A Market-Driven Approach to Product Family Design

Transcription

1 Deepak Kumar Graduate Student, Department of Mechancal Engneerng, Northwestern Unversty. Emal: We Chen (Correspondng author) Assocate Professor, Department of Mechancal Engneerng, Northwestern Unversty, 145 Sherdan Rd., Tech B4, Evanston, IL , USA, E-mal: Tmothy W. Smpson Professor, Departments of Mechancal & Nuclear Engneerng and Industral & Manufacturng Engneerng, The Pennsylvana State Unversty, Emal: 1

2 Deepak Kumar s a doctoral canddate n the Department of Mechancal Engneerng at Northwestern Unversty. He earned hs bachelor s degree (1999) n Mechancal Engneerng from Karnataka Regonal Engneerng College, Inda, and hs Master s degree (001) n Industral Engneerng and Operatons Research from Unversty of Illnos-Chcago. As part of hs master s research, he worked on developed data classfcaton algorthms for applcatons n medcal dagnoss and credt card authorzaton. Hs current research nterests are n demand modelng, decson-based desgn, and market-drven product famly desgn. He s the recpent of the Walter Murphy Fellowshp ( ) and s a student member of AIAA, ASME and INFORMS. Dr. We Chen s an Assocate Professor n the Department of Mechancal Engneerng at Northwestern Unversty. She earned a bachelor s degree (1988) n Mechancal Engneerng from Shangha JaoTong Unversty, a master s degree (199) from Unversty of Huston, and a doctorate (1995) from Georga Insttute of Technology. Her current research nvolves ssues such as robust desgn, relablty engneerng, smulaton-based desgn, multdscplnary optmzaton, and decson-based desgn under uncertanty. Dr. Chen was an Assocate Edtor of the ASME Journal of Mechancal Desgn ( ). She s now a revew edtor of Structural and Multdscplnary Optmzaton, and serves on the edtoral board of the Journal of Engneerng Optmzaton. She s a member of the ASME Desgn Automaton Executve Commttee. Dr. Tmothy W. Smpson s a Professor of Mechancal and Industral Engneerng and Engneerng Desgn at the Pennsylvana State Unversty. He receved hs Ph.D. and M.S. degrees n Mechancal Engneerng from Georga Tech n 1998 and 1995, and hs B.S. n Mechancal Engneerng from Cornell Unversty n Hs research and teachng nterests nclude product famly and product platform desgn, product dssecton and concurrent engneerng, and multdscplnary desgn optmzaton and vsualzaton. He s a member of ASME, AIAA, and ASEE and s an elected member of the ASME Desgn Automaton Executve Commttee and the AIAA Multdscplnary Desgn Optmzaton Techncal Commttee. He s an Assocate Edtor for ASME Journal of Mechancal Desgn and a Revew Edtor for Structural and Multdscplnary Optmzaton, and he s a member of the edtoral board of Engneerng Optmzaton.

3 Deepak Kumar 1 and We Chen Northwestern Unversty, Evanston, IL 6008 USA Tmothy W. Smpson 3 The Pennsylvana State Unversty, Unversty Park, PA 1680 USA Abstract In an effort to meet the dverse needs of today s hghly compettve global marketplace better, many companes are utlzng product famles and platform-based product development to ncrease varety, shorten lead-tmes, and reduce costs. Current research n the area of product famly desgn mostly focuses on the cost-savngs benefts of the platform-based approach and does not suffcently examne broader enterprse consderatons such as proft and market share. Furthermore, very few exstng desgn methods ntegrate market consderatons (e.g., customer preferences, competton) wth product development efforts n ther formulaton. In ths work, n addton to ntegratng market consderatons wth tradtonal product famly concerns (e.g., modular desgn, decsons regardng shared parts and processes), the scope of the product famly desgn problem s expanded to nclude the product lne postonng problem,.e., the problem of determnng the approprate market nche for each product varant n the famly. The novel Market-Drven Product Famly Desgn (MPFD) methodology proposed here s ntroduced to systematcally examne the mpact of ncreasng the varety n the product offerngs across dfferent market segments and explore the cost-savngs assocated wth commonalty decsons. A unque representaton scheme s also ntroduced to enable us to ntegrate the qualtatve market segmentaton grd wth mathematcally rgorous demand models, and the demand modelng approach employed n ths paper models the dssmlar mpacts of competton n dfferent market segments and plays a sgnfcant role n determnng the approprate platform leveragng strategy. The desgn of a famly of unversal motors s used to demonstrate the proposed approach. 1 Graduate Student, Department of Mechancal Engneerng, Northwestern Unversty, Emal: k-dleep@northwestern.edu. Correspondng author, Assocate Professor, Department of Mechancal Engneerng, Northwestern Unversty. 145 Sherdan Rd., Tech B4, Evanston, IL , USA, E-mal: wechen@northwestern.edu. 3 Professor, Departments of Mechancal & Nuclear Engneerng and Industral & Manufacturng Engneerng, The Pennsylvana State Unversty, Emal: tws@psu.edu. 3

