Assessing the inherent flexibility of product families for meeting ...

Int. J. Manufacturing Technology and Management, Vol. 10, Nos. 2/3, 2007

227

Assessing the inherent flexibility of product families for meeting customisation requirements Bin Dan* Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology, Kowloon, Hong Kong College of Economics and Business Administration, Chongqing University, Chongqing 400044, PR China E-mail: [email protected] *Corresponding author

Mitchell M. Tseng Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology, Kowloon, Hong Kong E-mail: [email protected] Abstract: This paper presents a systematic approach based on the axiomatic design theory to assess the inherent flexibility of the product family to generate the product variants for customers’ needs. Assuming a decoupled or un-couple product design, the inherent flexibility of a product family for meeting a customisation requirement is defined as the ratio between the effectively relative change and the required relevant changes due to cascade effects responding to the change of the corresponding functional requirement. The Flexibility Indices (FIs) of a base product with two specific conditions, the uncoupled design and modularised design are discussed. The variety generation equations are built, and the characteristics of Flexibility Index (FI) are observed. A simplification approach of comparing FIs is also proposed. To illustrate this concept, an example of FIs of a motorcycle product family is introduced and discussed. Keywords: mass customisation; Flexibility Index (FI); product family. Reference to this paper should be made as follows: Dan, B. and Tseng, M.M. (2007) ‘Assessing the inherent flexibility of product families for meeting customisation requirements’, Int. J. Manufacturing Technology and Management, Vol. 10, Nos. 2/3, pp.227–246. Biographical notes: Bin Dan is a Professor in the College of Economics and Business Administration at Chongqing University. He is also a visiting scholar in the Department of Industrial Engineering and Engineering Management at Hong Kong University of Science and Technology. He received his PhD in Mechanical Engineering from Chongqing University. His research interests are mass customisation, logistics and supply chain management. He has given various presentations, contributed a few chapters in books, published papers in journals and organised workshops and conferences. Copyright © 2007 Inderscience Enterprises Ltd.

228

B. Dan and M.M. Tseng Mitchell M. Tseng is a Professor in the Department of Industrial Engineering and Engineering Management at Hong Kong University of Science and Technology. He received his PhD in Industrial Engineering from Purdue University. His research interests are mass customisation, manufacturing systems design and service systems engineering. He has given various presentations, contributed a few chapters in books, published papers in journals and organised workshops and conferences.

1

Introduction

Mass customisation, aiming to provide customer satisfaction with increasing variety and customisation without a corresponding increase in cost and lead time (Tseng and Jiao, 1996), has recently received a significant amount of attention by the business and industry communities. It is a new paradigm for industries to deliver a wide range of products and services that meet specific needs of individual customers at a cost and efficiency near that of mass production (Silveira et al., 2001; Tseng and Du, 1998). Mass customisation has also several significant ramifications in business. It can potentially develop customer loyalty, propel company growth and increase market share by widening the product range (Pine, 1993). Mass customisation provides diverse end products that can be enjoyed by different customers. Customisation emphasises the difference among or uniqueness of products. An important step towards this goal will be the development and proliferation of design repositories that are capable of creating various customised products (Jiao and Tseng, 1999). Customised products are slight variations of standard configurations and are typically developed in response to a specific order by the customer (Ulrich and Eppinger, 2000). Owing to similarity among a group of customised products, reusability/ commonality suggests itself as a natural technique to facilitate increasingly efficient and cost-effective production realisation. Maximising reusability/commonality across internal modules, tools, knowledge, processes, components and so on means that the advantages of low costs and mass production efficiency can be expected to maintain the integrity of the product portfolio and the continuity of the infrastructure (Tseng and Jiao, 2001). Product family, as a set of products that share common technology and address a related set of market applications, is a means to improve the commercial variety while limiting the development, manufacturing and servicing efforts (Erens and Verhulst, 1997; Meyer and Lehnerd, 1997). Developing product families based on the existed product portfolio and production capability of a firm has been recognised as an effective means to provide customised products with a high reusability/commonality. However, high commonality within a product family can have major drawbacks, such as lacking distinctiveness, hindering innovation and creativity and compromising product performance (Thevenot and Simpson, 2004). Thus, it is necessary to resolve the inherent trade-off between commonality and distinctiveness, that is, to balance the commonality of the products in the family with the individual performance (i.e. distinctiveness) of each product in the family (Simpson, 2004). A few researchers had strived to develop design metrics for trade-off analysis of commonality and distinctiveness. Martin and Ishii (1997, 2000) developed quantitative tools to determine a customer preference for variety and to estimate manufacturing costs

