs, the concept of satisfaction functions is utilized to formulate explicitly the customer’s preferences and to integrate the competitive analysis of target market into the modelling and solution process. In addition, the relationships linking CAs and ECs and the ECs to each other are integrated by functional relationships. The proposed approach will be illustrated through a car door design example.
Keywords: quality function deployment; imprecise goal programming; satisfaction functions; customer’s preferences modelling

1. Introduction The competitiveness of firms within the globalized market requires higher product quality. The quality of a product is composed of many aspects such as attractiveness, maintainability, and ease r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies Published by Blackwell Publishing, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA 02148, USA.

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of use. In fact, a product must satisfy the customer’s needs. This focus on satisfying the customer’s needs places an emphasis on techniques such as quality function deployment (QFD), which improves the quality of the product and provides the customer with a high level of satisfaction. The concept of QFD is to translate the customer’s requirements, which are also known as customer attributes (CAs), into design requirements, known as engineering characteristics (ECs), and subsequently into parts’ characteristics, process design, and production requirements. QFD uses several matrices including product planning matrix, parts planning matrix, process planning matrix, and production/operation planning matrix to establish relationships between a company’s functions and customer satisfaction. These matrices are based on the ‘‘What-How’’ matrix, developed by Hauser and Clausing (1988), which is called House of Quality (HoQ) (Fig. 1). QFD is an iterative process performed by a multifunctional team that translates the customer’s needs into specifications of process steps. The matrices explicitly relate the data produced in one stage of the process to the decisions that must be made at the next process stage (Temponi et al., 1999). QFD was first developed and introduced in the late 1960s (Akao, 1990). A few years later, in 1972, QFD was implemented in Japan at the Kobe Shipyards of Mitsubishi Heavy Industries. Using the QFD, Toyota was able to reduce the start-up pre-production costs by 60% from 1977 to 1984 and to decrease the time required for its development by one-third (Hauser and Clausing, 1988; Kahraman et al., 2006). The QFD was introduced to US firms with its first application in Ford Motor Company, and has played an important role since then at companies such as General Motors, Chrysler, Digital Equipment, Hewlett-Packard, AT&T, Procter and Gamble, and Baxter Healthcare (Prasad, 1998). QFD has been applied as an analysis tool in various areas. A wide range of literature reviews over QFD applications was already presented by Chan and Wu (2002). In addition to the product development process, QFD has also found applications in the software development process (Haag et al., 1996; Chakraborty and Dey, 2007), electronics (Herzwurm and

Correlation between ECs Engineering Characteristics EC1
Customer’s Attributes Degree of importance

EC2

…….

ECn

Benchmarking of CAs
Customer Perceptions

CA1 CA2
………

Relationships between CAs and ECs

Min Max

CAm

Target levels of ECs Costs

Fig. 1. House of quality. r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

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Schockert, 2003; Kwong et al., 2007; Jeanga et al. 2009), information systems development (Han et al., 1998), supplier selection (Bevilacqua et al., 2006), education (Shieu-ming, 2004), healthcare (Foester, 2001; Moores, 2006) R&D projects (Stehn and Bergstrom, 2002), and construction (Dikmen et al., 2005; Lee et al., 2009). Traditional methods for setting the expected targets for ECs are usually subjective or based on heuristics. For example, through a team consensus and using a hierarchy priorization procedure (Armacost et al., 1994; Bode and Fung, 1998), feasible solutions rather than optimal ones are offered. Given that an HoQ contains many CAs and ECs, it is difficult and tedious to obtain a feasible competitive design using such a process. In particular, many tradeoffs have to be made among the ECs, as well as among many implicit or explicit relationships interrelating the EC levels and the EC levels with the CAs. In practice, such relationships are typically vague and imprecise. The imprecision or ambiguity arises mainly from the fact that the CAs that tend to be subjective, qualitative, and non-technical need to be translated into the ECs that should be expressed in more quantitative and technical terms. Furthermore, data available for product design are often limited, inaccurate, or vague at best, particularly when developing an entirely new product (Park and Kim, 1998; Kim et al., 2000). Several authors have attempted to address these methodological problems by using mathematical programming and decision-making aid tools. However, they have lacked effectiveness in integrating customer’s preferences in the formulation of the model, calculating levels of satisfaction achieved with a certain set of EC targets, addressing the relationships between ECs and CAs, or representing the imprecision that is inherent in the process. Indeed, the goal programming (GP) model will be utilized for deriving optimum target levels of ECs in QFD. The customer’s preferences will be introduced explicitly through the concept of satisfaction functions (Martel and Aouni, 1996, 1998). The revelation of these functions is based on benchmarking data to integrate competitive analysis by customer perceptions of CAs into the decision-making process. Moreover, the relationships linking CAs and ECs and the ECs to each other are integrated by functional relationships. In the next section, we present a literature review where we highlight some developments related to the QFD. A general model of product planning is defined in Section 3. In Section 4, we propose a combined benchmarking and imprecise GP approach for integrating explicitly the customer’s preferences in the QFD planning. The proposed methodology is illustrated through an example of a car door design (Section 5). The purpose of the sixth section is to present some concluding remarks.