4 I. Nomenclature A = Customer Desred Attrbutes A wa = Cross-Sectonal area of the armature wre (m ) A wf = Cross-Sectonal area of the feld wre (m ) C = Total cost assocated wth the product famly C D = Desgn cost C L = Labor cost C M = Materal cost C n = Choce set avalable to customer n C O = Overhead costs C R = Repar/warranty costs E = Engneerng attrbutes G 1 = Product postonng substrng G = Commonalty substrng I = Current drawn by the motor (Amperes) L = Stack length (m) M = Manufacturng attrbutes N = Number of performance/prce ters n each market segment of the Market Segmentaton Grd N c = Number of wre turns on the motor armature (turns) N s = Number of wre turns on each feld pole (turns) O = Operatng condtons (e.g., temperature, pressure) P j = Prce of product n th ter and j th segment Q j = Demand for product launched n ter and segment j r = Radus of the motor (m) S = Demographc attrbutes or Customer-specfc nformaton (e.g., customer s age, ncome) S = Number of market segments n the Market Segmentaton Grd t = Thckness of the motor (m) U n = True utlty of th choce alternatve to the n th customer W n = Determnstc part of the utlty of th choce alternatve to the n th customer X = Desgn optons (e.g., shape, sze, materal) β = Coeffcents of the utlty functon n the demand model ε n = Random part of the utlty of th choce alternatve to the n th customer η = Effcency of the motor µ = Scale parameter used n the Nested Logt demand model; used to help nterpret the level of correlaton between the choce alternatves n the nest (market segment) II. Introducton In an effort to meet the dverse needs of today s hghly compettve global marketplace better, many companes are utlzng product famles and platform-based product development to ncrease varety, shorten lead tmes and reduce costs (Halman et al., 003). In general terms, a product famly refers to a set of products that have been derved from a common product platform to satsfy a varety of market nches (Smpson, 005). Indvdual members of the product famly normally share common parts and subassembles. Platforms, n the most general sense, are ntellectual and materal assets shared across a famly of products, and ther use helps mnmzng manufacturng complexty wthout compromsng the ablty to satsfy a varety of customer requrements. In addton to mprovng 4

5 economes of scale and scope, a product platform can facltate customzaton by enablng a varety of products to be quckly and easly developed to satsfy the needs and requrements of dstnct market nches (Pne, 1993). Most exstng product famly desgn approaches (Smpson et al., 001, Messac et al., 00b, Messac et al., 00a, Nayak et al., 00, Felln et al., 00, Farrell and Smpson, 003, Da and Scott, 006, Da and Scott, 004, Akund et al., 005) are targeted at dentfyng the optmal commonalty decson n order to mnmze the manufacturng cost whle meetng pre-specfed performance goals. It should be noted, however, that whle ncreasng commonalty may reduce costs, t mght also compromse the performance of some of the products n the famly. Our goal n ths paper s to ntegrate market consderatons wth manufacturng and product development consderatons n platform-based product famly desgn. Nested Logt (Wllams, 1977), a demand modelng approach that recognzes the dssmlar mpacts of competton n dfferent market segments, s ntegrated wthn a desgn optmzaton model to make decsons on product lne postonng 4 to determne approprate platform leveragng strateges whle smultaneously explorng the cost-savngs benefts of ncreased commonalty. Demand models help not only capture producton costs (as a functon of producton volume) more accurately but also estmate revenues (as a functon of market share). In recognton of the ncreasng mportance of market consderatons n product development, some recent developments (Moore et al., 1999, Kma and Chhajed, 001, L and Azarm, 00, Mchalek et al., 006, Mchalek et al., 005) have ncluded the use of a demand model as part of an enterprse-drven approach to the desgn of product famles. However, n our opnon, these developments have only dealt wth the problem of product lne postonng n a lmted way. Ether an arbtrary number of products s assumed for the product famly (Moore et al., 1999, Mchalek et al., 006) or an enumeraton-type methodology to s used to determne the optmal number of product varants (L and Azarm, 00); commonalty consderatons are usually gnored n the nterests of smplcty (Zhang and Jao, 005), but n realty, commonalty can mpact demand both postvely and negatvely. For nstance, commonalty n the cockpt has helped fuel demand for Arbus arcraft (Aboulafa, 000), but too much commonalty often leads to a lack of product dstnctveness (Robertson and Ulrch, 1998), whch hurts sales, and t can also lead to cannbalzaton of ones own product lne as products start to compete wth themselves (Km and Chhajed, 000, Fruchter et al., 006). A recent example can be found n the 4 Product postonng s usually defned n marketng terms as developng a product and assocated marketng mx that (a) s placed as close as possble n the mnds of target customers to ther deal n terms of mportant features and attrbutes, and (b) clearly dfferentates t from the competton. Product lne postonng refers to smlar efforts for the entre product lne. Here, product lne postonng decsons are those that determne the optmal number of products n the lne and ther correspondng producton volumes along wth the approprate market nches for each product n the lne. 5

6 automotve ndustry: Volkswagen reportedly saved 1.5 bllon USD per year due to lots of commonalty among ther four brands: Volkswagen, Aud, Skoda, and Seat (Bremmer, 1999, Wlhelm, 1997); however, too much commonalty caused consderable confuson and dramatcally hurt sales as people were buyng lower-end models nstead of hgher-end models (Mller, 1999). Volkswagen has snce set out to overhaul ther brands to make them more dstnct and mprove sales (Mller, 00, Anonymous, 00). In order to determne an acceptable level of performance loss n platform-based product development, t s mportant to consder product performance n the context of market consderatons (.e., compettors products and customer-preferences).also, current approaches do not adequately examne the mpact of competton or how new products added to a product famly compete wth exstng products n the famly. The novel Market-Drven Product Famly Desgn (MPFD) methodology proposed n ths work attempts to overcome the lmtatons of exstng approaches and offers a comprehensve strategy to deal wth the product famly desgn problem. It helps make decsons on 1) product lne postonng, ) commonalty (.e., decdng whch parts and processes are to be shared among dfferent products n the famly), and 3) the optmal confguraton of desgn varables for each product n the famly. These decsons are based on engneerng and manufacturng feasblty and economc consderatons estmated from a demand model that predcts market performance as a functon of product characterstcs and market condtons (e.g., customer demographcs, competton). The proposed methodology provdes a framework to examne the mpact of addng new products/removng exstng products to/from the famly. Unlke most exstng approaches that assume a sngle platform, the proposed research also deals wth the problem of determnng the optmal number of product platforms for the product famly (De Weck et al., 003). The rest of the paper s organzed as follows. Frst, background on the Market Segmentaton Grd, a technque used to artculate platform leveragng strateges, and Nested Logt, the demand modelng approach employed n ths work, s provded. Detals of the proposed MPFD methodology are presented n Secton IV. Secton V dscusses the case study that demonstrates the utlty of the proposed methodology, whle conclusons and future work are summarzed n Secton VI. III. Technologcal Base The prmary contrbuton of ths paper les n ntegratng market consderatons (.e., customer preferences and competton) nto the platform-based product famly desgn formulaton. In ths context, some background on platform leveragng strateges, demand modelng and ts role n enterprse-drven desgn s also provded 6

