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2 9 Optimize Variant Produt Design Based on Component Interation Graph Elim Liu and Shih-Wen Hsiao Open Aess Database Introdution Dominating markets with a single produt is inreasingly diffiult, and instead numerous industries are evolving towards mass ustomization, meaning the prodution of individually ustomized and highly varied produts or servies (Pine, 993). This proliferation of models allows onsumers to find a produt that best suits their individual needs. The need for inreasing produt variety and shorter development time brings more omplexity to the ompany than ever. Corporations are striving to balane ustomer satisfation and ost savings, and produt design is beoming essential for aomplishing this. Sine developing an entirely different produt is often uneonomial. A better method is to develop a produt arhiteture that enables a ompany to offer highly differentiated produts that share a substantial fration of their omponents. Therefore, introduing produt variety within a robust arhiteture offers one means of enhaning mass ustomization. Besides, an inrease in produt variety brings an inrease in the volume of information exhanged between ustomers, designers and marketing department. Due to suh inreased information proessing load, information tehnology is needed to takle this problem. This hapter investigates the produt variety design methodologies through the omputational design optimization methods, and developing produt arhiteture under the support of information tehnologies. It aims at providing produt designers a rational and systemati methodology in dealing with produt variety from both qualitative and quantitative viewpoints.. Related Literature The issue of produt variety has attrated growing researh interest during reent years. In993, Pine (993) began disussing the need for produt variety in Soure: Manufaturing the Future, Conepts - Tehnologies - Visions, ISBN , pp. 98, ARS/plV, Germany, July 6, Edited by: Kordi, V.; Lazinia, A. & Merdan, M. 55

3 55 Manufaturing the Future: Conepts, Tehnologies & Visions inreasingly ompetitive markets. Cohen (995) proposed using Master House of Quality for planning produt variety. Suh (99) viewed produt variety as the proper seletion of design parameters that satisfy variant funtional requirements. Ulrih (995) examined the relationships between produt arhiteture and produt variety, omponent standardization, modularity, and produt development. Erens (996) developed produt variety under funtional, tehnology, and physial domains. Fujita and Ishii (997) formulated the task struture of produt variety design, and Martin and Ishii (996, 997, ) proposed DFV (Design for Variety), whih is a series of methodologies with quantifying indies for reduing the influene of produt variety on produt life-yle ost, and thus helping design teams to develop deoupled produt arhitetures. These studies have established a basis for produt variety management. However, many investigations have agreed that the key to effiiently designing and delivering multiple produts is developing a good produt arhiteture (Meyer 993, Sawhney 998, Ulrih& Eppinger ). The advantages of developing produt arhiteture is that it enables a ompany to offer two or more produts that are highly differentiated yet share a substantial fration of their omponents. The olletion of omponents shared by these produts is alled a produt platform (Ulrih& Eppinger ). Erens (996) defined a produt platform as An arhiteture onept of ompromising interfae definitions and key-omponents, addressing a market and being a base for deriving different produt families. Robertson and Ulrih (998) proposed a method of balaning distintiveness with ommonality within produt arhiteture through identifying the importane of various fators going into this tradeoff. Fujita et al., (998, 999) utilized optimization tehniques to identify the optimum arhiteture of a module ombination aross produts in a family of airraft. Moreover, Yu et al., (998) defined produt family arhiteture based on ustomer needs by using the target value of produt features for alulating probability distributions. Additionally, Simpson, et al., (999) used the Produt Platform Conept Exploration Method (PPCEM) to design a ommon produt platform. This platform uses the market segmentation grid to help identify suitable sale fators of the platform that are saled or strethed to satisfy various requirements. Although most studies fous on optimizing produt struture, some studies have notied that investigating the physial arrangement and interation among omponents is the key for stable produt arhiteture. For example, the omponent-based DSM (design strutural matrix) method has been applied to

4 Optimize Variant Produt Design Based on Component Interation Graph 553 explore alternative arhitetures through lustering high interative omponents and arranging them in hunks (Pimmler & Eppinger 994, Wei ). Moreover, Sosa et al., () applied DSM to analyze the different types of interation between modular and integrative systems, and Salhieh & Kamrani (995) used the similarity matrix for integrating omponents into modules. These studies represent omponent relationships in terms of similarity or reiproal interation rather than information flows. However, during the embodiment design stage, variant designs of a single omponent an lead to numerous other omponents also requiring modifiation. The hierarhial struture of omponent interations first must be identified, after whih the influene of variety and subsequent design hanges an be estimated. To deal with this problem, this hapter illustrated two methodologies via identifying omponent design onstraint flows to build up feasible produt arhiteture. 3. Produt Design Based on Component Interation Graph 3. Produt design rational Studies of produt design have observed that designs are always ompleted through iteration. Design iteration ours when a new requirement is inputted into the design task, resulting in the related omponents needing to be redesigned, and leading to the speifiations of the other omponents that interat with the redesigned omponents having to hange their speifiations to fit the redesign. Therefore, the design proess beomes iterative, and so tremendous design efforts are required. This problem beomes partiularly important in planning produt arhitetures; produts must be designed to meet various ustomer needs, yet also share as many omponents as possible to minimize osts. This study attempted to solve this problem by modeling omponent sequential flow using ISM, interpretive strutural modeling. ISM is an algebrai tehnique for system representation and analysis that was first introdued by Warfield (973). ISM redues omplex system interations to a logially oriented graph. This study applies and modifies ISM to establish a hierarhial omponent interation struture, whih an help designers to determine omponent ommonality, variety, and design priorities.