2. The concept of the QFD The QFD is a concept that includes both customer requirement management and product development systems, and which begins by sampling the consumer’s needs and preferences for a product through marketing surveys or interviews and organizing them as a set of ECs. By analysing the relationships among ECs and between CAs and ECs, while considering cost and technical constraints as well as organizational strategies, the QFD team is responsible for determining the fulfilment levels of ECs (Chen and Weng, 2006). The QFD team makes tradeoffs between the customers’ requirements and what the organization can afford. These tradeoffs are r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

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based on the achievement of the CAs by considering some factors such as the business competition, the limitation of resources, and organizational constraints. The issue of tradeoffs in QFD gave rise to development of systematic approaches integrating mathematical programming and decision-making tools for the QFD planning process that allows maximizing the customer’s satisfaction. In the QFD literature, we distinguish two main approaches. The first trend represents QFD approaches based on normalized technical importance rating. Wasserman (1993) was the first to propose a formal model of QFD planning using a normalized transformation on the relationship values contained in the relationship matrix to account for the dependency effects among ECs. Wasserman (1993) formulated the QFD planning process as a linear programming model to select the mix of ECs under a limitation of a given target cost, which would result in the highest level of customer satisfaction. Based on this approach, several models have been developed. For example, Bode and Fung (1998), Park and Kim (1998), Fung et al. (2003), and Ramanathana and Yunfeng (2009) integrated factor resources and correlations among CEs. Tang et al. (2002), Chen and Weng (2003), Chin et al. (2009), and Zhang and Chu (2009) used fuzzy set theory to consider the imprecision and vagueness in the QFD planning process. The second trend represents QFD approaches based on functional relationships that reflect the interactions between CAs and ECs (Thurston and Locascio, 1993). They interpreted the HoQ approach as a general formulation of a multi-attribute design optimization problem. It was implicitly assumed that the functional relationships between CAs and ECs can always be identified using engineering knowledge. It would be difficult to justify this assumption in a general decision-making context. Moreover, the interrelationships among ECs were not properly considered in the model (Kim et al., 2000). Kim (1997) and Moskowitz and Kim (1997) proposed similar mathematical programming models to determine the target levels of ECs. Kim (1997) has developed approximate equations representing the association among ECs based on the designer’s subjective judgement. Furthermore, Moskowitz and Kim (1997) have proposed linear regression models that are fitted to the customer and technical competitive analysis data. The equations are used as constraints in the optimization problem to find optimal target values for ECs. When a designed experiment is not practically possible, these approaches may be useful (Yang et al., 2003). Dawson and Askin (1999) have proposed a nonlinear mathematical program to establish optimal ECs by considering the cost and the time of product development. A prescriptive optimization approach developed by Kim et al. (2000) allows determining the optimal target values of ECs in QFD by defining the major model components in a crisp or a fuzzy manner using multi-attribute theory combined with fuzzy regression and fuzzy optimization theory. Based on Kim et al. (2000)’s approach, Bai and Kwong (2003) have proposed an interactive approach based on a genetic algorithm. Instead of determining one set of exact optimal target values for ECs, their approach can generate a set of solutions. Recently, Chen et al. (2004) and Fung et al. (2006) have proposed fuzzy optimization models by integrating the target market competitive dimension and financial factors. Chen et al. (2004) proposed to apply the fuzzy linear regression theory combined with fuzzy optimization theory with symmetric or non-symmetric triangular fuzzy coefficients for modelling the functional relationships between ECs and CAs and among ECs. Fung et al. (2006) have developed a hybrid linear programming model by integrating the least-squares regression into fuzzy linear regression r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