Assessing the inherent flexibility of product families

229

of providing variety. They proposed the Commonality Index, Differentiation Index and Set-up Index to measure the number of unique parts, where a product is differentiated and added, and the product switchover costs separately (Martin and Ishii, 1997), and then developed the Generational Variety Index to indicate the amount of redesign required for a component to meet the future market requirements, and the Coupling Index to indicate the strength of the coupling between the components in a product (Martin and Ishii, 2000) based on the definition of the coupling founded by Ulrich (1995). Messac et al. (2002) proposed a Product Family Penalty Function (PFPF) to aid in the selection of common and scaling parameters for families of products derived from scalable product platforms. Then, Simpson and D’Souza (2004) applied the PFPF help to minimise the variations of design variables within the product family by minimising the percent variation. In the development process of a product family, it is important to describe and map the product family from the functional domain to the physical domain (Erens and Verhulst, 1997; Jiao and Tseng, 1999; Suh, 1990, 2001). The aforementioned researches about the commonality and distinctiveness focus on the components of a product family or a product platform in the physical domain. It is lack of research on the commonality and distinctiveness in the functional domain and the mapping between the two domains. Suh (1990, 2001) proposed two designed axioms: the Independence Axiom and the Information Axiom, which represent the important mapping relationship of product characteristics between the functional domain and the physical domain. These are adopted not only in the design of a single product but also in that of a product family. On the basis of the Information Axiom, Jiao and Tseng (2004) proposed customisability indices to assess the added value of customisation with respect to the impact of customisation on the loss of scale economy in design and production. On the basis of the Independence Axiom, this paper will propose a Flexibility Index (FI) to indicate the facility and adaptability of a product family mapping from the functional domain to the physical domain for mass customisation.

2

Product family for mass customisation

2.1 Description of product family A product family is a set of products that are derived from a common platform (Meyer and Lehnerd, 1997). Each individual product within the family (i.e. a product family member) is called a product variant. While possessing specific features/ functionality to meet a particular set of customer requirements, all product variants are similar in the sense that they share some common customer-perceived value, common structures and/or common product technologies, that form the platform of the family (Tseng and Jiao, 2001). A product can be described by a set of Functional Requirements (FRs) in the functional domain or a set of Design Parameters (DPs) in the physical domain. FRs are a minimum set of independent requirements, which completely characterise the functional needs of a product, while DPs are the key physical variables that characterise the design to satisfy the specified FRs (Suh, 2001).

230

B. Dan and M.M. Tseng

A product family can be generated by common bases, differentiation enablers and configuration mechanisms (Tseng and Jiao, 2001). The common bases are the shared elements among different products in the product family. These shared elements can be in the form of either common FRs in the functional domain or common DPs in the physical domain. The differentiation enablers are basic elements making products that are different from one another. They are the sources of variety within the product family. In the functional domain, the differentiation enablers can be in the form of optional FRs or selectable FR values, while in the physical domain, they can be embodied in choice or/and variable DPs. The configuration mechanisms define the rules and means of driving product variants. Three configuration mechanisms can be identified: selection constraints, include conditions and variety generation. The variety generation refers to the way in which the distinctiveness of a product embodiment can be created (Du et al., 2001). It focuses on the physical realisation of customised products.