5 Manufaturing the Future: Conepts, Tehnologies & Visions Computational proedure of ISM Phase: Inidene matrix onstrution First, a system is deomposed into a set of omponents that form a square matrix. The proedure begins with paired omparisons to identify whether a diret influene exists from omponent i (row) to j (olumn). The inidene matrix A =[aij] thus is defined as = otherwise to omponent j from omponent i diret influene exists a if ij a Fig. (a) represents the inidene matrix of an example system ontaining seven omponents. For example, the seond row of the matrix indiates that omponent diretly influenes omponents, 5, and 6. Phase : Reahability matrix dedution The reahability matrix R is deduted from inidene matrix A if a Boolean n- multiple produt of A+I uniquely onverges to R for all integers n>n, where n is an appropriate positive integer, I is a Boolean unity matrix, and + is addition in Boolean sense (Warfield, 995). Matrix R represents all diret and indiret linkages between omponents. Figure (b) represents the reahability matrix R derived from matrix A, in whih an entry rij= if omponent j is reahable by i, although the path length may be one or more A = R = (a) Original inidene matrix A (b) Reahability matrix R Figure a-b. Stepwise proedure of ISM

6 Optimize Variant Produt Design Based on Component Interation Graph 555 Phase 3: Cluster retrieval A tehnique for luster retrieval is inserted in the ISM proess to identify omponents that influene one another and form a loop (Roberts, 997). The reahability matrix R multiplies the transposed matrix of R, say R t ; thus in t R R, omponents i and j mutually interat if rij rji =. Figure () displays the output matrix of t R R, in whih lusters of omponents an be identified easily by rearranging omponent order. Figure (d) reveals four lusters in the system, namely: {}, {,6}, {3,5,7}, and {4} t R R = t R R = () Output matrix of t R R (d) Retrieval of lusters Figure -d. Stepwise proedure of ISM Phase 4: Obtained hierarhy graph Following luster retrieval, the order of reahability matrix R is rearranged (as shown in Fig. (e)), and the lustered omponents are integrated and treated as a single entity. The hierarhy graph then is obtained by identifying a set of omponents in matrix R that annot reah or be reahed by other omponents outside the set itself, removing the set from the original matrix R, and then repeating this proess for remaining matrix until a unique set of nodes that no other nodes an reah is obtained. For example, in Fig. (e), first is identified as an exit, sine it an not reah to other omponents; meanwhile, {, 6} and 4 were separated as entranes, beause they an not be reahed by other nodes. In this example, three levels of nodes were obtained (illustrated in Fig. (f)). The oriented links then onneted the nodes from soure to sink one based

7 556 Manufaturing the Future: Conepts, Tehnologies & Visions on the inidene matrix. Notably, the rounded retangles in Fig. (f) indiate the retrieved lusters, in whih the information flow forms a loop. R = Level Level Level 3 C 4 C 6 C 3 C 5 C 7 C C (e) Rearranged matrix R (f) Hierarhial interation graph of the system Figure e-f. Stepwise proedure of ISM 3.3 Analysis proedure The Analysis proedure omprises three main phases: market planning, QFD and the ISM approah. Figure presents the flow diagram for linking these phases. The first phase begins with produt market planning whih larifies the various requirements of different markets. The seond phase involves the QFD analysis, during whih the variant requirements are related to physial omponents with speifi values to identify relationship degree, yielding the relative importane of eah omponent towards the market variations. Finally, the inner interations between physial omponents are further examined via ISM analysis, with omponent design priority being represented using a hierarhial graph. The result obtained from QFD is inorporated into the hierarhial graph to identify the omponent to be redesigned in the influential path, deriving new produts that satisfy market nihes by redesigning finite omponents.

8 Optimize Variant Produt Design Based on Component Interation Graph Case Study for Variant Design Based on Component Interation Graph 4. Case bakground This study illustrated the design of a family of.5-liter automati drip offee makers from an eletroni applianes manufaturer (Company X). Ninety-five perent of the produts of this ompany are original design manufatured (ODM), and are mainly exported to Ameria, Europe, and Japan. Company X aims to provide produt varieties to simultaneously meet the requirements of eah segmented market, as well as to develop produt arhitetures in mass ustomization. Components of the original produt are listed in Table. 4. Analysis proedure Phase : Market Planning The market planning aims at two different markets (spatial variety) with two different launh times (temporal variety), onurrently developing four produts, as illustrated in Fig. 3. The launh time of the urrent produts is planned for after three months, while that of future produts is planned for after eight months. Phase : Identify the exterior drivers of variation To emphasize market differentiation, the QFD matrix lists the differenes in ustomer requirements rather than ommon requirements. In the ase, how to maintain offee temperature is the key driver for spatial market differentiation, beause the weather in Market is muh older than that of Market. Table illustrates the mapping from requirements into omponents, in whih the values 9, 5, 3,, and indiate the mapping relationships ranging from very strong, through to strong, ordinary, weak, and none, respetively. Table demonstrates that the most important omponent for Keeping offee temperature is the Carafe. Furthermore, the key drivers for temporal market differentiation are Ease of leaning, Comfortable to use, and Fashionable style. These requirements are listed in Table, along with their relative importane. The ritial omponents for these requirements inlude the Housing, Top over, and Carafe. The QFD results are input into the produt design, as desribed in Setion 4.3.