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to estimate the functional relationships under uncertainties. In these models, the fuzziness was treated only in estimating the functional relationships. Moreover, these functional relationships determined by fuzzy regression were considered as deterministic and strict constraints. Realistically, the functional relationships cannot be precise because they are computed from the benchmarking datasets, which are not necessarily precise and accurate. Besides the inherent shortcomings in each of the approaches mentioned above, there are some other general criticisms that could be addressed. In fact, these approaches contribute to reduce the subjectivity related to the QFD process. However, practitioners prefer to retain some control over the process and thus to be in charge to establish some required parameters of the QFD model. Moreover, they are reluctant to use a methodology that is perceived to be too theoretical and too complicated. Secondly, the functions representing customer satisfaction are built without taking into account the competition in the market place and the general customer perceptions. Consequently, these functions may not reflect accurately the customer’s preferences. Thirdly, most of these approaches (e.g., Kim et al., 2000; Bai and Kwong, 2003) are technically one-sided without considering the design budget, resulting in practice in an unreasonable and unreliable QFD plan. In fact, resources and cost budgets for achieving the target level of ECs for a product are not infinite, but limited. Therefore, the financial factor is also an important aspect and should not be neglected in QFD planning (Tang et al., 2002). Finally, there are different approaches to fuzzy mathematical programming, such as symmetric and asymmetric methods (Lai and Hwang, 1992). We also notice that these approaches only consider the case where the customers and the organization have particular membership functions (triangular and symmetric functions). The different models available in the QFD literature cannot be applied for all decision-making situations related to the QFD design process. Moreover, these models do not integrate explicitly the customer’s preferences. Thus, the aim of this paper is to introduce a comprehensive approach for the QFD planning process and design a model that can address some of the weaknesses related to the existing QFD formulations. A combined benchmarking and GP approach (based on the customer’s preferences) will be proposed to the design team in choosing target levels for ECs in an imprecise environment. This approach would allow the team to consider tradeoffs among various ECs, as well as to consider the imprecision or the fuzziness in the relationships linking CAs and ECs and the ECs to each other. Moreover, the proposed design approach helps to save time and determine a set of ECs that will result in the highest level of customer satisfaction subject to limited resources and other organizational restrictions. The decision-making process is more orderly and based on facts and data rather than opinion.

3. General QFD definition We have noticed that the basic concept of QFD in product design (new or improved) is to translate the CAs into determination of ECs that are generally conflicting. This can be illustrated by an HoQ. Assume that in a product design, m CAs denoted by CAi, i ¼ 1; 2; . . . ; m and n ECs denoted by ECj, j ¼ 1; 2; . . . ; n are considered. Let yi ðfor i ¼ 1; 2; . . . ; mÞ be the customer perception of the fulfilment degree of CAi, and xj ðfor j ¼ 1; 2; . . . ; nÞ be the fulfilment level of ECj. An HoQ provides information about the basic relationships between CAs and ECs and r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

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among ECs, along with the benchmarking dataset. This information can be used to establish the functional relationships expressing these interactions (Kim, 1997; Moskowitz and Kim, 1997; Dawson and Askin, 1999; Kim et al., 2000; Fung et al., 2006). Let fi ðfor i ¼ 1; 2; . . . ; mÞ be the functional relationships between yi and the levels of fulfilment of ECs, which means that yi ¼ fi ðx1 ; x2 . . . ; xn Þ and gj ðfor j ¼ 1; 2; . . . ; nÞ will be the functional relationships between xj and other fulfilment levels of ECs (i.e., xj ¼ gj ðx1 ; . . . ; xjÀ1 ; xjþ1 ; . . . ; xn Þ). Assume that there are multiple resources required for supporting the design of a product, including technical engineers, advanced equipment, tools, and facilities. Organizational resource constraints can then be formulated. Let Rl ðXÞ be the lth organizational resource constraint, l ¼ 1; . . . ; p, where p is the number of resource constraints. The product planning process, based on the first HoQ, consists of determining a set of x1 ; x2 ; . . . ; xn for ECs of a product to match or exceed the degree of overall customer satisfaction in the target market subject to limited organizational resources. The overall customer satisfaction can be measured in terms of satisfaction with the best levels of fulfilment of CAs on the market. Let CS be the degree of overall customer satisfaction for ðy1 ; y2 ; . . . ; ym Þ; the process of determining the fulfilment level of target values of ECs for a product can be formulated as a multi-objective optimization problem as follows: determine the optimal values of ECs x1 ; x2 ; . . . ; xn that maximize the overall customer satisfaction CS with ðy1 ; y2 ; . . . ; ym Þ, subject to two sets of constraints: G1: aspiration levels of the fulfilment degree of customer CAi, yi ðfor i ¼ 1; 2; . . . ; mÞ; G2: organizational resources, Rl ðXÞ. Additional constraints may be added to the above formulation as appropriate.

4. A combined benchmarking and imprecise GP for incorporating the customer’s preferences 4.1. Benchmarking of CAs in QFD The QFD design process begins by defining the desires and preferences of consumers of a product and organizing them as a set of CAs. Next, the CAs should be prioritized from the customers’ perspective. The analytic hierarchy process (Saaty, 1994) and the analytic network process (Saaty, 1996) have proven to be effective in generating the priorities of CAs using a group of customers (Fukuda and Matsuura, 1993; Karsak et al., 2002; Kahraman et al., 2006). After prioritizing the CAs, it should be viewed from the customer’s perspective using the concept of benchmarking. In the QFD design process, benchmarking compares the organization and its competitors in terms of quality performance regarding each CA, thus providing a solid factual foundation on which goals are set (Han et al., 2001). To a large extent, the quality of product is ultimately judged in terms of customer satisfaction. There are direct linkages between providing customer satisfaction and having a superior financial and competitive position (Zairi, 1996). Understanding and meeting customer satisfaction is one of the pillars of achieving speedto-market for manufacturers (Youssef, 1992). Customer satisfaction level is one of the critical success factors that are candidates for benchmarking (Camp, 1989). Understanding customer perceptions is essential to remain competitive. To do this, an organization should not only know the degree of customer satisfaction of the current product or service but also the customer r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