2.2 Generation of product variants in a customised product family Customised products are usually improvement products, not completely new products, so the product variants in a customised product family can be generated by a base product and some operations of variety generation. Four basic methods of variety generation can be identified, including scaling, attaching, detaching and swapping (Du et al., 2001), as shown in Figure 1. They are also called scaling, adding, removing and substituting (Simpson, 2004). Figure 1

Basic methods of variety generation: (a) scaling (b) attaching (c) detaching and (d) swapping

Scaling is that the value (V) of a DP changes from V(1) to V(2), following the change of corresponding FR. Attaching is that a DP corresponding an optional FR is attached to a base product or product variant to create a new product variant. Detaching is that a DP corresponding an optional FR is detached from a base product or product variant to create a new product variant. Swapping is that a DP of a base product or product variant is substituted by another DP to meet another value of corresponding


231

FR. More complex variety generation methods can be composed of employing these basic methods recursively with reference to the hierarchical decomposition of product structures.

3

Flexibility index

To meet the diverse customers’ requirements may induce increase of cost because of the complexity of design. Thus, there is a broad economic question of the cost of design changes that offer the possibility of meeting customers’ needs. Though the question of the price of implementing the changes, such as changing tools, fixtures, materials and finishing, depends on the fluctuation of market price, it is not the intent of this paper to address the issue of market price. Instead, from the design theory perspective, the shadow price (or marginal output) of design changes for meeting customers’ requirements can be addressed independent of the implementing cost. High variety and low complexity are the contradictories of a customised product family. With an effort to meet the potential individual requirements of customers and attract customers, manufacturers may advertise a wide variety product line designed to appeal to every customer’s taste. However, there is a significant potential drawback to high variety strategies. If a customer is overwhelmed by huge assortment offered or frustrated by the complexity involved with making a choice, he/she may delay the decision or give up purchasing (Huffman and Kahn, 1998). In addition, there are costs to actually providing the customised products. The key to customer satisfaction in the design for mass customisation is to provide customers the effective product variants mapping their requirements, but not to overwhelm and frustrate them by the huge assortment and complexity. Customisation suggests to do for part of product features rather than for each of them (Kahn, 1998; Moore et al., 1998), so it is efficient and tangible to select the suitable part of FRs and DPs of a product family for customisation rather than all of them. On the basis of the axiomatic design theory, FI is proposed to evaluate the flexibility of FRs and DPs of a product family, which can assist to select the customised FRs and DPs.

3.1 Definition of flexibility index A customised product family can be generated from a base product. In the context of axiomatic design, in an ideal design, the number of DPs is equal to the number of FRs, and the FRs always maintained independent from each other (Suh, 2001). Product design can be considered as mapping between the FRs in the functional domain and the DPs in the physical domain, described by design equation (1). {FR} = [ A]{DP}

(1)

where [A] is the design matrix. According to the Independent Axiom of design, an uncoupled design with a diagonal design matrix or a decoupled design with a lower triangular design matrix is accepted (Suh, 2001). An uncoupled design can be considered as a kind of decoupled design, whose off-diagonal elements in the design matrix are zero.

232


Generally, a decoupled design of a base product with n FRs and n DPs can be expressed in Equation (2).  FR1   A11  FR   A  2   21  =  M   M FR n   An1

0 L 0   DP1  A22 L 0  DP2    M O M  M   An 2 L Ann  DPn 

(2)

In an FR, FRi, is changed to FRi + δ FRi for customisation, the corresponding DP, DPi, will be changed to DPi + δ DPii adapted to the change of FRi, and DPj, j = i + 1, i + 2, …, n, will also be changed to DPj + δ DPji to eliminate the influence of the change of DPi. The change of DPi, δ DPii, is valuable change for customisation of FRi, whereas the change of DPj, δ DPji, j = i + 1, i + 2, …, n, are valueless change for customisation of FRi. δ DPii and δ DPji, j = i + 1, i + 2, …, n, can also be expressed as