9 558 Manufaturing the Future: Conepts, Tehnologies & Visions Market planning Identify variant requirements related to the speifi markets Component Component Requirement Component The QFD approah Requirement Component The influene degree of design requirements on eah omponent Component n Requirement m Relative importane of Component eah omponent regarding to the market-driven variety Component Component Component n The ISM approah The inidene matrix The degree of eah omponent influened by others T r o a ompon nt n lu n s towar Figure. Flow diagram of the analysis phases Hierarhial graph derived from ISM Temporal variety Spatial variety Prototype (Produt ) Produt Produt 3 Produt 4 Market Market Current Future Figure 3. Market planning of the offee maker

10 Optimize Variant Produt Design Based on Component Interation Graph 559 Component Spatial differentiation requirement top Cover top Cover base spout spout seat top over base water tank over water tank base silione ring water outlet pipe pipe onnetion seat base over paking valve heating element swith hot plate ring hot plate up bank arafe handle over arafe handle arafe arafe over housing filter holder paking valve filter holder Keep offee temperature Table. QFD matrix of the spatially differential requirements Component No. Temporal differentiation requirement Ease of leaning Comfortable to use Fashionable style Total Table. QFD matrix of the temporally differential requirements Rwlative Weight Phase 3: Identify the interior hierarhial interations In this approah, senior design engineers of ompany X perform the inidene matrix by investigating the relationships between eah pair of omponents. Table 3 lists the original inidene matrix. The ells in the inidene matrix are marked with if the omponents in rows onstraint the speifiations of the omponents in olumns. The related design onstraints are doumented in the form d (i, j), where i denotes the soure omponent providing a onstraint to omponent j. For example, d (4, 5) indiates that the Top Cover Base (omponent 5) should fit the diameter of the Spout Seat (omponent 4). This inidene matrix is then manipulated through the ISM proedures illustrated in Setion 3.. Fig.4 shows the hierarhial graph of the design onstraint flow derived through ISM. In this graph, the irles represent omponents, the oriented lines are design onstraints provided by the soure omponents, and the rounded

11 56 Manufaturing the Future: Conepts, Tehnologies & Visions retangles indiate that a set of mutually interative omponents, whih are integrated as a module. These modules and other omponents then are further grouped into hunks aording to the frequeny of their interations. Table 4 lists the inidene matrix after appropriate rearrangement of the order. Four hunks are formed in the produt, namely C housing hunk, C water tank hunk, C3 base hunk, and C4 arafe hunk. The preedene of the four hunks is determined by the inter-hunk interations. Part Name No. top over top over set spout spout seat top over base water tank over water tank base silione ring water outlet pipe pipe onnetion seat base over paking valve heating element swith hot plate ring hot plate up bank arafe handle over arafe handle arafe arafe over housing filter holder paking valve filter holder Table 3. The original inidene matrix of offee maker omponents 4.3 Design proedure The results of the analysis illustrated in previous setion are applied in the produt design; four produts were designed onurrently to satisfy requests of different markets. The design proedure is demonstrated in the following paragraphs.

12 Optimize Variant Produt Design Based on Component Interation Graph 56 Chunk module/omponent No C 4 C 3 C C Top over module 3 Spout module 4 holder paking valve Filter module 7 8 Tank module 6 5 Base module 9 Heating plate module 4 3 Water pipe module 6 Heating element Carafe outfit module 6 Carafe 5 Note: Grayed ells indiate the inter-hunk interations. Table 4. Inidene matrix after appropriate rearranging the order Level 4 3 Level Level Level Component Module Constraint Figure 4. Hierarhial graph of omponent interation

13 56 Manufaturing the Future: Conepts, Tehnologies & Visions Phase : Design for spatial variety Table indiates that Carafe (part No.5) design is essential for maintaining offee temperature. Therefore, the Carafe is redesigned to meet the requirement: the wall should be thikened and use heat insulation material, the shape slenderized and the top narrowed to redue heat loss. To identify the influene of the new Carafe design, Fig.5 (extrated from Fig.4) shows the inidene diagram of the Carafe. In this figure, the design onstraints the Carafe exports to the sink nodes are listed below: d(5, ): The Heating Plate module should fit the diameter of Carafe base (fixed). d(5, ): The Cup Bank should fit the diameter of Carafe body (hanged). d(5, 4): The Carafe Handle should fit the ar and weight of Carafe body (hanged). d(5, 6): The Carafe Cover should fit the diameter of Carafe rim, and the re quested thermal ondition (hanged). d(5, 7): The Filter Module should fit the Carafe height (hanged). 5 Carafe 3 Filter Holder 7 5 Heating plate module Carafe outfit module Top over module Component Varied design onstraint Module Fixed design onstraint Soure of variant design Figure 5. Inidene diagram of arafe (omponent 5)