7 A. Market Segmentaton Grd The wdespread use of market segmentaton s the nevtable consequence of the ncrease n competton and the global nature of today s market place. A varety of data-drven approaches have been proposed n the lterature (Wedel and Kamakura, 1999, Llen and Rangaswamy, 004) to formally segment the market, ncludng Conjont Analyss (Green and Kreger, 1991, Zufryden, 1977, Dobson and Kalsh, 1993, Cho and DeSarbo, 1994), clusterng (Mazanec, 1984) and neural networks (Velldo et al., 1999). However, our focus n ths study s to add rgor to a more qualtatve approach that has been ganng ground n the past decade, namely, the Market Segmentaton Grd (Meyer and Lehnerd, 1997). It should be noted that the MSG s used for product dfferentaton and not for the segmentaton of the customer-populaton. In recent years, the Market Segmentaton Grd has become the de facto method to vsualze product dfferentaton and platform leveragng strateges n the product famly desgn communty (Maron and Smpson, 006). Hgh cost & Performance Md-Range Low cost & Performance Hgh End Platform Low End Platform Hgh cost & Performance Md-Range Low cost & Performance Platform A Scaled down Scaled up Platform C Meyer and Lehnerd (1997) ntroduced the Market Segmentaton Grd shown n Fgure 1 to more Segment A Segment B Segment C Segment A Segment B Segment C (a) Horzontal Leveragng Hgh cost & Performance Md-Range Low cost & Performance Platform Segment A Segment B Segment C (c) Beachhead Approach (b) Vertcal Leveragng Fgure 1. Platform Leveragng Strateges Illustrated Usng the Market Segmentaton Grd. (Adapted from Meyer and Lehnerd (1997)) clearly artculate platform leveragng strateges n a gven market. In a MSG, the total market for a product famly s defned through a matrx of market nches that dentfy partcular user groups and prce/performance ters. Market segments are plotted horzontally n the grd whle prce/performance ters are plotted vertcally the ntersecton of each prce/performance ter wth each market segment defnes a specfc market nche. The horzontal leveragng strategy llustrated n Fgure 1(a) s one n whch subsystems and/or manufacturng processes are leveraged across dfferent market segments wthn the same prce or performance ter. The vertcal leveragng strategy, see Fgure 1(b), scales key platform subsystems and/or manufacturng processes across prce/performance ters wthn a market segment. The advantage of ths strategy s 7

8 the capablty of the company to leverage ts knowledge about a partcular market segment wthout havng to develop a new platform for each prce/performance ter. The beachhead approach shown n Fgure 1(c) combnes horzontal leveragng wth vertcal leveragng to develop an effectve, low-cost platform wth effcent processes. It s able to scale up the performance characterstcs of the platform for low-end users to the md-end and hgh-end users, as well as be appled to dfferent market segments. In the product famly lterature, MSGs have only been used as vsual ads to arrve at the approprate platform leveragng strategy. In ths work, the effectveness of the MSG s enhanced by mathematcally expressng the product postonng decsons and platform leveragng strateges n the MSG, and ncludng t drectly n the optmzaton formulaton. We also recognze that all products n the market do not compete equally, and products n a gven market segment compete more closely wth each other than wth products n other market segments. The segmentaton n the market, as llustrated n the MSG, s modeled usng the Nested Logt technque, whch s dscussed next. B. Role of Demand Models n Enterprse-drven Desgn Current desgn approaches vew demand modelng as a crtcal lnk between market research and engneerng product development. Product demand Q plays a crtcal role n assessng both the revenue and lfe cycle cost C, and ultmately the proft (.e., net revenue) V (see Fgure ). Demand, Q, s expressed as a functon of the customerdesred attrbutes, A (.e., what product attrbutes do customers care about), customer demographc attrbutes, S, prce P and tme t. By lnkng attrbutes A to correspondng engneerng desgn attrbutes E, the optmal level of E can be dentfed through maxmzng the expected value of proft (enterprse-level utlty optmzaton) to gude product development. Proft V = Q P - C Prce Lfecycle Demand Q = f(a, S, P, t) Cost C = f(e, Q, t) Customer-desred attrbutes Customer demographc attrbutes tme Engneerng attrbutes Fgure. Role of Demand Modelng n Enterprse-Drven Desgn 8

9 C. Nested Logt Nested Logt s a probablstc modelng technque used to express the choce-behavor of ndvdual customers and can be used whenever some choce-alternatves are smlar to others (Wllams, 1977). The NL demand model has been appled n a varety of stuatons, ncludng energy, travel demand forecastng, housng, telecommuncatons, and arlne revenue management (Fornash and Koppelman, 1993, Tran et al., 1987, Ben- Akva, 1973, Tran, 1986, Lee, 1999, Garrow and Koppelman, 004). In the product famly desgn problem consdered here, the key decson s the selecton of the most proftable market nche (.e., the market segment, and performance/prce combnaton) for each new product beng launched. Snce multple market segments are beng consdered, t s mportant to model the dssmlar nature of competton n dfferent market segments accurately. The mathematcal structure of the NL demand model allows us to capture the segmentaton of the market, and estmate more accurate and realstc demand models. The rest of the dscusson s geared towards provdng a basc understandng of some of the relevant mathematcs behnd the NL model. Accordng to the Random Utlty Maxmzaton (RUM) theory (McFadden, 001), the bass for most demand modelng technques, each ndvdual n has a utlty functon U n assocated wth each of the alternatves, choosng the one whch maxmzes hs/her utlty. The utlty U n can be dvded nto a determnstc component W n, and a random component ε n. The determnstc part utlty W can be parameterzed as a functon of observable ndependent varables (.e., customer desred attrbutes A, socoeconomc and demographc attrbutes S, and prce P). The utlty functon terms are represented wth the double subscrpt n representng the n th respondent (.e., customer) and the th choce alternatve. U = n W n + ε n (1) The most commonly used demand modelng technque s Multnomal Logt (McFadden, 1974), whch s derved assumng that the error terms ε n are ndependent and dentcally dstrbuted and follow an extreme value dstrbuton. Consder the form of the choce probablty functon for Multnomal Logt (MNL) models n Eq. (). In ths expresson, Pr(:C n ) refers to the probablty of choosng alternatve from choce set C n avalable to customer n, µ refers to the scale parameter, W n refers to the utlty of alternatve to customer n and s expressed n terms of unknown β s and explanatory varables Z (.e., customer desred attrbutes A, socoeconomc and demographc attrbutes S, and prce P). Usually, µ s set to 1 and the choce model s estmated for unknown β s by maxmzng 9