M. S. Cherif et al. / Intl. Trans. in Op. Res. 17 (2010) 85–102 Table 1 Benchmarking of CAs CAi yi y1 . . . yn Customer perception y0 i Comp1 ... Compv Min yli Max yu i Worst yw i

91

Best yb i

where: yli and yu : lower and upper bounds of aspiration levels with respect to yi, respectively (e.g., yli ¼ 1 and yu ¼ 5 if a five-point scale i i is used); y0 : customer perception of the fulfilment degree of CAi of the organization under study; i Comp1, Comp2. . . Compv: the main competitors in the target market, where v is the number of competitors; yb and yw : customer perceptions of the fulfilment degree of CAi with respect to yi, of the best and the worst competitor, i i respectively.

satisfaction of the competitors’ products. The customer’s satisfaction of the current product is related to the customer perception regarding how much the product meets the customer’s needs (Shen et al., 2000). In our approach, the competitive analysis provided by the benchmarking allows the development of the customer satisfaction functions of CAs that determine the optimal conception. A synthesis of the competitive analysis data of CAs is shown in Table 1. Note that if customer perception of the fulfilment degree of CAi of the organization seems to be the best (worst) regarding his main competitors, then yo ¼ yb ðyw ¼ yo Þ. i i i i

4.2. The establishment of satisfaction functions for CAs Customer satisfaction is measured in terms of satisfaction with the maximum levels of fulfilment of CAs. In such a case, the QFD team establishes the aspiration levels, yli and yu , for each CA i (aspiration interval). Then, the customer satisfaction will monotonously decrease with a design (X) where the yi ðXÞ tends towards the yli and it will increase when the yi ðXÞ tends towards the yu i (where yi ðXÞ is the perception of the fulfilment degree of CAi at X). Thus, customer’s preferences À on CAi at X can be through a satisfaction function, denoted as Fyi ðdÀi Þ, which measures how y satisfactory it is when yi ðXÞ takes on a particular value. The values of dÀi measure the negative y deviations from the maximum level yu . i The explicit consideration of customer’s preferences with respect to the fulfilment of CAs regarding the maximum aspiration level of each CAi (yu ) is as follows: based on competitive i analysis, we have defined yb and yw as customer perceptions of the fulfilment degree of CAi with i i respect to yi of the best and the worst competitor, respectively. Obviously, the customer would be completely satisfied when yb )yi )yu . His preferences decrease as the fulfilment degree of CAi i i tends towards the fulfilment degree of the worst competitor,yw , i.e., yw )yi < yb . The customer i i i would be completely dissatisfied when the fulfilment degree of CAi is lower than yw , i.e., i yli )yi < yw . For the purpose of illustration, we will consider the following customer satisfaction i function. r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

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1

0

Fig. 2. CAi fulfilment satisfaction functions.

However, the customer can consider a different shape of the satisfaction functions. The choice of these functions is based on their accuracy of reflecting the customer’s preferences. According to Fig. 2, the customer is completely satisfied with a design (his degree of satisfaction will be at its h i maximal value of 1) when negative deviations from the goals are within the interval dÀi 2 0; dÀb . y yi i i The customer satisfaction is decreasing for deviations belonging to the interval: dÀi 2 dÀb ; dÀw . y y y i i

Obviously, the customer is completely dissatisfied with a fulfilment degree of CAi between yw and i yli (i.e., dÀl )dÀi < dÀw ). A design with a fulfilment having a negative deviation greater than dÀl (it y yi yi yi is a kind of a veto threshold) will be rejected by the customer. This threshold makes the proposed model a partially non-compensatory model in the sense that a bad fulfilment cannot be compensated by a good one. À The satisfaction functions Fyi ðdÀi Þ can be expressed as follows: y 8 À if 0)dÀi )dÀb ; > fi1 ðdyi Þ ¼ 1; y yi < À fi2 ðdÀi Þ ¼ ðdÀw À dÀi Þ=ðdÀw À dÀb Þ; if dÀb < dÀi )dÀw ; Fyi ðdyi Þ ¼ y yi y yi y yi yi yi > : fi3 ðdÀ Þ ¼ 0; if dÀw < dÀi )dÀmin : yi y y y i i

The equivalent representation of this function requires the introduction of three binary variables bi1 ; bi2 and bi3 . These variables are defined as follows:  1; if 0)dÀi )dÀb ; y yi bi1 ¼ 0; otherwise:  1; if dÀb < dÀi )dÀw ; y yi yi bi2 ¼ 0; otherwise: and bi3 ¼  1; if dÀw < dÀi )dÀl ; yi y yi 0; otherwise:

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À Thus, the functions Fyi ðdÀi Þ can be written in the following equivalent form: y À Fyi ðdÀi Þ ¼bi1 fi1 ðdÀi Þ þ bi2 fi2 ðdÀi Þ þ bi3 fi3 ðdÀi Þ y y y y

93

¼ bi1 ð1Þ þ bi2 ðdÀw À dÀi =dÀw À dÀb Þ þ bi3 ð0Þ y y y y i i i

¼ bi1 þ bi2 dÀw =ðdÀw À dÀb Þ À bi2 dÀi =ðdÀw À dÀb Þ: y y y y y y i i i i i

Note that the terms À of the functions are nonlinear terms. Our objective is to maximize the customer’s satisfaction for the fulfilment of CAs. Thus, the À satisfaction functions Fyi ðdÀi Þ are to be maximized. The equivalent representation to the y mathematical program, which aims to maximize these functions, can be written as follows: Max: Z ¼ bi1 þ bi2 dÀw =ðdÀw À dÀb Þ À bi2 dÀi =ðdÀw À dÀb Þ y y y y y y i i i i i

bi2 dÀi =ðdÀw y yi

dÀb Þ yi

À Fyi ðdÀi Þ y

ð1Þ

Subject to: dÀb bi2 þ dÀw bi3 )dÀi )dÀb bi1 þ dÀw bi2 þ dÀl bi3 ; y y y y y y i i i i i

X3 k¼1 bik ¼ 1;

bik ¼ f0; 1g and dÀi *0 ðfor k ¼ 1; 2; 3 and i ¼ 1; 2; . . . ; mÞ: y
À It should be noted that if yb ¼ yu and/or yw ¼ yli , the shape of Fyi ðdÀi Þ as well as its i i i y mathematical program change. Figure 3 shows the shape of the function and the corresponding À mathematical program of Fyi ðdÀi Þ for three such cases. y

4.3. Integrating the customer’s preferences in the imprecise GP model The definition of each objective related to each CAi is as follows: yi þ dÀi À dþi ¼ yu i y y dÀi y dþi y ðfor i ¼ 1; 2; . . . ; mÞ; ð2Þ and are variables of negative and positive deviations from aspiration levels (goals) yu . where i We have indicated that multiple resources are required for supporting the design of a product. If the resources can be aggregated in financial terms, the fulfilment/improvement costs of ECs can be determined. Generally, a design of a product requires a based budget for the fulfilment of minimum levels of ECs, denoted by xlj . It is the minimum budget required for the design of a product. Then, an improvement budget B of ECs above their minimum levels can be determined by the organization. Let cj be the improvement cost per unit of ECj above the minimum level, and xj be the number of units of improvement of ECj, i.e., xj ¼ xj À xlj . An improvement budget constraint can be introduced as follows: Xn c x )B; ð3Þ j¼1 j j where xj ¼ xj À xlj ; xj ffi gj ðX j Þ and X j ¼ ðx1 ; . . . ; xjÀ1 ; xjþ1 ; . . . ; xn ÞT . r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

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Case

Function Shape
Max Z =
1

Mathematical Program

Suject to :

(A)

0

and

Max Z =
1

(B)

Suject to:

0

and

1

Max Z = Suject to :

(C)

and
0

Fig. 3. Particular cases for customer’s satisfaction functions.

This budget constraint allows taking into account the limits of the improvement budget and interaction between CAs and ECs, and the correlation among ECs. Based on Martel and Aouni’s (1996, 1998) models and by considering the satisfaction functions À Fyi ðdÀi Þ presented in Equation (1), functional relationship, the goal presented in Equation (2), and y the design budget constraints of Equation (3), the multi-objective programming model for deriving optimum targets of ECs can be constructed as follows: Max: CS ¼ Subject to: yi þ dÀi À dþi ¼ yu ðfor i ¼ 1; 2; . . . ; mÞ; i y y Xn c x )B ðfor j ¼ 1; 2; . . . ; nÞ; j¼1 j j yi )yu ðfor i ¼ 1; 2; . . . ; mÞ; i xlj )xj )xu ðfor j ¼ 1; 2; . . . ; nÞ; j r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