14 Optimize Variant Produt Design Based on Component Interation Graph 563 The onstraint of d(5, ) is fixed (represented as dotted line in Fig.5), and thus parts, are left unhanged. However, onstraints d(5, ), d(5, 4), d(5, 6), and d(5, 7) are hanged (represented as solid lines in Fig. 5) owing to the new arafe speifiation, resulting in the design of the Filter Module and Carafe Outfit Module having to be hanged to math the altered onditions. In the Carafe Outfit Module, the omponents are redesigned to fit the new Carafe. However, the design hange of the Filter Module must refer not only to the Carafe, but also to other omponents that provide onstraints on the Filter Module, as shown in Fig.6. Thus in redesigning the Filter Module, the onstraint from the Carafe beomes the soure of variant design (represented as solid line in Fig.6), while the others are fixed onstraints (represented as dotted lines in Fig. 6) listed below: d(, 7): The Housing should fit the Base. d(8, 3): The Filter Holder should fit the Filter Holder Paking Valve diameter. d(4, 5): d(3, 3): The Top Cover Base should fit the Spout Seat diameter. The Filter Holder should fit the Spout shape. Under these onstraints, the design of Filter Module (parts 7, 5, and 3) is hanged from V-shaped to U-shaped to fit the new Carafe design. Furthermore, onstraint from the Filter Module is: d(5, ): The Top Cover should fit the Basket Holder rim diameter. Sine the speifiation of the Basket Holder rim is fixed, omponent and need not hange their design. Consequently, Table 5 lists the design solution driven by spatial market differentiation. No. Redesigned omponent 5* Thermal arafe * Cup bank of thermal arafe 3* Handle over of thermal a- 4* Handle of thermal arafe 6* Cover of thermal arafe 7* U-shaped housing 5* U-shaped over base 3* U-shaped filter baseket Table 5. List of variant omponents for Market

15 564 Manufaturing the Future: Conepts, Tehnologies & Visions Carafe Filter holder paking valve Spout module Base 3 Filter module 7 5 Top over module Component Module Soure of variant design Varied design onstraint Fixed design onstraint Figure 6. Constraint flow diagram of the filter module Phase : Design for temporal variety Table indiates that the ritial omponents for realizing temporal variety are the Housing (part 7), Top Cover (part ), and Carafe (part 5). Aording to the hierarhial graph in Fig. 4, for these three omponents, the Carafe oupies the upper level in the interation hierarhy. This arrangement means that the Carafe design should be addressed first, followed by that of the Housing and finally, the Cover. However, the inidene and osts involved in arafe redesign are quite high. The strategy of Company X thus is to over design this omponent; that is, to improve the quality of the urrent speifiations apable of handling future market requests. Therefore, the Carafe is upgraded for easy leaning, pouring and dishwasher-safe in both the urrent and future versions. Therefore, aording to the design priority, the produt variety should fous on redesigning the Housing (part 7). To failitate usability, the design team tends to substitute swing-out housing for the fixed housing. This hange divides the omponent into two new parts; namely, the Swing-out Filter Housing and the Support. The Swing-out Filter Housing is further differentiated into either U-shaped or V-shaped. The original design onstraints of the Housing are laid on the two new parts, respetively (see Fig. 7). Thus the shape of the Swing-out Housing must fit the Carafe; and the design of the Support must

16 Optimize Variant Produt Design Based on Component Interation Graph 565 fit the Base. The variant design of the Housing diretly influenes the Top Cover (part ); meanwhile, for onvenient to use, the Top Cover is hanged from a lift up to a fixed design. Finally, Table 6 lists the variant design driven by temporal market differentiation. Carafe 5 Base 3 Filter module 7 5 Support 7 Top over module Component Module Soure of variant design Varied design onstraint Fixed design onstraint Figure 7. Constraint flow diagram of the new design No. R s n ompon nt 7* Swing out filter basket 7* Support * Fixed top over Table 6. List of variant omponents for Future market 4.4 Result Table 7 lists the omponents of the four produts derived via the proposed methodology. Among these omponents, most of the variety ours in hunks and 4, while hunks and 3 remain virtually unhanged, and thus are onsidered platforms of this produt arhiteture. Moreover, the design team further suggested that omponents of the upper levels of hunk 3, inluding Water Pipe Module, Heating Element, Base Module, and Heating Plate Module, should be standardized to redue the redesign effort and prodution ost.