10 the lkelhood. The MNL model mples equal competton between all pars of alternatves, an napproprate assumpton n many stuatons, whch s famously known as the Independence of Irrelevant Alternatves (IIA) n the lterature (see (Tran, 003) for detals). µ Wn µ β Zn e e Pr( : Cn ) = = () µ Wnj ' µ β Znj e e j C n The Nested Logt (NL) model, on the other hand, can ncorporate elements of unequal competton by modelng correlaton among the choce alternatves. The NL technque assumes that the set of alternatves can be parttoned nto subsets, called nests. The technque s best explaned wth an example. A hypothetcal automoble market that only ncludes cars from the sports and sedan segments s consdered. Whle the sports segment has two cars (.e., A and B), the sedan segment has only one (.e., C). The stuaton s represented n the choce tree shown n Fgure 3. Whle the groupng of the two sports segment alternatves n one nest and the sedan n the other nest represents the customer s decson makng process (.e., he or she s assumed to consder sports cars A and B as more smlar to each other than to sedan C), t also serves to llustrate the smlarty n the error components. The followng utlty and error functons for the dfferent alternatves further clarfy ths pont: j C n ' Utltes U U U C B A = W = W = W C B A + ε ; C + ε + ε B + ε + ε A sports sports ; ; Error terms ε C ε + ε B ε + ε A sports sports ~ G(0,1) ~ G(0,1) ~ G(0,1) (3) It should be noted that the error terms for alternatves n the sports segment (.e., A and B) are no longer ndependent; they share an error component (.e., ε sports ). Whle both error components (.e., ε A & ε sports correspondng to alternatve A and ε B & ε sports correspondng to alternatve B) play a role n selectng between the entre sports segment and the famly sedan segment, only the uncorrelated error components (.e., ε A for alternatve A and ε B for alternatve B) are mportant when choosng among the nested alternatves A and B. The NL choce probablty functons for the dfferent car alternatves n the hypothetcal vehcle market are lsted next, and all expressons are wth respect to customer n. 10

11 Overall vehcle market n a) For the alternatve n the sedan segment Pr ( C : C ) n Wn, C = Wn, C Wn, C + µ sports Γn, sports e + e e (4) SPORTS segment SEDAN segment (Car C) b) For the alternatve n the sports segment Car A Car B Fgure 3. Choce Tree Representaton for a Hypothetcal Automoble Market Pr ( A: C n n sports) = e W µ e n, A sports W µ n, A sports + e W µ n, B sports (5) In these two probablty expressons, sports sports Γ s equal to ln( e + e ) and s referred to as the logsum n, sports W n, A W µ n, B µ parameter and C = {A,B,C} s the choce set avalable to customer n; Pr ( C : C ) s the probablty of choosng n alternatve C from the vehcle market, and Prn ( A : Cn sports) s the condtonal probablty of choosng alternatve A assumng the sports segment has been already chosen. Fnally, µ sports s the scale parameter assocated wth the sports segment and plays an mportant role n modelng unequal competton. A value closer to 0 ndcates that the alternatves n the sports segment (.e., A and B) compete more closely wth each other for market share than wth alternatves that do not belong to the sports segment (.e., C), and a value closer to 1 ndcates that the wthnsegment competton s not sgnfcant. The motvaton behnd the use of a NL demand model n product famly desgn s to model the mpact of market segmentaton on the market share of each of the products n the famly by explotng NL s unque error structure. Ths s accomplshed by groupng products n each market segment under a separate nest n an NL choce tree representaton smlar to the one shown n Fgure 3 whch s then followed by the estmaton of the NL model by determnng the values of the unknown β s and scale parameter (µ) for each of the nests (.e., segments). n n 11

12 IV. The Market-Drven Product Famly Desgn Methodology The proposed Market-Drven Product Famly Desgn (MPFD) methodology seeks to ntegrate market consderatons wth tradtonal product famly desgn ssues (e.g., commonalty, manufacturng cost) to desgn the most proftable product famles unlke tradtonal product famly desgn methods whch mostly focus on the cost benefts. The MPFD methodology (see Fgure 4) conssts of the followng four steps: 1) creaton of the market segmentaton grd, ) estmaton of the Nested Logt demand model and buldng a choce smulator program, 3) constructon of models for product performance and cost, and 4) optmzaton of the product famly by maxmzng proft. Each of the steps s performed sequentally, but Steps ) and 3) can be accomplshed n parallel f desred. A short dscusson on each of the MPFD steps follows. A. Step 1) Creaton of the Enhanced Market Segmentaton Grd Data on the exstng market s requred to create an enhanced Market Segmentaton Grd (MSG) that ncludes nformaton not only about the market segments and the performance/prce ters but also about the compettors n each nche (.e., the market segment and performance/prce combnaton). Collectng market data nvolves gatherng sales data deally at the level of the ndvdual customer n order to determne the choce set avalable to each ndvdual customer as well as ncorporate bases assocated wth demographcs (e.g., age, ncome). Informaton on the performance characterstcs of compettors products n the market must also be collected and can be usually obtaned from product catalogs. An mportant consderaton s the choce of the performance attrbute to nclude n the grd as the vertcal axs of the MSG. The use of Dfferentatng Attrbutes (DA), defned n (Robertson and Ulrch, 1998) as characterstcs that customers deem mportant n dstngushng between products, s used for ths purpose. For example, nteror nose level s a DA for automobles; customers generally expect dfferent values of ths DA for dfferent knds of vehcles, such as audble cues from the engne n sporty vehcles but near slence n luxury vehcles (Robertson and Ulrch, 1998). In ths work, DAs are assumed to be dentcal to the customer-desred attrbutes (A) descrbed earler. Developng the market segmentaton grd n ths step s ndependent from developng the product desgn detals and buldng product performance models (Step 3), and t s ths aspect of our methodology that enables the seamless ntegraton of the market analyss wth the engneerng modelng actvtes. 1