Xm i¼1 À oyi Fyi ðdÀi Þ y

ð4Þ

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dÀi ; dþi ; yi and xj *0 ðfor j ¼ 1; 2; . . . ; n and i ¼ 1; 2; . . . ; mÞ; y y where yi ffi fi ðXÞ; X ¼ ðx1 ; . . . ; xn ÞT ; xj ffi gj ðX j Þ; X j ¼ ðx1 ; . . . ; xjÀ1 ; xjþ1 ; . . . ; xn ÞT ; yi: customer perception of the CAi fulfilments; xj: fulfilment level of ECj; fi: functional relationship between CAi and ECs; gj: functional relationship between ECj and other ECs; xj ¼ xj À xlj : quantity improvement of ECj ; oyi : relative importance weight assigned to CAi; yu : best customer i perception of the fulfilment degree of CAi (aspiration level for yi); and xlj and xu : minimum and j maximum fulfilment level of xj. The objective is to maximize an overall customer satisfaction with the fulfilment degrees of CAs under a design budget constraint. The functional relationships of model 4 may be used as strict (deterministic) or flexible (imprecise) constraints. When the constraints are strict, the violation of any constraint by any amount will make the solution (design) infeasible. Considering the fact that, in practice, the estimated functional relationships would probably be imprecise, permitting small violations would be more realistic. This can be done through imprecise (flexible) constraints. The flexibility on functional relationships can be expressed as follows: ð1 À aÞfi ðXÞ)yi )ð1 þ aÞfi ðXÞ; ð1 À aÞgj ðX j Þ)xj )ð1 þ aÞgj ðX j Þ; ð5Þ ð6Þ

where a ð0)a)1Þ is the degree of flexibility that can be allowed in the functional relationships’ constraints. Taking into account this flexibility allowed in the functional relationships and assuming the case where yb < yu and yw > yli , model 4 can be transformed as follows: i i i   Xm À Max: CS ¼ oyi bi1 þ bi2 dyw =ðdÀw À dÀb Þ À bi2 dÀi =ðdÀw À dÀb Þ ð7Þ y y y y y i¼1 i i i i i

Subject to: yi þ dÀi À dþi ¼ yu ðfor i ¼ 1; 2; . . . ; mÞ; i y y dÀb bi2 þ dÀw bi3 )dÀi )dÀb bi1 þ dÀw bi2 þ dÀl bi3 ; yi y yi yi yi yi Xn c x )B ðfor j ¼ 1; 2; . . . ; nÞ; j¼1 j j ð1 À aÞfi ðXÞ)yi )ð1 þ aÞfi ðXÞ ðfor i ¼ 1; 2; . . . ; mÞ; ð1 À aÞgj ðX j Þ)xj )ð1 þ aÞgj ðX j Þ ðfor j ¼ 1; 2; . . . ; nÞ; yi )yu ðfor i ¼ 1; 2; . . . ; mÞ; i xlj )xj )xu ðfor j ¼ 1; 2; . . . ; nÞ; j X3 b ¼ 1 ðfor j ¼ 1; 2; . . . ; n and i ¼ 1; 2; . . . ; mÞ; k¼1 ik bik ¼ f0; 1g ðfor i ¼ 1; 2; . . . ; m and k ¼ 1; 2; 3Þ; dÀi ; dþi ; yi and xj *0 ðfor j ¼ 1; 2; . . . ; n and i ¼ 1; 2; . . . ; mÞ; y y where yi ffi fi ðXÞ; X ¼ ðx1 ; . . . ; xn ÞT ; xj ffi gj ðX j Þ; X j ¼ ðx1 ; . . . ; xjÀ1 ; xjþ1 ; . . . ; xn ÞT : The solution of this model (with a > 0) gives the competitive fulfilment levels of ECs and CAs providing a better customer satisfaction. r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

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5. Numerical example To illustrate the proposed model, we consider the same example of the car door design as given by Hauser and Clausing (1988), Wang (1999), Moskowitz (1993), Kim et al. (2000), and Bai and Kwong (2003). The HoQ has five CAs and six ECs. The available data (for customer and technical competitive analysis) are limited (the usual case in practice) and consist of only seven data points, which have been collected from the organization and its six main competitors (Kim et al., 2000). The information regarding these CAs and ECs as well as the benchmarking data for CAs are summarized in Tables 2 and 3. ~ ~ The fuzzy relationship equations, fi and gi were generated using the fuzzy regression method and the benchmarking data set (Kim et al., 2000; Bai and Kwong, 2003). For example, y1 and x1 can be obtained by using the following equations: y1 ffi 8:11 À 0:56x1 þ 0:04x4 x1 ffi 15:05 À 0:54x2 þ 0:54x4 : ð8Þ ð9Þ

Moreover, assume that the improvement costs by one unit of ECj (for j 5 1, 2, . . . , 5) above their minimum levels are c1 5 25, c2 5 50, c3 5 45, c4 5 55, c5 5 20, and c6 5 1.5. To establish the satisfaction function of the fulfilment degree of CA1, we consider that the customer perception of the fulfilment degrees of the best competitor (Comp3) and the worst competitor (organization) are yb ¼ 4 and yw ¼ yo ¼ 1:6. Thus, the customer is completely satisfied 1 1 1 when the fulfilment degree y1 is between the fulfilment degree of competitor Comp3 and the
Table 2 Information regarding the ECs ECs Energy to close the door (x1) ft-lb 11 8 12 Check force on level ground (x2) lb 12 9 15 Check force on 10% slope (x3) lb 6 5 9 Door seal resistance (x4) lb/ft 3 1 5 Road noise reduction (x5) db 9 5 10 Water resistance (x6) psi 70 50 100

Measurement units Organization’s car door Minimum Maximum

Table 3 Benchmarking data of CAs for the car door design example CAi (yi) Customer perception (yli ¼ 1 and yu ¼ 5) i Comp1 Easy to close from outside (y1) Stays open on a hill (y2) Rain leakage (y3) Road noise (y4) Cost (y5) 3.7 1.8 2.9 4.9 2.5 Comp2 3.3 1.1 2.7 2.2 3.8 Comp3 4.0 3.6 3.9 3.0 2.9 Comp4 3.2 2.9 3.1 3.8 3.5 Comp5 1.7 1.4 2.8 4.2 4.3 Comp6 2.7 3.5 4.0 3.2 3.6 yo i 1.6 1.7 3.7 3.0 4.0

Values in bold indicate the best and worst competitor in the target market as determined by customer perceptions of degree of fulfilment of CAs.

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1

0 1 3.4 4

Fig. 4. CA1 fulfilment satisfaction function.

maximum fulfilment degree, i.e., 4)y1 )5. The customer preferences decrease as the fulfilment degree of CA1 tends towards the fulfilment degree of the worst competitor, which is the organization for this attribute, yw ¼ yo ¼ 1:6, i.e., 1:6)y1 < 4. The corresponding graph of the 1 1 satisfaction function is shown in Fig. 4. À The satisfaction function Fy1 ðdÀ1 Þ is at its maximal value of 1 (i.e., the customer is completely y satisfied) when negative deviations are within the interval dÀ1 2 ½0; 1Š: The customer’s satisfaction y will decrease within the interval dÀi 2 Š1; 3:4Š: Obviously, the customer is completely dissatisfied y with a CA1 fulfilment between 1.6 and 1 (i.e., 3:4 < dÀ1 )4). A design with a fulfilment degree y lower than 1 (i.e., dÀ1 > 4) will be rejected by the customer. The analytical form of the satisfaction y À function Fy1 ðdÀ1 Þ is as follows: y Max: Z ¼ b11 þ 1:4167b12 À 0:4167b12 dÀ1 y Subject to: b12 þ 3:4b13 À dÀ1 )0; y dÀ1 À b11 À 3:4b12 À 4b13 )0; y b11 þ b12 þ b13 ¼ 1; b11 ; b12 ; b13 ¼ f0; 1g and dÀ1 *0: y By considering the fuzzy relationship equation of y1 (8) and the customer aspiration level yu ¼ 5, the customer goal constraint for CA1 can be written as follows: 1 0:56x1 À 0:04x4 þ dÀ1 À dþ1 ¼ 3:11: y y ð11Þ To apply model 4 to the customer satisfaction functions, it is necessary to consider the relative importance weights assigned to each specified CA (oy1 ¼ 0:3; oy2 ¼ 0:2; oy3 ¼ 0:1; oy4 ¼ 0:1 and oy5 ¼ 0:3). The objective function of model 7 can be written as follows:
À À À À À Max: CS ¼ 0:3Fy1 ðdÀ1 Þ þ 0:2Fy2 ðdÀ2 Þ þ 0:1Fy3 ðdÀ3 Þ þ 0:1Fy4 ðdÀ4 Þ þ 0:3Fy5 ðdÀ5 Þ: y y y y y

ð10Þ

ð12Þ

This objective function will be optimized subject to the functional relationship, goals and design budget constraints, as well as to the satisfaction function constraints. Using the LINGO software, the optimal solution obtained for various levels of flexibility a is summarized in Table 4. CS r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

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Current values (before optimization) x1 x2 x3 x4 x5 x6 y1 (0.3) y2 (0.2) y3 (0.1) y4 (0.1) y5 (0.3) CS (%) B (CU) 11 12 6 3 9 70 1.6 1.7 3.7 3.0 4.0 40.46 440

a50 10.31 11.59 6.58 2.81 8.12 65.54 2.45 1.81 3.70 2.93 4.3 56.69 443.61

a 5 0.05 8.48 13.61 7.57 2.27 6.27 59.58 3.28 2.82 3.48 3.47 4.3 77.44 467.77

a 5 0.10 8.00 14.85 8.35 2.95 6.29 60.4 3.37 3.12 4.11 3.81 4.29 91.68 591.9

Table 5 The current CS values for main competitors Competitors CS (%) Organization 40.46 Comp1 43.39 Comp2 42.93 Comp3 68.87 Comp4 60.08 Comp5 41.83 Comp6 65.00

represents the percentage of overall customer satisfaction (objective function value), and B denotes the values of the improvement budget expressed in cost units (CU). The CS value was computed for the six main competitors within the market place (see Table 5). The CS values and B will be used as performance criteria to compare the results. We compare the existing designs of this example of the organization and its competitors with those obtained by solving model 7, focusing on customer perception of the design quality and improvement budget. First, we need to examine where the organization initially stands in relation to its competitors. The customer competitive analysis information contained in Table 3 indicates that the organization’s product currently is weak in CAs y1, y2 and y4, moderate in y3 and strong in y5, and has the lowest value of CS (40.46%) among the seven competitors. Competitors Comp3 and Comp6 have the highest values of CS (68.87% and 65.00%, respectively), and competitor Comp4 also has a high CS value of 60.08%. The best CS value of the design from model 7 with crisp functional relationship constraints (i.e., a 5 0) is much higher than the current organization’s CS value (56.67% compared with 40.46%) and is comparable to that of competitor Comp4 (60.08%). Compared with the organization’s current design, the model improved y1, y2 and y5 (which have importance weights of 0.3, 0.2 and 0.3, respectively) by trading off y4, which is a least significant attribute with importance weights of 0.1. Moreover, a small increase in the improvement budget (3.61 CU about 0.8%) increased the customer satisfaction by 16.21%. The EC values were determined to achieve such value trade-offs in the most efficient way. r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

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In this example, competitors Comp3, Comp4 and Comp6’s car doors have higher CS values than the design from the model with crisp constraints. According to Kim et al. (2000), this could happen because the optimization uses as constraints the functional relationships assessed from the benchmarking dataset, which are not perfect. Thus, it would be more sensible to permit some flexibility in the constraints to obtain more realistic results. When comparing the solution (design) obtained with a 5 0.05 with that of a 5 0, we notice that CS increased by 20.77%. If the organization decides to carry out this level of customer satisfaction, it should increase its budget improvement by 24.16 CU (about 5.5%). With 5% flexibility, the model improved y1, y2 and y4 by trading off with y3, which is a least significant attribute with importance weights of 0.1. Moreover, the model yielded y1 and y2 significantly higher than the design without flexibility as well as the organization’s current design. The values of y1, y2, and y4 are particularly negatively correlated with x1 and x5, and positively with x2 and x3. In order to increase y1, y2 and y4, the resulting design reduced the levels of x1 and x5 (i.e., from 10.31 to 8.48 for x1 and from 8.12 to 6.27 for x5) and increased the levels of x2 and x3 (i.e., from 11.59 to 13.61 for x2 and from 6.58 to 7.57 for x3). The model considers all such interactions between CAs and ECs as well as those among the ECs simultaneously, and determines the optimal EC levels. Taking into account these interactions and with a flexibility between 0% and 5%, we notice that for x1, x4, x5 and x6 the lower is better, and for x2 and x3 the higher is better. Comparing the design with 10% flexibility with the designs with 0% or 5% flexibility, we notice that the values of x4, x5 and x6 have increased (slightly for x5 and x6) and the value of y3 has also increased. Then, with a flexibility between 5% and 10%, we notice that, for x1 the lower is better and for x2, x3 and x4 the higher is better. This implies that large flexibility will allow less interaction among the model elements. Then, the QFD team should allow flexibility only if the achieved customer satisfaction is weak. In this example, the organization could be satisfied with a customer satisfaction of 77.44%. If it would like to reach a level of 91.68%, it should then increase its current improvement budget by 34.52%. In fact, the assessed functional relationships are virtually never precise. It would be reasonable to relax the system equations in some way to compensate for the fuzziness of the relationships (Kim et al., 2000). Without allowing such flexibility, the designers cannot achieve what is realistically attainable (e.g., a 20.75% increase in customer satisfaction, when 5% flexibility was allowed).

6. Concluding remarks In this paper, in order to overcome the shortcomings of the conventional QFD process as well as of current approaches, we have proposed a GP approach with satisfaction functions combined with the benchmarking tool and functional relationships in order to enhance the effectiveness and efficiency of QFD as a means to integrate explicitly the customer’s preferences into the product design process. The proposed model allows the QFD team to consider many aspects of the design process such as: (a) the interactions between CAs and ECs, (b) cost tradeoffs among the various ECs, and (c) the imprecision related to the CAs. The proposed approach can be useful for the QFD planning process because it proceeds through a simple and comprehensive process that requires less information from the manager. r 2009 The Authors. Journal compilation r 2009 International Federation of Operational Research Societies

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The manager is more involved in the product design process where a series of sensitivity analyses can be performed to assess the effects of changes in decision elements. The developed model can be applied to a wide variety of product design problems where multiple design criteria and functional design relationships are involved in an uncertain, qualitative, and fuzzy manner. The output of this paper offers new research directions within the quality field.

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