17 566 Manufaturing the Future: Conepts, Tehnologies & Visions Chunk Component No. Produt Produt Produt 3 Produt 4 Fastened top over V V Lifted-up over * V V Top Cover base V V V V Spout 3 V V V V Spout seat 4 V V V V Filter holder paking valve 8 V V V V V-shaped filter holder 5 V V U-shaped filter holder 5* V V V-shaped filter basket 3 V V U-shaped filter basket 3* V V V-shaped fixed housing 7 V U-shaped fixed housing 7* V V-shaped swing out filter housing 7* V U-shaped swing out filter housing 7* V C Support 7* V V Water tank over 6 V V V V C Water tank 8 V V V V Silione ring V V V V Water outlet pipe 3 V V V V Pipe onnetion seat 4 V V V V Paking valve 6 V V V V Heating element 8 V V V V Base V V V V Base over 5 V V V V Swith 9 V V V V Hot plate ring V V V V C3 hot plate V V V V Glass arafe 5 V V Thermal arafe 5* V V Cup bank of glass arafe V V Cup bank of thermal arafe * V V Handle over of glass arafe 3 V V Handle over of thermal arafe 3* V V Handle of glass arafe 4 V V Handle of thermal arafe 4* V V Cover of glass arafe V V C4 Cover of thermal arafe 6* V V Table 7. Components list of the produt family 4.5 Comparison of existing and proposed designs A team of engineers and managers of Company X estimated the sales volume, marketing, variable (raw material/ prodution pries) and fixed (engineering/ injetion mold) osts for the proposed designs, and ompared these estimates to those for produts designed independently. Table 8 lists the omparison.

18 Optimize Variant Produt Design Based on Component Interation Graph 567 The profit is alulated using the following funtion: P i = S i (PR i -VC i )-FC i -MC i () Where Pi, Si, PRi, VCi, FCi, MCi are the profit, sales volume, prie, variable ost, fixed ost, and marketing ost of produt i, respetively. Table 8 illustrates that the primary ost differene between the two design strategies lies in the fixed ost. The proposed designs signifiantly redued the fixed ost for developing new produts through sharing most omponents. The seond row from the bottom shows that the profits assoiated with independently developing produts and 4 is minus 73% and 65% of urrent produt, respetively. Therefore, the best deision seems to be not to develop any produt in Market. However, the proposed designs generate a total profit 7% in urrent markets and 54% in future markets higher than if produt was the only produt launhed. The result shows the potential savings and profit available using this methodology. No produt family design Produt family design using this methodology % of urrent produt Produt Produt Produt 3 Produt 4 Produt Produt Produt 3 Produt 4 Sales volume Prie VC FC 4 MC Profit Total profit urrent= 7 future= 43 urrent= 7 future= 54 Note: VC, FC, MC are the variable, fixed and marketing osts, respetively. Table 8. Comparison of independently developed and the proposed designs

19 568 Manufaturing the Future: Conepts, Tehnologies & Visions 4.6 Design strategies based on the omponent interation graph approah The hierarhial graph ould optimize variant design in the following design strategies:. Design strategies for the soure omponents: - a: Differentiated ustomer requirements diretly drive design variation of these omponents. And sine the inidene and effort for the design hanges are relative huge, this variation must be obvious and valuable to ustomers. To ahieve stable produt arhiteture, over-design of dominant omponents might be unavoidable for extending omponent lifeyle. - b: If the omponents are remained unhanged, they should be onsidered to be standardized or fixed speifiation, and beome ore platform of the produt family.. Designs of the sink omponents are more likely to hange to omply with both the altered design onstraints and the requests of ustomer requirements. However, the ost and inidene of altering these omponents is relatively low. Furthermore, the redesign should inorporate the onstraints provided by the soure omponents. 3. Components that with their speifiation flow forms an interation loop are likely to be further modularized or integrated. 5. Produt Design Based on Analyti Network Proess 5. The rational for using the ANP approah for optimizing produt design The approah in setions 3 and 4 illustrated a produt variety design based on the omponent relationship struture graph. The graph forms design onstraint flows from soure omponents to the sink ones. However, in some illstrutured produt arhitetures, the omponent relationships may form a

20 Optimize Variant Produt Design Based on Component Interation Graph 569 ompliated network, and the ISM approah may not be applied suessfully. Therefore, we developed an integrated approah via analyti network proess (ANP) ( Saaty, 996) tehnique to fix this problem. The differenes between ISM and ANP are that (). ANP treats omponent relationship as relative importane (from to ) rather than binary; ().ANP mathematially opes with the network struture well, while the ISM, hierarhial struture. ANP is a general form of the widespread multi-riteria deision tehnique, AHP (analyti hierarhy proess) (Saaty, 99). AHP employs unidiretional hierarhial relationship among levels, while ANP enables onsideration of the interrelationships among the deision levels and attributes. The distinguishing features of ANP make it suitable for dealing with the hierarhial mappings as well as omponent oupling problems in determining the influene of variety on eah design element. In this approah, the analysis result of ANP is then input to the goal programming (GP, Dantzig 963) models for determining the standardized and variant parts of produt arhiteture. The GP model handles multiple objetives and minimizes deviation from desired goals, and thus provides a feasible and onsistent solution for optimizing produt family design. Although many researhers use mathemati models, suh as (Reiter & Rie 966, Ringuest & Graves 989) most methodologies are assumed independent among design alternatives. In this study, we integrated ANP and GP approahes for aommodating interdependene among design alternatives that is first applied in the produt variety optimization problem. 5. Computational proedure of the ANP The proedure of optimizing design variety via the ANP was summarized as follows: The first step was to estimate the qualitative hanges in ustomer requirements (CRs) in eah future market ompared to the urrent produt. The importane of the CRs were ompared and alulated, orresponding to the first step of the matrix manipulation onept of ANP. The CRs were then deployed into engineering harateristis (ECs) by omparing the ECs with respet to eah CR. The ECs were further deployed into omponents by omparing the relative ontributions of omponents to eah EC. Finally, the interdependene priorities of the omponents were further examined by analyzing the ouplings among omponents. The supermatrix utilized to model the proedure in matrix notation, whih is formed from four submatries, is