13 HIGH )Estmate Demand Model Performance ters MED LOW 1)Create Market Segmentaton Grd Nested Logt Model Choce Smulator SGMT-1 SGMT- SGMT-3 Market segments BEACHHEAD STRATEGY 3)Buld Models for Product Performance 4) Proft Maxmzaton Model Models to express relatonshp between desgn varables and product performance Models to express relatonshp between product archtecture and product cost. Optmal product postonng decson Optmal product platform(s) Optmal product specfcatons Fgure 4. The MPFD Methodology to Desgn Platform-Based Product Famles B. Step ) Estmaton of the Demand Model The nformaton n the MSG has to be converted nto an equvalent choce tree representaton before the estmaton of the NL model. A hypothetcal vehcle market s used to descrbe ths procedure. The MSG conssts of four market segments along the horzontal axs (correspondng to sports, famly sedan, SUV, and luxury segments) and three performance/cost ters on the vertcal axs, leadng to twelve nches n all (see Fgure 5(a)). For smplcty, horsepower s used as the performance measure along the vertcal axs. The grd s populated wth cars from three manufacturers: A, B and C. Consder the tree representaton of the grd n Fgure 5(b) n whch the cars under each segment are grouped together n a nest. Ths representaton s used to group cars that compete more closely wth each other and enable the use of the Nested Logt technque. Such a choce tree representaton may also be used to smulate the customer s decson-makng process,.e., customers may choose among dfferent vehcle segments before choosng among the dfferent vehcles n each segment. The next step nvolves the estmaton of the Nested Logt (NL) demand model. Each nest n the NL model corresponds to a partcular market segment. In ths work, termnology for desgn attrbutes s borrowed from our 13

14 earler work on Decson-Based Desgn framework (Wassenaar et al., 006, Km et al., Kumar et al., 006, Wassenaar and Chen, 003)). The demand model used n ths work, establshes the relatonshp between the customer desred attrbutes, A, the socoeconomc and demographc attrbutes, S, prce, P, and the demand, Q,.e., Q(A, S, P). In order to ad engneerng decson-makng, customer desred attrbutes (A) are replaced by correspondng engneerng attrbutes E n the model, where E are any quantfable product propertes that are used n the engneerng product development process. Estmatng a NL demand model s smlar to estmatng a MNL model (Wassenaar and Chen, 003, Wassenaar et al., 006, Kumar et al., 006) except that the scale parameter (µ) correspondng to each of the nests has to be estmated. As dscussed earler, the values of the scale parameters help evaluate the valdty of the nestng structure and also serve as a measure of the wthn-segment competton. Once the NL demand model s estmated, t can be used repeatedly to estmate the mpact of desgn changes or the effect of addng/removng products from the lne usng a choce smulator program. A choce smulator s a computer program that smulates the demand model and uses the market data as nputs to estmate changes n market share for each product as a functon of engneerng attrbutes, customer demographc attrbutes and prce values (.e., E, S, and P). One challenge n buldng a choce smulator for the product famly optmzaton problem s the complexty ntroduced due to the addton of multple products nto the market smultaneously--new products encoded n the product lne postonng decson have to be grouped wth smlar compettors products n correspondng market segments and the data set has to be updated n each optmzaton teraton. C. Step 3) Constructon of Models for Product Performance and Cost Buldng models for product performance functons E(X) nvolves buldng models that represent the relatonshp between engneerng attrbutes E and desgn optons X (whch ncludes decsons on sze, shape, materal, etc.) through engneerng analyss. These relatonshps can be expressed through analytcal models, fnte element models, smulaton models, metamodelng technques, etc. Smlarly, cost s modeled as a functon of the desgn optons (X). The cost model s used to evaluate the benefts of dfferent commonalty decsons (.e., shared parts and processes between dfferent product varants n the product famly). In ths work, the total cost (C) s expressed n terms of materal cost (C M ), labor cost (C L ), repar and warranty costs (C R ), desgn costs (C D ), and overhead costs (C O ). Materal cost s expressed n terms of producton volume V, desgn optons X, and manufacturng attrbutes M. Examples of manufacturng attrbutes (M) are toolng and fxturng specfcatons, producton plans and schedules, and nventory control schemes. The repar/warranty costs (C R ) are expressed as a 14

15 functon of the product s relablty, whch n turn s expressed as a functon of X and operatng condtons O (e.g., temperature, pressure). These two models can be used to make trade-offs between cost and performance, n conjuncton wth the demand model. HIGH COST & PERFORMANCE A1, B1 C C4 MEDIUM RANGE A B3,C3 B4 LOW COST & PERFORMANCE C1 B A3 A4 SGMT 1 SPORTS CAR SGMT FAMILY SEDAN SGMT 3 SGMT 4 SUV LUXURY (a) Market Segmentaton Grd SPORTS CAR FAMILY SEDAN SUV LUXURY A1 B1 C1 A B C A3 B3 C3 A4 B4 C4 (b) Equvalent decson (choce) tree representaton Fgure 5. A MSG and Its Equvalent Choce Tree Representaton D. Step 4) Optmzaton of the Product Famly The product famly desgn optmzaton problem prmarly nvolves the determnaton of the (1) optmal product lne postonng decson, whch nvolves choosng the optmal number of product varants n the famly and the market nches they should target, () optmal commonalty decsons (.e., the number of platforms n the famly and the desgn varables that should be shared by product varants assgned to each of the platforms), and (3) optmal levels of engneerng desgn attrbutes (E), and correspondng desgn optons for each product n the famly. In ths work, the problem s formulated as an all-n-one problem to make these decsons smultaneously and solved n a sngle stage usng an teratve procedure. In each teraton, a random bnary strng that has nformaton on () product lne postonng decsons as well as () commonalty decsons s suppled to the proft maxmzaton model. The product lne postonng substrng (.e., the part of the bnary strng that s used to make the product lne 15

16 postonng decson) not only sets bounds on the performance varable used to defne ters along the vertcal axs (e.g., power n the case of electrc motors) but also has an mpact on the market share garnered by each new product snce the product lne postonng substrng decdes the targeted market segment and therefore the compettors products whch have the bggest mpact on the market shares for each new product. Fgure 6 llustrates how a bnary strng can be used to represent product lne postonng decsons. Consder a MSG wth three segments and three performance ters formng a (3x3) grd. A one-dmensonal bnary strng whose sze corresponds to the number of the cells n the MSG s used to represent such a grd. The 1 s n the strng and the crossed cells n the grd correspond to the decsons to ntroduce products n correspondng market nches. Smlarly, the 0 s n the strng and uncrossed cells correspond to decsons to not launch products n the correspondng nche. Compettors products are represented n the MSG n Fgure 6 by shaded cells are not represented n the strng. Consder segment two (correspondng to column n the MSG): the two crossed squares ndcate that the frm s consderng launchng two new products n that segment whle the two shaded boxes represents compettors products n the correspondng nches. In all, four products compete for market share n ths segment. It should be noted that compettors products are not numercally encoded n the bnary strng (the correspondng blocks n the bnary strng are only shaded for ease of understandng), and only a one tme converson of the compettors products n the grd to equvalent nodes n the Nested Logt tree s necessary. Fgure 7 llustrates how product lne postonng and product commonalty decsons can be smultaneously encoded n a numerc strng. The strng s essentally dvded nto two parts: the frst part of the numerc strng corresponds to the product lne postonng decson, and the second part s used to store commonalty decsons. Each product s by an ordered par (market ter, market segment) 16

17 Cost & Performance X x x x x Bnary strng representaton Choce Tree representaton Market segments Boxes wth x s ndcate the presence of products n the market segmentaton grd Shaded boxes n the market segmentaton grd ndcate presence of compettors products n the market segmentaton grd 1 Represents a decson to launch a product n that nche 0 Represents a decson to NOT launch a product n that nche. The shaded block only ndcates that there s a competton n the correspondng market nche Represents Market Segment Represents the product correspondng to the X n the Market Segmentaton Grd (MSG) and 1 n the bnary strng representaton Represents compettors products and corresponds to the shaded boxes n the market segmentaton grd. Fgure 6. Equvalent MSG, Bnary Strng and NL Tree Representatons or a Gven Product Lne Postonng Decson. For example, Product {1: (3,1)} ndcates that Product 1 s from market segment 1 and market ter 3. Assumng each of the products n the famly has three desgn varables (say x 1, x, x 3 ), then each product s represented by a 4- bt commonalty sub-strng. The frst bt represents the platform ndex, and the followng three bts are bnary commonalty decson varables, whch ndcate f the correspondng desgn varable s common across all the products sharng the platform. For example, f the thrd commonalty decson varable s 1, then t ndcates that the desgn varable x 3 s beng shared. From Fgure 7, t s clear that Products {1: (3,1)} and {: (,)} share Platform 1 and Products {3: (3,3)} and {4: (1,3)} share Platform. Products 1 and share Desgn Varable, and Products 3 and 4 share Desgn Varable 3. It should be noted that the product lne postonng and commonalty substrngs together express the platform leveragng strategy. In ths manner, exstng products can be represented n the strng by fxng the values of the bts correspondng to the (ter, segment) pars to 1 durng the optmzaton. Includng the exstng product(s) n the formulaton can help when redesgnng and/or re-prcng that product (.e., determnng optmal levels of E, and P). Cost savngs due to sharng parts and producton nfrastructure and parts wth exstng products can also be explored. 17

18 SGMT-1 SGMT- SGMT-3 PRODUCT 1 PRODUCT PRODUCT 3 PRODUCT 4 substrng for the product postonng decson substrng for the commonalty decson x 1 x x NICHE SEGMENT ndex: (nche, segment) Product 1: (3,1) Product : (,) Product 3: (1,3) Product 4: (3,3) Platform ndex Commonalty decson varables 0-ndcates desgn varable not shared 1-ndcates desgn varable s shared (x 3 s shared) share platform 1 wth Product 1:(3,1) desgn varable Product :(,) as platform varable 1 3 3,1 3,3 PRODUCT 1, 1,3 PRODUCT 4 PRODUCT PRODUCT Product 3:(1,3) Product 4:(3,3) share platform wth desgn varable 3 as platform varable Note: Compettors products are not ncluded n the MSG and choce tree representatons Fgure 7. Strng Representaton of Product Lne Postonng and Commonalty Decsons The product famly desgn problem s formulated as shown n Fgure 8. The formulaton captures the key product famly desgn decsons consdered n ths work. The set of desgn optons correspondng to product s represented as X j. N represents the number of market ters n each market segment, and S represents the number of market segments. X jk represents the k th varable correspondng to product E j corresponds to performance characterstcs of the product. E j can be expressed as a functon of desgn optons X j usng relatonshps r. Desgn constrants are expressed as g(x,e) 0. The market segment-specfc varable bounds for desgn optons of all products X j n segment j are represented by LB j and UB j whle Π G 1,G corresponds to the proft wth respect to bnary strng G:{G 1,G }. Product lne postonng decsons are represented by G 1 whle commonalty decsons are expressed usng G. It s expressed as a functon of demand Q j, prce P j, the demand and prce values for product (,j), and cost C. Whle a descrpton of the dfferent cost components was provded earler, t should be noted that both G 1 and G have a drect mpact on cost snce G 1 decdes the number of product varants and the producton 18