δ DPii = α DPii DPi δ DPji = α DPji DPj ,

(3)

j = i + 1, i + 2,K , n

where α DPii is called valuable relative change, which is needed by adapting the change of FRi, and αDPji, j = i + 1, i + 2, …, n, are called valueless relative change, which should be best eliminated. The FI of DPi, FIi, which depicts the efficiency of the change of DPs for customising FRi, can be defined as the ratio of the effective change α DPii to the required relevant changes due to cascade effects of the effective changes. The larger FIi means that the change of DPi make less impacts on other DPs, so the DPi is more suitable for customisation in the physical domain. The FIi is expressed as FIi =

α DPii

∑

α j =1 DPji

n

=

α DPii α DPii + ∑ j =i +1 α DPji n

=

1 1 + ∑ j =i +1 α DPji α DPii n

(4)

Then, 0 ≤ FIi ≤ 1. If m DPs (1 ≤ m ≤ n) of a base product are chosen to customise, the FI of the base product, FIB, is equal to the product of the m FIs of the chosen DPs, that is, m

FI B = ∏ FICi

(5)

i =1

where FiCi is the FI of the ith chosen DP, i = 1, 2, …, m. Then, 0 ≤ FIB ≤ FiCi , i = 1 ,2, …, m.

3.2 Basic equations for customisation On the basis of Equations (2) and (3), we get Aiiα DPii DPi = δ FR i j −1

∑A k =i

jk

α DPki DPk + A jjα DPji DPj = 0,

j = i + 1, i + 2,K , n

(6)


233

Equation (6) is called basic equation for customisation. Then,

α DPii =

δ FRi Aii DPi j −1

α DPji = − ∑ k =i

(7a)

A jk DPk α , A jj DPj DPki

j = i + 1, i + 2, K , n

(7b)

Introduce coefficients, which are Cii = 1 j −1   Ajk C ji = ∑  − Cki ,  A  k =i  jj 

j = i + 1, i + 2,K , n

then

α DPji =

DPi C jiα DPii , DPj

j = i + 1, i + 2,K , n

Introduce parameters, which are

α ji =

α DPji DPi = C ji , DPj α DPii

Replace the α DPji α DPii

j = i + 1, i + 2,K , n

(8)

in Equation (4) by Equation (8), then the FI can also be

expressed as FIi =

1 1 + ∑ j = i +1α ji n

=

1 1 + ∑ j = i +1 C ji DPi / DPj n

(9)

Aij = 0 ∀i ≠ j → FIi = 1

3.3 Uncoupled design If the design of a base product is uncoupled, Aij = 0, i ≠ j

we obtain

α DPji = 0,

j = i + 1, i + 2,K, n, i = 1,2, K , n

then FIi = 1, i = 1,2,K , n FI B = 1

Thus, a base product with uncoupled design can get the maximum FIs.

(10)

234


3.4 Modularity When the design matrix of a decoupled design can be divided into submatrices, that is,  FR1   A1  2   FR   0  =  M   M FR N   0

0   DP1    L 0   DP 2    O M  M   L AN  DP N  L

0 A2 M 0

(11)

the design is called modularised design. Each group of DPs, mapping a group of FRs, can be integrated into a module. The design equation (11) can be transformed into N equations, that is,

{FR } =  A  {DP } {FR } =  A  {DP } 1

1

1

2

2

2

(12)

L

{FR } =  A  {DP } N

N

N

If a DP in a module is changed, the DPs in other modules will not be influenced by this change. For example, when DPi in module I is changed to DPi (1 + α DPii) to meet the change of FRi, DPj in module J, J ≠ I, need not be changed, that is,

α DPji = 0, j ∈ J , i ∈ I , J ≠ I Therefore, the different modules of a modularised product can be customised independently.