21 57 Manufaturing the Future: Conepts, Tehnologies & Visions onstruted as follows: G CRs ECs C Goal(G) Customer Requiremen ts(crs) W () Engineerin g Charateri stis(ecs) W Components (C) W 3 W 4 where W denotes a matrix representing the relative importane of CRs for satisfying eah speified market goal; W represents the mappings of the CRs to eah ECs, W3 representing the impat of ECs to eah omponent, and W4 denoting the oupling relationship among omponents. Using the above notations, the priorities of the omponents (W) were alulated by multiplying W4 and W3. The overall priorities of the omponents (W ANP ) that reflet the degree of required hanges of omponents in response to the nihe of eah market, then were alulated by multiplying W, W, and W. 6. Case Study for Optimizing Produt Variety Using the ANP Approah This setion presented an illustrative example of a water ooler family design (Martin & Ishii, ). The proposed methodology was further demonstrated using a stepwise form. 6.. Survey ustomer requirements and segment the future markets Produt variety planning begins with surveying ustomer requirements. Figure 8 illustrated three future markets defined by the design team, along with the desired produt features in these envisioned markets. Current (Home Future (Home Future (Business Use) Redued energy High water us- Low water us- Future 3 (Home Redued ost Smaller foot-

22 Optimize Variant Produt Design Based on Component Interation Graph 57 Figure 8. Market planning of the water ooler for three envisioned markets. 6. The ANP approah Phase. Estimate relative importane of CRs in eah market For this water ooler example, the main CRs were Fast Cooldown, High Capaity, Low Energy Consumption, Compat, Rapid Pouring, and Low Cost. Figure 8 depits the desired produt features for eah market. Aording to the planning, the design team estimated the range of hanges of the CRs for eah market using using Saaty s -9 sales (Saaty, 99) pairwise omparisons as shown in Table 9. To avoid omparison inonsistenies, a onsisteny ratio measured the probability that the pairwise omparison matrix was randomly filled. The upper limit for the onsisteny ratio was., whih signified that up to % hane was tolerable for the omparison onduted in random manner. The proedure was applied in eah market. The resulting relative weights of CRs ompose W, as shown in Eq. (3). M W = M M3.45 Fast ooldown.45 High apaity.45 Low energy use.49 Compat.45 Rapid pouring.49 Low ost (3) where M, M, M3 represent Markets,, and 3, respetively.

23 57 Manufaturing the Future: Conepts, Tehnologies & Visions Future Market 3 Fast ooldown High apaity LEC Compat Rapid pouring Low ost Relative weight Fast ooldown /9 /9.45 High apaity /9 /9.45 Low energy onsumption (LEC) /9 /9.45 Compat 9.49 Rapid pouring /9.45 Low ost.49 Consisteny Ratio=.68E-9 Table 9. Pairwise omparison matrix of CRs for the goal of Market 3. Phase. Translating CRs into ECs The ECs used in the produt design inlude Cool Down Time (min), Cool Water Volume (gal), Power Consumption (W), Width, Depth (in), Volume Flow Rate (gal/min), and Cost ($). If a CR was fulfilled via two or more ECs, the design team was required to ondut a pairwise omparison to assess the relative importane of the ECs with respet to the CR. Table maps the relations between CRs and ECs. For example, In olumn 5 of Table, two ECs (Width and Depth) speify the request of Compat speifiation of equal importane, thus, their weighted values were both.5. W Fast ooldown High apaity LEC Compat Rapid pouring Low ost Cool down time(min) Cold water volume(gal) Power onsumption(w) Width(in) Depth(in) Volume flow rate(gal/min) Cost($) Table. Matrix W, the mappings of CRs to the relative ECs.

24 Optimize Variant Produt Design Based on Component Interation Graph 573 Phase 3. Deploying the ECs to produt omponents Again, the design team performed AHP to evaluate the relative importane of the omponents ontribution to eah EC, and the aggregation of relative importane weights for omponents in eah EC formed matrix W3, as shown in Table. In whih the zeros were assigned to the ells if the EC had no effet on the omponents. Phase 4. Examining inner dependenes among omponents In this ase, the omponents are seriously oupled. The degree of the oupling relations between omponents was identified using a series of pairwise omparisons. Table displays the inner dependene matrix of omponents with the Fan as ontrolling omponent, in whih Plumbing and Insulation were exluded beause of not impating the Fan. The shema was performed in eah omponent, and obtained the resulting eigenvetors as shown in Table 3. The matrix indiated the inner dependene among omponents, in whih zeros indiated the eigenvetors of the unrelated omponents. W3 Cool down time Cold water volume Power onsumption Width Depth Volume flow rate Fan Heat Sink TEC Power Supply Chassis Plumbing Reservoir Insulation Fasia Table. Aggregation of relative importane for omponents in eah EC Cost