19 volumes of dfferent products n the famly whle G decdes whch of the X s are shared between dfferent product varants. Gven a) Market data Sales data of dfferent products, buyer-specfc nformaton (e.g., age, ncome) b) Demand model Demand as a functon of product attrbutes and buyer-specfc nformaton. Includes estmates for utlty functon coeffcents (β), scale parameters (µ), etc.; Q (E,S,P) c) Models for Product Performance Analytcal and Smulaton models expressng relatonshp between E j and X j E j = r(xj ) N, j S d) Cost models Models for dfferent cost components; materal cost (C M ), labor cost (C L ), desgn cost (C D ), repar/warranty costs (C R ), overhead costs (C O ), etc. C = C Q, X,M + C Q, X,M + C X,O + C + C G1, G, X, M, O N, j S ( ( ) ( ) ( ) M j j L j j Fnd a) Product Postonng substrng (G 1 ) Contans nformaton on number of products, and market nches correspondng to each of them. b) Commonalty substrng (G ) Contans nformaton on the number of platforms, the products sharng each platform, and platform composton (.e., whch desgn varables to share n each platform) c) Desgn Optons (X) Choce of shape, sze, materal, etc., represented by X j, the vector of all desgn varables X jk correspondng to product (,j) Maxmze a) Proft Π = Q G,G,X, j j ( E,S P ) P C j, j Satsfy a) Desgn constrants Relatonshps between E and X, and between dfferent X g(x,e ) 0; N, j S LB j j j X jk UB ; j j X jk X j R j j, N, j S D O Fgure 8. Formulaton for Proft Maxmzaton-Based Product Famly Desgn V. Case Study: Desgn of a Famly of Unversal Electrc Motors The desgn of a famly of unversal motors s used to demonstrate the mplementaton of the proposed methodology. Motvated by Black & Decker s case study reported n (Lehnerd, 1987) an example problem nvolvng the desgn of a famly of unversal electrc motors was frst used n (Smpson, 1998) and subsequently used by a number of researchers n the communty as revewed n (Smpson, 006). Exstng formulatons of the unversal electrc motor product famly desgn problem are brefly dscussed n the next secton. Ths s followed by 19

20 dscussons on the enhancements to the unversal electrc motor product famly desgn problem, wth specal emphass on market and manufacturng consderatons. The secton concludes wth a dscusson on the results and nterpretatons assocated wth the case study. A. Formulaton of the Unversal Electrc Motor Product Famly Desgn Problem n the Lterature A schematc of a unversal motor s shown n Fgure 9. As shown n the fgure, a unversal motor s composed of an armature and a feld, whch are also referred to as the rotor and stator, respectvely. The armature conssts of a metal shaft and slats (armature Fgure 9. Unversal Motors Schematc (Source: Smpson et al. (001)) poles) around whch wre s wrapped longtudnally as many as a thousand tmes. The feld conssts of a hollow metal cylnder wthn whch the armature rotates. Addtonal detals on unversal motors can be found n (Chapman, 1991). The objectve of the desgn problem s stated as Desgn a famly of ten unversal electrc motors that satsfes a varety of torque and power requrements by scalng a common motor platform Smlar to the orgnal Black & Decker case study, the aforementoned work seeks to fnd the optmal product famly assumng a pre-specfed product platform. Indvdual products n the famly share dentcal values for all motor desgn varables except stack length (L) and current drawn by the motor (I). The motor desgn varables that are of nterest are tabulated n Table 1. The termnal voltage V t s fxed at 115 Volts to correspond to standard household voltage. A mathematcal model for the desgn of a unversal electrc motor (Smpson et al., 001) relates the desgn varables {N c, N s, A wa, A wf, r, t, I, L} to the performance measures Power (P), Torque (T), Mass (M), and Effcency (η). The soluton to the unversal motor product famly desgn problem should also satsfy the set of constrants gven n Table. The constrant on magnetc ntensty (H) ensures that the magnetc flux wthn each motor does not exceed the physcal flux carryng capacty of steel. The constrant on feasble geometry ensures that the thckness of the stator (t) does not exceed the radus (r) of the stator; the thckness of the stator s measured from the outsde of the 0

21 motor nward. The requred output power (P) s taken as 300W, and the ten torque values (T) for the motor famly range from 0.05 Nm to 0.50 Nm, and there are mnmum expectatons for effcency and mass of each of the motors. The product famly desgn objectves are to mnmze mass (M), and maxmze effcency (η) of each of the motors n the famly whle sharng the pre-specfed platform varable. Most of the aforementoned approaches requre specfyng the unversal electrc motor platform a pror. Some researchers do not mpose ths restrcton and attempt to optmze the choce of platform varable(s) usng a varety of formulatons: the varaton-based method (Nayak et al., 00), penalty functons (Messac et al., 00b), senstvty analyss and cluster analyss (Da and Scott, 004) and a genetc algorthm-based approach (Akund et al., 005). However, these approaches only seek to mnmze loss n motor performance (.e., motor effcency and mass) due to the commonalty decsons wthout modelng manufacturng and market consderatons explctly. B. Descrpton of the Enhanced Unversal Electrc Motor Product Famly Desgn Problem Formulaton In order to model the market for unversal motors, n addton to achevng an understandng of dfferent market segments for the unversal motor, data on the sze of the market, specfcatons of compettors products, and market shares of dfferent compettors products needs to be collected. The product platform decsons also requre an understandng of the manufacturng process and assocated cost components. Dscussons on the unversal electrc motor market and the manufacturng cost model used for the product famly desgn follow. Varable Table 1. Unversal Motor Desgn Varables and Bounds Descrpton N c Number of wre turns on the motor armature (turns); ( 0 Nc 1500) N Number of wre turns on each feld pole (turns); ( 0 Ns 500) s A Cross-Sectonal area of the armature wre (m -6 6 ); ( A ) wa A Cross-Sectonal area of the feld wre (m -6 6 ); ( A ) wf r Radus of the motor (m); (0.01 r 0.10) t Thckness of the motor (m); ( t 0.10) I Current drawn by the motor (Amperes); (0.1 I 6.0) L Stack length (m); (0.01 L 0.1) wf wa 1

22 Table. Unversal Motor Desgn Constrants Name Constrant Magnetzng Intensty, H H 5000 Amp. turns/m Feasble Geometry t<r (m) Power, P P=300W Torque, T T = { 0.05,0.1,0.15,0.15,0.0,0.5,0.30,0.35,0.40,0.50}Nm Effcency, η η Mass, M M.0kg 1. Descrpton of the Hypothetcal Unversal Electrc Motor Market The hgh performance characterstcs and flexblty of unversal electrc motors have led to a wde range of applcatons (Venott and Martn, 1986), especally n household use where they are found n products such as electrc drlls and saws, blenders, vacuum cleaners, and sewng machnes. A hypothetcal market for unversal motors s assumed to comprse manufacturers of products that use the unversal electrc motor. One of the prmary goals n ths paper s to demonstrate the mpact of market consderatons on product famly desgn. Towards ths end, hypothetcal market data for unversal electrc motors s constructed for the study. A descrpton of the resultng Market Segmentaton Grd (MSG) follows. A MSG wth four market segments household/ktchen applances, power tools, cordless power tools, and garden/lawn tools s presented n Fgure 10. Power and Cost are used as the Dfferentatng Attrbutes for defnng ters wthn each segment wth the understandng that motors wth hgher power cost more. It should be noted that the overlap between the power bounds for adjacent ters n a segment mples competton among unversal electrc motors from dfferent ters n the same segment. As llustrated n Fgure 10, the segment for household/ktchen applances ncludes (manufacturers of) blenders, vacuum cleaners, washng machnes, and gas-heated dryers. The power tools segment ncludes drlls, varous types of saws (e.g., band saw, crcular saw, and jgsaw), sanders and fastenng tools. The cordless power tools segment ncludes approxmately the same product mx as the power tools segment except for the fact that the motors used n these devces are requred to run on battery-operated (DC) power supply. Fnally, the garden/lawn tools segment ncludes strng and hedge trmmers, garbage dsposal unts, yard blowers and lawn mowers. The dstngushng characterstc of the motors n each segment s ncluded under each of the segments n the MSG representaton. The motors used n household applances tend to operate at hgher speeds whle motors used n power tools are characterzed by hgher torque requrements. The motors n the cordless power tools segments share the hgher torque characterstc. In addton, they are also requred to be lghter and more

23 effcent snce they need to be portable and operate on a battery-operated power supply. Fnally, the motors n the garden tools segment are characterzed by hgher power requrements and tend to be bgger and heaver. In all, data for 3 motor manufacturers and 40 ndustral customers (devce manufacturers) was generated for the hypothetcal unversal electrc motor market, and a segment-wse lstng of product offerngs s provded n the Appendx. The sze of the market s assumed to be 40,000 motors, and demand s assumed to be unform across all the ndustral customers (.e., 1000 motors each). The ndustral customers are assumed to choose among dfferent motors based on the motor s attrbutes (.e., Prce P, Power (P: E 1 ), Effcency (η: E ) and Mass (M: E 3 )). Customers n each segment are assgned the same order quantty to smplfy the analyss. Hgh Power Hgh Cost 500W - 600W 600W - 700W 350W - 450W 800W - 900W Md-Range 400W - 550W 500W - 650W 50W - 400W 750W - 850W Low Power Low Cost 300W - 450W 450W - 550W 150W - 300W 600W - 750W Household/ktchen applances Power tools Cordless Power tools Garden/ Lawn tools Hgher rpm Hgher torque Hgher effcency Battery power supply Lghter Hgher Power Heaver Fgure 10. Market Segmentaton Grd for Unversal Motor Product Famly A number of NL demand models were estmated and on the bass of behavoral nterpretatons and goodness of ft estmates, the model n Table 3 was chosen for further consderaton. The model coeffcents (for attrbutes A = Prce, Power, Effcency, and Mass) have sgns consstent wth our understandng of preference behavor for dfferent motor attrbutes. For example, prce has a negatve coeffcent, and effcency has a postve coeffcent, mplyng that manufacturers prefer cheaper and more effcent motors. The values of all scale parameters are 3

24 between [0 1], whch justfes the nestng structure (.e., the use of dfferent nests for each market segment) that we employed. As dscussed earler, the value of the scale parameter assocated wth a partcular market segment provdes an ndcaton of the level of competton among the dfferent product offerngs n that segment. All the scale parameters have farly low values, ndcatng that the wthn-segment competton s sgnfcant n all four segments. Ths means that whenever a new product s ntroduced nto one of the four market segments (say power tools segment), the market shares of the exstng products change but the market shares of the products n the remanng segments (.e., Segments 1, 3, and 4) reman relatvely unaffected. µ 1 and µ have lower values than µ 3 and µ 4, ndcatng that the wthn segment competton n Segments 1 and (.e., household applances and power tools segments) s hgher than the wthn-segment competton n Segments 3 and 4 (.e., cordless power tools and garden tools segments). The estmaton of the demand model s followed by buldng the choce smulator so that the market consderatons can be ntegrated nto the product famly optmzaton problem. The choce smulator program requres the product lne postonng strng (see Fgure 7) and the performance specfcatons (.e., Prce, Power, Effcency and Mass) of each motor n the strng as nputs. In turn, t calculates the market share both n terms of revenue as well as actual quanttes for each of the motors n the market. Table 3. Results of Demand Model Estmaton for the Unversal Motor Market Parameter Prce (P) Power Effcency (η ) Mass (M) Scale parameters for each market segment µ µ 1 µ µ 3 3 Coeffcent The demand model also helps demonstrate the roles of competton and segmentaton (on the market shares of ndvdual motors) n the market. Fgure 11 llustrates the dfference n market share of the exstng products (correspondng to products wth seral numbers 1 to 3 n the fgure) before and after the ntroducton of a new product (Product 4) n Segment, n Fgure 11(a) and Fgure 11(b), respectvely. The product lne postonng decson under consderaton nvolves ntroducng a sngle new product n the hgh power/hgh cost nche n the power tools segment (.e., n (ter, segment) (3,)) wth the specfcatons gven n Table 4. Whle the ntroducton of Product 4 (code: NEW) n Segment takes away sgnfcant market share from the other products n the segment (.e., Products 10-14), the market share of each product n the remanng segments (segments correspondng 4