3.5 Variety generation equations 3.5.1 Scaling Obviously, scaling may be regarded as changing a DP of a base product to meet the change of corresponding FR, so it should adapt itself to the basic equations for customisation. When a DP, for example, DPi, is scaled from DPi (Vi(1)) to DPi (Vi(2)) to meet the change of FRi, δ FRi, the final value of DPi is

(

)

(

)

DPi Vi (2) = DPi Vi (1) +

δ FR i Aii

and the scaled value of DPi, δ DPii, that is, the valuable change for customisation of FRi, is

δ DPii = DPi (Vi (2) ) − DPi (Vi (1) ) =

δ FRi Aii

where, DPi (Vi (1) ) and DPi (Vi (2) ) are the same DP with different values. Then, the valueless change for customisation of FRi, δ DPji, can be calculated by

δ DPji = α DPji DPj = C ji δ DPii ,

j = i + 1, i + 2,K , n


235

If α DPji = 0, j = i + 1, i + 2, …, n, that is, FIi = 1, then δ DPji = 0, j = i + 1, i + 2, …, n, that is, the valueless change for scaling DPi is not generated.

3.5.2 Attaching When an additional FR is added to a base product, a corresponding DP is attached to the base product. A DP, which can meet the FR and maintain an uncoupled or a decoupled design, is accepted. When a DP, DPi, mapping an additional FR, FRi, is attached to a base product with n FRs and n DPs, DPj, j = i + 1, i + 2, …, n, will be changed to DPj (1+α DPji) to eliminate the influence of attaching DPi. There are i −1

FR i = Aii DPi + ∑ Aki DPk k =1

A ji DPi +

j −1

∑A

k = i +1

jk

(13)

α DPki DPk + A jjα DPji DPj = 0 j = i + 1, i = 2,K , n + 1

Equation (13) is called attaching equations. Let i −1

δ FR i = FR i − ∑ Aki DPk k =1

and

α DPii = 1 the attached equations can be transformed into Aiiα DPii DPi = δ FR i j −1

∑A k =i

jk

α DPki DPk + A jjα DPji DPj = 0 j = i + 1, i + 2,K, n + 1

(14)

the same as the basic equations for customisation. Thus, the approach to the customisation of base product also can be applied to attaching. If there are several DPis, DPi1 , DPi2 , …, DPiL , which can meet FRi, and each DPi corresponds to a group of Aji, j = i, i + 1, …, n + 1, that is, DPi1 → A1ji ; DPi2 → A 2ji , …, DPiL → A Lji , the FIis corresponding to the DPis are obtained by FIli =

1 1 + ∑ j = i +1 DPil DPj C lji n +1

, l = 1,2,K, L

where Ciil = 1 C lji = −

Alji Ajj

+

j −1

 Ajk

∑  − A

k = i +1



jj

 Ckil ,  

j = i + 1, i + 2,K , n + 1

Then, the DPi with the maximum FI is the best one to be attached.

(15)

236


3.5.3 Detaching When an FR and corresponding DP, for example, FRi and DPi, are detached from a base product, DPj, j = i + 1, i + 2, …, n, will be changed to DPj (1 + α DPji) to eliminate the influence of detaching DPi. Detaching can be considered as scaling with δ DPii = –DPi that is αDPii = –1. Then, there are

δ DPii = −DPi j −1

∑A k =i

jk

α DPki DPk + A jjα DPji DPj = 0

(16)

j = i + 1, i + 2,K , n

called detaching equations. If FIi = 1 that is α DPji = 0, j = i + 1, i + 2, …, n, then the valueless change for detaching DPi is not generated.

3.5.4 Swapping If a DP is swapped by another DP to meet the change of corresponding FR, the new DP to maintain uncoupled or decoupled design can be accepted. When DPi is swapped by DPi S to meet the change of FRi, δ FRi, DPj, j = i + 1, i + 2, …, n, will be changed to DPj (1 + α DPji) to eliminate the influence of the swapping. There are AiiS DPiS − Aii DPi = δ F R i

( A DP S ji

S i

j −1

) ∑A

− A ji DPi +

k = i +1

jk

α DPjk DPk + A jjα DPji DPj = 0

j = i + 1, i + 2,K , n

(17)

called swapping equations. There are two scenarios of swapping. Scenario 1: A Sji = Aji, j = i, i + 1, i + 2, …, n. The swapping equations can be transformed into Aiiα DPii DPi = δ F R i j −1

∑A k =i

jk

α DPki DPk + A jjα DPji DPj = 0

j = i + 1, i + 2,K , n

(18)

where

α DPii =

DPiS − DPi DPi

the same as the basic equations for customisation. Thus, this scenario can be regarded as scaling for

δ DPi = DPiS − DPi


237

Scenario 2: at least one A Sji ≠ Aji, j = i, i + 1, i + 2, …, n. This scenario can be considered as detaching of DPi and then attaching of DPi S . The detaching equations are D α DP ii = −1 j −1

∑A α k =i

jk

D DPki

(19)

D DPk + Ajjα DP ji DPj = 0

and the attaching equations are i −1

FR iS = AiiS DPiS + ∑ Aki DPk k =1

A Sji DPiS +

j −1

∑

k = i +1

(20)

A A A jk α DP ki DPk + A jj α DPji DPj = 0

j = i + 1, i = 2,K , n

where FR iS = FR i + δ FR i

Then D A α DPji = α DP ji + α DPji ,

j = i + 1, i + 2,K , n

(21)

In terms of the analysis of the two scenarios, both the original DP and the new one for swapping are better those with larger FIs, especially FI = 1, the best.

3.6 Characteristics of flexibility index According to the definition of FI, base equation for customisation and variety generation equations, the characteristics of FI are observed as follows. 1

For DPi, Aij = 0 ∀I ≠ j → FIi = 1.

2

The larger FIi is, the more suitable for customisation the FRi and DPi are, because to choose a customised DP with larger FI can result in more efficiency of premium on customisation. The FR and corresponding DP with FI = 1 are the most suitable ones for customisation.

3

A based product with uncoupled design is the best for mass customisation. For an uncoupled design with n FRs and n DPs, the off-diagonal elements in design matrix are 0, then, FIi = 1, i = 1, 2, …, n, and the FI of the base product, FIB, is also equal 1.

4

The different modules of a modularised product can be customised independently, because they do not influence each other.

5

Scaling can be regarded as changing a DP of a base product to meet the change of corresponding FR. It is best to choose an FR and corresponding DP with FI = 1, because the valueless change for scaling the DP is not generated.

238


6

If there are several choices for DPs, which can be attached to meet an additional FR, the DP with the maximum FI is the best one. It is best to attach an FR and corresponding DP with FI = 1 to a base product, because the valueless change for the attaching is not generated.

7

Detaching can be considered as scaling with α DPii = −1. It is best to detach an FR and corresponding DP with FI = 1 from a base product, because the valueless change for the detaching is not generated.

8

There are two scenarios of swapping. When A Sji = Aji, j = i, i + 1, i + 2, …, n, the swapping can be regarded as a kind of scaling. When at least one A Sji ≠ Aji, j = i, i + 1, i + 2, …, n, the swapping can be considered as detaching and then attaching. Both the original DP and the new one for swapping are better when they are with larger FIs, especially FI = 1, the best.

4

Simplification approach of comparing FIs

The relationship among FRs and DPs can be found conveniently, so it is easy to judge if Aji ( j = i + 1, i + 2, …, n; i = 1, 2, …, n) of a decoupled design is equal to zero or not. However, sometimes the precise values of the elements of the design matrix cannot be obtained easily, then it is difficult to calculate the precise values of FIs. Now, a simplification approach of comparing FIs is introduced in this section. To have a robust design, assume that the off-diagonal elements are much smaller than the diagonal elements (Suh, 2001), that is, Aji