25 574 Manufaturing the Future: Conepts, Tehnologies & Visions Fan Fan HS TEC PS Chassis Reservoir Fasia Relative Weights Fan Heat Sink(HS) 3 3/ TEC / /3 3/.48 Power Supply (PS) /3 3 5/.96 Chassis Reservoir 4/3.34 Fasia.4 Consisteny Ratio=.3 Table. Pairwise omparison matrix with the Fan as ontrolling omponent. W4 Fan HS TEC PS Chassis Plumbing Reservoir Insulation Fasia Fan Heat Sink TEC Power Supply Chassis Plumbing Reservoir Insulation Fasia Table 3. Aggregation interdependene matrix among omponents. Phase 5. Synthesis the overall priorities of omponents Aording to Eq.(), the interdependent priority of the omponents, W, was alulated as W = W 4 W 3 (4) The overall priorities of the omponents regarding the goals of the three markets were alulated as follows:

26 Optimize Variant Produt Design Based on Component Interation Graph 575 M ANP W = W W W= M M3.89 Fan.77 Heat sink.3tec.78 Power Supply.3Chassis.Plumbing.53Reservoir.39Insulation.98 Fasia (5) where M, M, M3 represent Markets,, and 3, respetively. The ANP result revealed the priority for redesigning omponents to satisfy market goals. For example, in Market, the first omponent requiring redesign was Power Supply, with a relative importane value of.44, whereas Reservoir and Chassis were identified as the most important omponents in Markets and 3 with relative importane values of.49 and.3, respetively. 6.3 Optimization The optimization of the produt arhiteture is to ahieve a stable produt platform that enable variant produts to be highly differentiated yet share as many substantial portions of their omponents as possible, thus reduing the manufaturing and design osts. Phase : Platform omponent seletion There are two onsiderations in seleting the platform omponents. First, omponents with high engineering osts should be the initial fous. Seond, a produt platform stresses on omponent ommonality; therefore, the omponents with low W ANP fators -whih are less sensitive and more stable in response to the hanging environment, are suitable as platform items. Therefore, a weighted GP (Shniederjans, 995) algorithm is utilized for seleting platform omponents that satisfy two goals: () high engineering ost, and () ontrol the W ANP weight loss under a tolerable ratio. Furthermore, to onsider the relative importane of different markets and to regulate the possible inommensurability problem of different goals (Ringuest & Graves, 989), the general GP is as follows:

27 576 Manufaturing the Future: Conepts, Tehnologies & Visions + min ost d ANP + d ω ω n λ i i= subjet to n i = x i i + d d + n =, i i = (6) n m i= j= ANP ij + σ w x + d d = λ, j m j= i σ =, x {,}, i=,, n; j i + +, j=,, m d d, d, d, ; λ ; ost ANP where ω, ω denote the importane weights, d, d, d and d + denote the negative and positive deviation variables of the goals, respetively; xi is the binary variable representing whether the ith omponent is assigned as a platform item ( if xi =) or not (when xi =), i denotes the engineering ost of the ith omponents, σ j denotes the relative importane of market j, + ANP w ij represents the ith omponent weight in the jth market, and λ is a ontrollable variable indiating the tolerable ratio of weight loss. Phase : Variant omponent seletion This phase onsidered the distintiveness of eah produt for satisfying speifi market needs. Therefore, ertain omponents were seleted redesigned ahieve the distintiveness under limited design budget. Therefore, the GP was employed to satisfy two goals: () selet the omponents with high W ANP fators, and () ontrol the ost under a budget. Following the same priniple of regulation inommensurability, the general GP is as follows: To selet the redesigned omponents for market j:

28 Optimize Variant Produt Design Based on Component Interation Graph 577 min ω subjet to + d B + ANP d budget ω n ANP j w jk k = n k = w ANP jk x k + d d + = n k = w ANP jk n + k xk + d d = B j, k= + + x k {,}, d, d, d, d, j=,, m; k=,, n k i if the ith omponent has been assigned as a platform item, (7) where ANP budget ω and ω denote the importane weights, and d, + d, d and d + represent the negative and positive deviation variables of the first and seond goals, respetively; xk represents a binary variable representing whether the kth omponent is assigned as a redesigned item ( if xk =) or not (xk =). Notably, the variable xk should not ontain omponents that have been determined as platform items. w is priority rating of the kth omponent in the ANP jk jth market, k denotes engineering ost of the kth omponent, and Bj represents design budget of the jth market. 6.4 Result Table 4 lists the engineering ost for redesigning eah omponent. The data and the W ANP weight in Eq.(5) is input into the GP models via LINDO software. The platform omponents seleted by the GP under variant weight loss (variable λ ) are shown in Table 4. After examining the solutions, the design team strategially set the weight loss at %, yielding Fan, Heat Sink, and Insulation as the omponents shared aross the produt family. Furthermore, the GP model of Eq.(7) was applied for seleting the redesign omponents in the three envisioned markets, yielding the result listed in Table 5, in whih the GP solutions identified the fouses for redesign as being TEC, Power Supply, Plumb-

29 578 Manufaturing the Future: Conepts, Tehnologies & Visions ing and Reservoir in Market ; Chassis, Plumbing and Reservoir in Market ; and Power Supply, Chassis, Plumbing and Fasia in Market 3. Variable Component Redesign ost$ GP solutions x Fan, V V V V x Heat Sink, V V V V V x 3 TEC, V V V x 4 Power Supply 3, x 5 Chassis, V V x 6 Plumbing, x 7 Reservoir, x 8 Insulation 3, V V V x 9 Fasia, λ % % 3% 4% 5% Table 4. Platform omponents seleted under variant weight loss ( λ ). Variable Component x3 TEC V GP Solutions Market Market Market 3 x4 Power Supply V V x5 Chassis V V x6 Plumbing V V V x7 Reservoir V V x9 Fasia V Table 5. Components seleted for redesign in three markets. 7. Conlusion This hapter illustrates the authors urrent studies on managing produt variety in different degrees of produt arhiteture maturity (Liu & Hsiao 5, Hsiao & Liu 5). We suggested that the oasion in implementing the first

30 Optimize Variant Produt Design Based on Component Interation Graph 579 approah (setions 3, 4) is when produt arhiteture is under onstruted; the interations of omponents have not been investigated. Appliations of the approah to produt arhiteture provide the hierarhial graph of omponent interations. Furthermore, the methodology provides the following advantages for developing produt family:. The methodology larifies the speifiation flow between omponents rather than merely symmetri relationship similarity or orrelation. Thus the neessary information is provided for determining not only lustering but also preedene among omponents. The inidene matrix with the doumented design onstraints provides a omputable way for design knowledge representation.. The hierarhial graphial diagram provides designers with a userfriendly display for larifying the influene of eah omponent variation. 3. The hierarhial struture along with the QFD analysis helps produt family developers to identify whether the omponents should be standardized, altered, or modularized. Furthermore, the oasion in implementing the seond approah (setions 5, 6) is when omponent interations have been learly defined and formed ompliated networks, a flexible and omprehensive deision support system is needed in trading off the produt variety, standardization, and resoure utilization. In the approah, The interdependent nature inherent in the produt design proess was onsidered using the ANP approah. The use of ANP weights, and resoure limitations in the multi-objetive goal programming provided feasible and more onsistent solutions, thus yielding the optimal solutions in determining the platform omponent as well as the variant omponents foused on during the redesign phases. The appliation of the methodologies presented in this hapter an easily be extended to inlude additional deision riteria, suh as the manufaturability, sustainability, and assembly in designing produt families. Subsequent researh will address these points. 8. Referenes Cohen, L. (995). Quality Funtion Deployment: How to Make QFD Work for

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33 58 Manufaturing the Future: Conepts, Tehnologies & Visions tegrative systems. Proeedings of the ASME International Design Engineering Tehnial Conferenes and Computers and Information in Engineering Conferene, Paper No. DETC/DTM-457. Baltimore, Maryland. September. Suh, N.P. (99). Priniples of Design, Oxford University Press, ISBN: , New York. Ulrih, K.T. (995) The role of produt arhiteture in the manufaturing firm. Researh Poliy, Vol. 4, ISSN: Ulrih, K.T. & Eppinger, S.D. (). Produt Design and Development, MGraw-Hill, ISBN: 9-73, New York. Warfield, J.N. (973). On Arranging Elements of a Hierarhy in Graphi Form. IEEE Transations on Systems, Man, and Cybernetis, Vol.3, No., - 3. ISSN: Warfield, J.N. (995). A Siene of Generi Design: Managing Complexity Through System Design (nd edition), Iowa State Press, ISBN: , Iowa. Wei, M.J.V.; Greer, J.L.; Campbell, M.I.; Atone, R.B. & Wood, K.L. (). Interfaes and produt arhiteture. Proeedings of the ASME International Design Engineering Tehnial Conferenes And Computers and Information in Engineering Conferene, Paper No. DETC/DTM Pittsburgh, Pennsylvania. September. Yu, J.S. Gonzalez-Zugasti, J. P. & Otto, K.N. (998). Produt Arhiteture Definition Based on Customer Demands. Proeedings of 998 DETC ASME Design Theory and Methodology Conferene. Paper No. DETC98/DTM Atlanta, Georgia. September 998.

34 Manufaturing the Future Edited by Vedran Kordi, Aleksandar Lazinia and Munir Merdan ISBN Hard over, 98 pages Publisher Pro Literatur Verlag, Germany / ARS, Austria Published online, July, 6 Published in print edition July, 6 The primary goal of this book is to over the state-of-the-art development and future diretions in modern manufaturing systems. This interdisiplinary and omprehensive volume, onsisting of 3 hapters, overs a survey of trends in distributed manufaturing, modern manufaturing equipment, produt design proess, rapid prototyping, quality assurane, from tehnologial and organisational point of view and aspets of supply hain management. How to referene In order to orretly referene this sholarly work, feel free to opy and paste the following: Elim Liu and Shih-Wen Hsiao (6). Optimize Variant Produt Design Based on Component Interation Graph, Manufaturing the Future, Vedran Kordi, Aleksandar Lazinia and Munir Merdan (Ed.), ISBN: , InTeh, Available from: mponent_interation_graph InTeh Europe University Campus STeP Ri Slavka Krautzeka 83/A 5 Rijeka, Croatia Phone: +385 (5) Fax: +385 (5) InTeh China Unit 45, Offie Blok, Hotel Equatorial Shanghai No.65, Yan An Road (West), Shanghai, 4, China Phone: Fax: