AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING

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1 Tools and Mthods of Comptiti Enginring, Editd by Horáth and Xirouchakis 2004 Millprss, Rottrdam, ISBN AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING Jrmy J. Michalk Dpartmnt of Mchanical Enginring Unirsity of Michigan USA Frd M. Finbrg School of Businss Administration Unirsity of Michigan USA Panos Y. Papalambros Dpartmnt of Mchanical Enginring Unirsity of Michigan USA ABSTRACT Markting and nginring dsign dcisions ar typically tratd as sparat tasks both in th acadmic litratur and in industrial practic, and thir intrdisciplinary intractions ar not wlldfind. In this articl, analytical targt cascading (ATC), a hirarchical optimization mthodology, is usd to fram a formal optimization modl that links markting and nginring dsign dcision-making modls by dfining and coordinating intractions btwn th two. For complx products, nginring constraints typically rstrict th ability to achi som dsirabl combinations of product charactristic targts, and th ATC procss acts to guid markting in stting achiabl targts whil dsigning fasibl products that mt thos targts. Th modl is dmonstratd with a cas study on th dsign of houshold scals. KEYWORDS Analytical targt cascading, markting, optimal product planning, dsign optimization, discrt choic modls, logit, conjoint analysis. INTRODUCTION Markting and nginring contributions to product dlopmnt ar typically tratd sparatly both in industry and in th acadmic litratur. Rsarch on product dlopmnt dcision-making in th markting community has historically diffrd from rsarch in th nginring dsign community in scop, prspcti, product rprsntation, and mtrics of prformanc and succss. An oriw of ths diffrncs is proidd in Tabl, xcrptd from a comprhnsi litratur riw of product dlopmnt dcision rsarch by Krishnan and Ulrich (200). Sparating ths disciplins hlps in th organization and managmnt of information but can also caus communication difficultis and disjoint dcision-making rsulting in infrior product dcisions. Krishnan and Ulrich not this as a waknss, particularly for complx or tchnologydrin products. Howr, th two communitis do Prspcti on Product Typical Prformanc Mtrics Dominant Rprsntational Paradigm Exampl Dcision Variabls Critical Succss Factors Tabl Markting A product is a bundl of attributs Fit with markt, markt shar, consumr utility, profit Customr utility as a function of product attributs Product attribut lls, pric Product positioning and pricing, collcting and mting customr nds Enginring Dsign A product is a complx assmbly of intracting componnts Form and function, tchnical prformanc, innoatinss, cost Gomtric modls, paramtric modls of tchnical prformanc Product siz, shap, configuration, function, dimnsions Crati concpt and configuration, prformanc optimization Comparison of Markting and Enginring Dsign Prspctis

2 ha diffrnt foci and aras of xprtis, and attmpting to intgrat thm compltly may b disadantagous. This articl offrs a mthod to formally link dcisions by th two communitis whil maintaining thir disciplinary idntity; th rsulting modl mploys th formalism of Analytical Targt Cascading (ATC) (Kim, 200). An xpandd rsion of this papr (Michalk t al., 2004) proids furthr dpth from a markting prspcti and dmonstrats that coordinating markting and nginring dcision modls using ATC rsults in solutions suprior to thos obtaind through disjoint dcision-making... Markting Product Planning Modls Kaul and Rao (995) proid an intgrati riw of product positioning and dsign modls in th markting litratur. Thy diffrntiat btwn product positioning modls, which inol dcisions about abstract prcptual attributs, and product dsign modls, which inol choosing optimal lls for a st of physical, masurabl product charactristics. In this articl w work only with masurabl product charactristics; howr, a comprhnsi framwork similar to th on proposd by Kaul and Rao could b usd to includ prcptual attributs, product positioning, and consumr htrognity. In this articl, conjointbasd product dsign modls from th markting litratur will b rfrrd to as product planning modls. Optimal product planning in th markting litratur is typically posd as slction of optimal pric and product charactristic lls that achi maximum profit or markt shar. For complx products, whr nginring constraints may prnt som combinations of product charactristic lls from bing tchnically attainabl, it is difficult to dfin xplicitly which combinations of charactristics ar fasibl. For such products, planning dcisions mad without nginring input may yild infrior or infasibl solutions..2. Enginring Product Dsign Modls Th nginring dsign optimization litratur focuss on mthods for choosing alus of dsign ariabls that maximiz product prformanc objctis. Papalambros and Wild (2000) proid an introduction to nginring dsign optimization modling tchniqus, stratgis and xampls. Whn multipl conflicting optimization objctis xist, th solution is a Parto st of optimal products, and th choic of a singl product from that st rquirs xplicit xprssion of prfrncs among objctis. Such prfrncs ar notoriously difficult to dfin in practic. Som mthods us intracti, itrati sarchs to licit prfrncs, rlying on intuition in naigating th Parto surfac and choosing an appropriat dsign (Diaz, 987). Rcnt fforts in th dsign litratur tak th approach of rsoling tradoffs among tchnical objctis by proposing modls of th producr s financial objcti (Hazlrigg, 988; Li and Azarm, 2000; Gupta and Samul, 200; Wassnaar and Chn, 200). Gu t al. (2002) build on this work using th collaborati optimization framwork to coordinat dcision modls in th nginring and businss disciplins. Hr w propos a rlatd mthodology, but w coordinat product planning and nginring dsign modls using th ATC mthodology, which has pron conrgnc charactristics for arbitrarily larg hirarchis (Michlna t al., 2002; Michalk and Papalambros, 2004), and w draw upon tchniqus from th markting litratur to dlop xplicit mathmatical modls of dmand basd on data. 2. METHODOLOGY Using th ATC framwork, discussd in dtail blow, th joint product dlopmnt problm is dcomposd formally into a product planning subproblm and an nginring dsign subproblm. Th product planning subproblm inols choosing th dsird targt product charactristics and pric that will maximiz th producr s xpctd profit, whr profit dpnds on dmand. Th nginring dsign subproblm inols choosing a fasibl dsign that will achi th targt product charactristics as closly as possibl. Using th ATC procss, th two subproblms ar sold itratily until a consistnt optimal product dsign is achid. 2.. Analytical Targt Cascading Analytical targt cascading is an optimization mthodology for systms dsign that works by dcomposing a complx systm into a hirarchy of intrrlatd subsystms (Kim 200). ATC rquirs a mathmatical modl for ach subsystm that computs th subsystm rspons as a function of th dcisions at that subsystm. Th subsystm modls ar organizd into lmnts of a hirarchy, as in th xampl shown in Figur, whr th top ll rprsnts th orall systm and ach lowr ll 2 Jrmy Michalk, Frd Finbrg and Panos Papalambros

3 VEHICLE ELECTRONICS POWERTRAIN BODY CHASSIS... CLUTCH ENGINE TRANSMISSION... BLOCK CYLINDER HEAD CRANKSHAFT Figur Exampl ATC hirarchy for a hicl dsign rprsnts a subsystm of its parnt lmnt. Papalambros (200) proids an oriw of th ATC litratur, and Michalk and Papalambros (2004) proid dtails of th gnralizd ATC formulation. In th ATC procss, top-ll systm dsign targts ar propagatd down to subsystms, which ar thn optimizd to match th targts as closly as possibl. Th rsulting rsponss ar thn rbalancd at highr lls by itratily adjusting targts and dsigns throughout th hirarchy to achi consistncy. Michlna t al. (2002) and Michalk and Papalambros (2004) prod undr assumptions of conxity that by using crtain classs of coordination stratgis to coordinat lmnts in th ATC hirarchy, th ATC formulation will conrg, within a usr-spcifid tolranc, to th sam solution as if all ariabls in th ntir systm wr optimizd simultanously (or, all-at-onc ). Using ATC can b adantagous bcaus it organizs and sparats modls and information by focus or disciplin, proiding communication only whr ncssary. Som problms that ar computationally difficult or impossibl to sol all-at-onc can b sold using ATC, and in som cass ATC can rsult in improd computational fficincy bcaus th formulation of ach indiidual lmnt typically has fwr dgrs of frdom and fwr constraints than th all-at-onc formulation. In th formulation and xampl prsntd in this articl, thr ar only two lmnts: th markting product planning subproblm M and th nginring dsign subproblm E, which is th child of M. Howr, for complx systms ATC allows th flxibility to modl th nginring subproblm as a hirarchy of subsystms and componnts rathr than with a singl lmnt. For xampls of complx systms nginring dsign using ATC, s Kim t al. (2002), and Kim t al. (2003) Th Markting Product Planning Subproblm In th product planning subproblm, a simpl modl of profit Π is calculatd as rnu minus cost, such that ( ) Π= q p c c () V I whr q is th quantity of th product producd and sold (product dmand), p is th slling pric, c V is th ariabl cost pr product, and c I is th instmnt cost. This modl is simplifid and ignors such financ-rlatd concrns as th tim alu of mony, fixd costs, risk and uncrtainty; howr, this simpl modl will suffic to dmonstrat broad trnds and proid insight into th gnral forcs at work. Th pric p is tratd as a dcision mad by th firm, and for simplification in this articl c V and c I ar considrd constant across all possibl product dsigns. Product dmand q dpnds on th pric p and charactristics z of th product, and discrt choic analysis and conjoint analysis ar usd to modl and prdict q as a function of z and p. It is assumd in this articl that th producr is a monopolist; howr, gam thory could b usd to modl oligopoly comptition following Michalk, Skrlos and Papalambros (2003). Discrt Choic Analysis A st of statistical mthods largly unfamiliar to nginring audincs has bn dlopd, first in logistics and urban planning and thn in conomics, to prdict choics mad in uncrtain nironmnts (Louir t al., 2000; Train, 2003). Th chif thortical dific is that of random utility modls. In such modls, a dcision-makr is prsumd to dri utility from ach altrnati in a st of possibl altrnatis, to an xtnt partially prdictabl in trms of obsrd coariats. In markting applications, ths coariats ar typically product (or houshold-spcific) charactristics, whos alus can b usd to obtain an orall attraction for ach altrnati, whr attraction rfrs to th obsrabl, dtrministic componnt of utility. Bcaus w cannot prdict consumr utility prfctly, ths attraction alus must in turn b combind with an rror trm in ordr to dtrmin choic probabilitis for ach altrnati (and th probability that non of AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING 3

4 th altrnatis is chosn, oftn calld th outsid good ). Formally, thr is a st of product altrnatis numbrd through J with attraction alus {, 2, J } and associatd rrors {ξ, ξ 2, ξ J } plus an outsid good, indxd as altrnati 0, with rror ξ 0 and attraction alu 0 normalizd to zro ( 0 = 0). Th probability P j that w obsr a choic of altrnati j is th probability that altrnati j has th highst utility: Pj = Pr j + ξ j j + ξ j, j J (2) Computational fficincy dpnds critically on th distribution assumd for th ξ random rror trms in Eq.(2). Errors can tak sral forms, and it gnrally rquirs xtrmly larg sampls for assumptions about distributional rror to ha any substanti impact; consquntly, rsarchrs oftn work with rror spcifications allowing th most tractability. For xampl, if rrors ar assumd to b normally distributd, thn th form of P j is calld th multinomial probit modl, which dos not admit of closd-form xprssions for choic probabilitis in trms of undrlying attractions. Howr, if ξ trms ar assumd to b Typ II xtrm-alu (or Gumbl) distributd (i.., Pr[ξ < x] = xp[-xp(-x)]), thn it can b shown that j Pj = + j J j whn th utility of th outsid good 0 is normalizd to zro (s Train 2003 chaptr 3 for proof). This form is calld th multinomial logit modl (MNL). Th MNL modl allows a connint closd-form solution for choic probabilitis P j that is spcially attracti in trms of optimization. Using (3), choic probabilitis for any subst of products can b calculatd asily. En if all products ar offrd by a singl ntity (i.., a monopolist), th prsnc of th outsid good nsurs that dmand for a st of unattracti products will b low, with probability of not choosing a product gin by: P = + j j j J (3) (4) It is assumd that can b masurd as a function of obsrabl quantitis such as product charactristics, pric, consumr charactristics, tc. In this papr w considr only product charactristics and pric. Any numbr of ruls for mapping pric p and product charactristic alus z onto attraction alus ar possibl. In practic, product charactristics and pric ar discrtizd, and th mapping is assumd a linar function of discrt pric and product charactristic lls. Th attraction j for product j is thn writtn as K L k j = βklz jkl, (5) k= l= whr Z jkl is a binary dummy ariabl such that Z jkl = indicats altrnati j posssss charactristic/pric k at ll l, and β kl is th part-worth cofficint of charactristic/pric k at ll l. Hr pric p is discrtizd and includd in Z as th last trm (k=k). On adantag of using discrt lls is that it dos not prsum linarity with rspct to th continuous ariabls. For xampl, w cannot assum that a $5 pric incras has th sam ffct for a $0 product as it dos for a $25 product. Gin a st of obsrd choic data, alus can b found for th β paramtrs such that th liklihood of th modl prdicting th obsrd data is maximizd. A grat dal of rsarch in markting is dotd to rcoring modl paramtrs through latnt classs, finit mixturs or using Hirarchical Bays mthods (Andrws, Ainsli, and Currim, 2002); howr, hr w simply us th standard maximum liklihood formulation. Th log of th sampl liklihood for a particular indiidual on a particular choic occasion n is: j J n Φ n ( j) K xp ln + xp Lk k= l= K β Z kl Lk j J n k= l= jkl β Z kl jkl whr Φ n (j) = if th obsrd choic on choic occasion n is altrnati j and Φ n (j) = 0 othrwis. Hr n is th st of altrnatis on choic occasion n. Eq.(6) is maximizd with rspct to th β trms aftr summing across all indiiduals and choic occasions. In this way, th part-worths β kl ar obtaind for ach ll l of ach attribut k. (6) 4 Jrmy Michalk, Frd Finbrg and Panos Papalambros

5 In all random utility modls, such as th logit usd hr, on must carful about modl idntification: for xampl, adding a constant trm to all attraction alus shifts thm upward to th sam xtnt and dos not chang choic probabilitis prdictd by th logit modl. Thus, in using Eq.(5), thr ar an infinit numbr of solutions for optimal bta alus that prdict quialnt choic probabilitis and thrfor ha idntical liklihood alus. Standard practic is to impos an idntification constraint on th systm of cofficints, which unambiguously chooss just on among all possibl 'optimal' solutions. Such constraints typically st a linar combination of th cofficints to zro. For clarity, w slct from th infinity of quialnt solutions th on solution whr th man bta alu Σ l β kl /L k is th sam for all k. By adding this constraint, th modl has + Σ k (L k ) dgrs of frdom, and th solution is uniquly dfind. Th part-worths rtrid with maximum liklihood stimation corrspond to discrt alus of th product charactristics and pric. For xampl, w may ha a crtain part-worth for a pric of $0 and anothr for a pric of $5. To optimiz or continuous alus of pric (as wll as charactristics simultanously), it is ncssary to stimat utility for intrmdiat alus, such as $2. Thr ar sral possibl mthods allowing intrpolation btwn ths discrt part-worth alus for ach charactristic and pric, ordinarily a typ of splin function. W aoid linar splins du to thir indiffrntiability at knots (th stimatd alus) and instad us highr-ordr polynomial splins, ithr quadratic or cubic, dpnding on which proids a closr fit. Finally, th attraction can b writtn as a function of th continuous ariabl product charactristics alus z and pric p using a splin function Ψ k of th part-worths β kl for ach charactristic/pric k. If pric is rprsntd as k=k, th attraction is writtn as K (, ) ( ) ( ) =Ψ z p = Ψ z +Ψ p, (7) j k j k K k= whr th angl brackt notation <z j > k dnots th k th lmnt of th ctor z j. Th modl spcification is compltd by inoking a known markt potntial s so that dmand q j is rlatd to choic probabilitis as q = sp = s j + j j j j J Markt potntials can b gin xognously at th outst or stimatd through a arity of tchniqus basd on historical data or tst markts (Lilin, Kotlr and Moorthy, 992). Conjoint Analysis Maximum liklihood stimation can b usd to fit bta paramtrs to any st of obsrd choic data; howr, collinaritis in th charactristics and pric of th choic sts can mak accurat paramtr stimation difficult and can caus problms gnralizing to nw choic sts (Louir t al., 2000). Conjoint analysis (CA) has bn widly usd to dlop fficint, orthogonal and balancd sury dsigns (xprimntal dsigns) to dtrmin which product charactristics ar important to consumrs, and appropriat lls for ach charactristic. Thr is ast litratur on conjoint analysis and appropriat xprimntal dsigns, and w dirct th radr to any of th classic or rcnt articls, notably Louir s (988) xpository articl and Kuhfld s (2003) xhausti account. Conjoint studis prsnt subjcts with a sris of products or product dscriptions, which thy aluat. Products can b prsntd in arious ways, but charactristic lls ar always mad clar, ithr in list form, pictorially, or both. Subjcts can indicat thir prfrncs among products by ranking (i.., putting in an ordrd list), rating (for xampl, on a -0 scal) or choosing thir faorit from a st. Each mthod has crtain adantags; howr, choic-basd conjoint is considrd most natural, sinc this is what ral consumrs do. Consquntly, w follow that approach hr, offring succssi sts of products and asking which is most prfrrd in ach, or whthr non is accptabl (th no choic option). To aoid th combinatorial xplosion rquird if all possibl pairings of attribut alus ar usd, an fficint dsign is gnratd. Efficint dsigns spcially tailord to conjoint studis ar supportd in a numbr of softwar packags, such as Sawtooth, SPSS and SAS. In our cas study (discussd latr), with six attributs of 5 lls ach, thr ar 5 6 = 5,625 possibl products, yt a highly fficint conjoint dsign rquirs only 50 choic sts of siz of 3.. (8) AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING 5

6 2.3. Th Enginring Dsign Subproblm In th nginring subproblm, dsign charactristics z ar calculatd as a function of th dsign ariabls x using th rspons function r(x), whr x is constraind to fasibl alus by constraint functions g(x) and h(x). Gnral procdurs for dloping rspons functions r(x), and constraint functions g(x), and h(x) to dfin a dsign spac ar wll stablishd in th dsign optimization litratur (Papalambros and Wild, 2000); howr, modling spcifics ar ntirly product dpndnt. Th objcti function of th nginring subproblm is to minimiz diation btwn th product charactristics achid by th dsign z E and th targts st by markting z M. Using ATC notation introducd in Michalk and Papalambros (2004), this objcti function is writtn as ( ) 2 M E 2 w z z, (9) whr 2 2 dnots th squar of th l 2 norm, w is a wighting cofficint ctor, and indicats trmby-trm multiplication. For complx products, nginring constraints typically rstrict th ability to mt som combinations of product charactristic targts, and th ATC procss acts to guid markting in stting achiabl targts whil dsigning fasibl products that mt thos targts Complt ATC Formulation Figur 2 shows th complt ATC formulation of th product dlopmnt problm for a singl-productproducing monopolist (thr is only on product, so th indx j is droppd for simplicity). In th product planning subproblm, pric p and product charactristic targts z M ar chosn to maximiz profit Π, whr Π is calculatd as rnu minus cost as in Eq.(), and dmand q is calculatd using th logit modl in Eq. (8) and Eq.(7), subjct to th constraint that th targts z M cannot diat from th charactristics achid by nginring z E by mor than ε, and ε is minimizd. In th nginring dsign subproblm, dsign ariabls x ar chosn to minimiz th diation btwn charactristics achid by th dsign z E and targts st by markting z M subjct to nginring constraints g(x) and h(x). Ths two subproblms ar sold itratily until th systm conrgs. Th wighting updat mthod (Michalk and Papalambros, 2004) is usd to find wighting cofficint alus w that Markting Product Planning Subproblm maximiz Π ε with rspct to z, p, ε Figur 2 ATC Formulation of th Product Planning and Enginring Dsign Product Dlopmnt Problm produc a solution satisfying usr-spcifid tolrancs for inconsistncy btwn markting and nginring for ach trm in z. This mthod is important for cass whr th top ll subproblm dos not ha an attainabl targt. 3. CASE STUDY Th dmonstration cas study inols dial-radout houshold scals. This particular durabl consumr product was chosn bcaus scals ha high pntration, ar not highly diffrntiatd, ar inxpnsi, and ha clarly idntifiabl componnts and consumr bnfits. 3.. Markting Product Planning Subproblm M w z z M E ε subjct to ( ) 2 2 whr Π= ( ) z M q p c c q = s + =Ψ z Fi product charactristics wr adoptd bcaus of thir dsign rlanc and th ability to dfin mtrics to masur thm. Ths factors, shown in Tabl 2, ar also adrtisd or isibl in onlin scal -commrc. Othr factors, such as brand nam and warranty, wr not includd in th study in ordr to focus on factors affctd by th dsign of th V ( p) M, Enginring Dsign Subproblm w z z with rspct to x subjct to g( x) 0 h( x)= 0 minimiz ( ) 2 M E 2 whr z r ( x ) E = z E I 6 Jrmy Michalk, Frd Finbrg and Panos Papalambros

7 Figur 3 Scrn shot of th onlin scal conjoint sury product. Factors that ar difficult to masur or difficult for consumrs to assss bfor us, such as asy to clan, wr ignord. An fficint choic-basd conjoint analysis sury was usd to collct data on consumr prfrncs. Th sury was implmntd onlin to simulat aspcts of onlin purchas dcision-making. Th sury can b found at ~lstojan, and a scrn captur is proidd in Figur 3. Th sury includs fifty qustions, ach of which asks th rspondnt to choos among thr scals or slct th no choic option. Th scals ar dscribd by numrical alus, a drawing, and a clos-up of th dial. Th sury includs som scals with physically infasibl charactristic combinations bcaus rsponss to ths qustions sr to infr trad-offs in consumr prfrncs. Fi lls wr chosn for ach product charactristic in th conjoint analysis as shown in Tabl 2. Th lls wr chosn to span th rang of alus of products in th markt, basd on a sampl of 32 diffrnt scals sold on th intrnt, to nsur ralism and to captur anticipatd trad-offs. Data wr collctd from 84 rspondnts, who wr solicitd from onlin nwsgroups and from nginring and markting studnts at th Unirsity of Michigan. Rspondnt data from th sury was usd to stimat th modl s β paramtrs using Eq.(6) summd or all rspondnts and all sury qustions and a modifid Nwton-Raphson sarch algorithm (Grn, 2003). Th rsulting β alus ar proidd in Tabl 2. Six cubic splins Ψ k wr fit to ths β alus (on for ach charactristic and on for pric), and th logit modl was usd to calculat dmand q for th monopolist using Eq.(7) and Eq.(7). Basd on discussions with a scal manufacturr, a ariabl cost c V of $3 pr unit and an instmnt cost c I of $ million was assumd for this xampl. Th Wight Capacity (z ) Intral Mark Gap (z 4 ) 200 lbs /32 in lbs /32 in lbs /32 in lbs /32 in lbs /32 in Platform Aspct Ratio (z 2 ) Siz of Numbr (z 5 ) in in in in in Platform Ara (z 3 ) Pric (p) 00 in $ in $ in $ in $ in $ Tabl 2 Logit cofficint part-worth β alus AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING 7

8 markt siz s was assumd to b fi million popl, th approximat yarly markt for dial scals in th Unitd Stats. x 2 (dial diamtr) x 8 (rack lngth) x 9 (pitch diamtr) 3.2. Enginring Dsign Subproblm Th nginring dsign modl was dlopd through rrs nginring: thr scals wr disassmbld, and th componnts and functionality wr studid, as shown in Figur 4. W chos to rstrict our focus to dial-radout scals to kp th dmonstration simpl; howr, th modl could b xpandd to includ digital scals. Th modl of th dial-radout scal is basd on th topology of scals found in th markt: lrs A proid mchanical adantag and transfr th forc of th usr s wight from th cor B onto a coil spring C which rsists displacmnt proportionally to th applid forc. Anothr lr D is usd to transfr th rtical motion of th spring to th horizontal motion of a gar rack E. Th pinion gar F translats linar motion of th rack to rotational motion of th dial G. This basic topology is common among th products obsrd, but dimnsions ary, and th ratio of dial-turn pr applid forc dpnds on th dimnsions of th lrs, th rack and pinion, and th spring proprtis. This dsign topology was paramtrizd and modld using fourtn dsign ariabls, ight fasibility constraints, and fi rspons functions that calculat product charactristics as a function of th dsign ariabls. A G F E D C A F E D C G Figur 4 Disassmbld dial radout scal B B x 3 x 4 x 6 (spring constant) x 7 Figur 5 shows th dsign ariabls usd for th scal. Othr dimnsions wr considrd fixd paramtrs, and th dial numbr siz and tick mark gap wr calculatd basd on scal dimnsions. Th rspons and constraint functions wr drid using gomtric and mchanical rlationships. W omit ths driations hr for brity and focus; howr, th ntir nginring modl is proidd in th Appndix Rsults x 2 x 5 x x 0 (piot horizontal arm lngth) x (piot rtical arm lngth) Figur 5 Dsign ariabls for th scal Th nginring dsign and markting subproblms wr sold itratily until conrgnc. At th solution, shown in Tabl 3, th optimal scal dsign is boundd by acti nginring constraints that nsur th dial, th spring plat, and th lrs ar small nough to fit insid th scal. Non of th ariabl bounds wr acti at th solution, and th optimal scal charactristics ar within th rang of scals found in th onlin markt. This dsign rprsnts th joint optimal solution obtaind through coordinatd communication btwn markting and nginring modls, and it is suprior to th solution obtaind by considring disjoint markting and nginring dcision modls squntially, as discussd in an xpandd rsion of this papr (Michalk t al., 2004). Mkt. Variabls Enginring Dsign Variabls p $26.4 x 0.7 in. x in. z 254 lbs. x 2.0 in. x in. z x in. x in. z 3 34 in 2 x in. x.59 in. z in. x in. x in. z 5.33 in. x lb./in. x 3.56 in. x in. x 4.60 in. Tabl 3 Optimal scal dsign x 3 x 4 8 Jrmy Michalk, Frd Finbrg and Panos Papalambros

9 4. CONCLUSIONS This articl prsntd and dmonstratd a mthodology for dfining a formal link btwn markting product planning and nginring dsign dcision-making. Th ATC framwork is spcially suitabl in allowing disciplinary sparation whil rtaining rigorous linking and coordination. For th markting community, this mthod will hlp in working with complx products whr som combinations of dsird charactristics ar tchnologically impractical or physically impossibl. Th infasibl st is typically a function of th tchnical dcisions of th product and is difficult to xprss as a function of th targt charactristic lls without xhausti numration. Using this mthod allows constraints to b drid in trms of dsign dcisions and thn linkd through th modl to product charactristics. For th nginring dsign community, this mthod will hlp to put dsign dcisions into th largr contxt of th firm and its objctis. This contxt can hlp to rsol tradoffs among compting prformanc objctis in multiobjcti optimization by proiding information about th rlati importanc of ach nginring objcti in th contxt of xplicit modls of dmand and th producr s objctis. This articl focusd on th basic lmnts of th links btwn markting and nginring dsign. Th mthodology can b xtndd in sral ways. Modls of dmand htrognity can b introducd to dsign product lins. Multipl product topologis can b includd for product arity, and dsign topologis could potntially b gnratd automatically (Campbll, Kotosky and Cagan, 998). Cost modls can b intgratd to th nginring subproblm such that th markting product planning subproblm sts targt production cost and th nginring dsign subproblm dsigns products that mt th cost targts. In addition, modls of product familis can b usd to study commonality ffcts on product cost structur (Fllini, Kokkolaras and Papalambros, 2003), and manufacturing instmnt dcisions, particularly considring rconfigurabl and flxibl quipmnt (Korn t. al., 999), can b includd in th modl. Finally, if th conjoint analysis sury can b dsignd optimally to aoid qustions about infasibl product charactristic combinations, thn th xpns of th sury can b rducd and th accuracy improd. ACKNOWLEDGMENTS Th authors gratfully acknowldg Laura Stojan for hr fforts in supporting th cas study through rsarch, modling of th scal, and implmntation of th sury. Th authors also acknowldg Fray Adigüzl and Ptr Ebbs for thir hlp computing th fficint choic-basd conjoint dsign for th cas study. This work was sponsord by th Rackham Antilium intrdisciplinary projct at th Unirsity of Michigan and th Rconfigurabl Manufacturing Systms Enginring Rsarch Cntr at th Unirsity of Michigan. Th support of ths sponsors is gratfully apprciatd. NOMENCLATURE Trm-by-trm ctor multiplication c I Instmnt cost c V Variabl cost pr product g Vctor function of inquality constraints h Vctor function of quality constraints j Product indx J Numbr of product altrnatis k Product charactristic indx l Product charactristic ll indx n Choic occasion numbr p Slling pric P j Probability of choosing altrnati j q Product dmand Vctor rspons function that calculats r product charactristics s Siz of th ntir markt Dtrministic componnt of utility w Vctor of wighting cofficints x Vctor of dsign ariabls Vctor of product charactristics achid by z E nginring Vctor of product charactristic targts st by z M markting Z Binary charactristic ll indicator ariabl β Part-worth cofficint ε ATC diation tolranc ariabl Π Profit Splin function to intrpolat part-worths for Ψ k charactristic/pric k Φ Binary function indicating obsrd choic ξ Random (rror) componnt of utility AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING 9

10 APPENDIX: MARKETING AND ENGINEERING SUBPROBLEMS Markting Modl Maximiz profit with rspct to pric and product charactristic targts Objcti Function Nam Dscription Valu Units Scald Formula f Maximiz profit whil minimizing diation from nginring dsign f = Π+ ε Profit $67,990,263 $ Π= q p c c Π ε Wightd diation 89,277 - Dcision Variabls : z M,p Eng. Dsign : z E Nam Dscription Units Scald Min Max Valu D. % D Wight z Wight Capacity 255 lbs %.0E+05 z2 Platform aspct ratio %.0E+05 z3 Platform Ara 34.0 in^ %.0E+05 z4 Siz of gap btwn -lb intral marks 0.59 in %.0E+05 z5 Siz of numbr (lngth).334 in %.0E+05 p Pric $26.4 $ ε = ( V ) I w( z z ) 2 M E 2 Intrmdiat Calculations Nam Dscription Valu Units p Intrpolatd part worth of pric Intrpolatd part worth of capacity Intrpolatd part worth of aspct ratio Intrpolatd part worth of ara Intrpolatd part worth of gap Intrpolatd part worth of numbr siz Total dtrministic componnt of utility S Markt Shar 58.95% - q Dmand 2,947,574 units Ψβ ( z, p) S = + q= s + Formula Paramtrs Nam Dscription Valu Units s Siz of markt 5,000,000 - cv Variabl cost pr unit $3.00 $ ci Instmnt cost $,000,000 $ u0 Utility of th outsid good 0-0 Jrmy Michalk, Frd Finbrg and Panos Papalambros

11 Objcti Function Nam Dscription Valu Scald Formula Last f Minimiz normalizd squard targt diation 8.9E E-06 f = w z z 9.E+04 Product Charactristics : z E (x,y) Targts : z M Nam Dscription Valu Units Formula Min Max Targt % D Wight z Wight Capacity 254 lbs 4π xxx x+ x2 x3 + x4 z = x x x + x + x x + x %.0E+05 z2 Platform aspct ratio z x4 = x %.0E+05 2 z3 Platform Ara 34.0 in^2 z3 = x4x %.0E+05 z4 Siz of gap btwn -lb intral marks 0.56 in x2 z4 = π z %.0E+05 z5 Siz of numbr (lngth).334 in πy x2 2tan y0 z 2 z5 = 2 πy + tan y2 z %.0E+05 Dsign Variabls (x) Nam Dscription Valu Units Rf. Valus (from r. ng.) Min Max x Lngth from bas to forc on long lr 0.7 in x2 Lngth from forc to spring on long lr.0 in x3 Lngth from bas to forc on short lr 0.72 in x4 Lngth from forc to joint on short lr 4.46 in x5 Lngth from forc to joint on long lr 4.20 in x6 Spring constant 23.4 lb/in x7 Distanc from bas dg to spring 0.50 in x8 Lngth of rack 5.00 in x9 Pitch diamtr of pinion 0.3 in x0 Lngth of piot's horizontal arm 0.52 in x Lngth of piot's rtical arm.59 in x2 Dial diamtr 9.36 in x3 Cor lngth.56 in x4 Cor width.60 in Constraints (g(x,y),h(x,y)) Nam Dscription Valu Units Formula g Rack lngth must b sufficint to span btwn piot and cntr of dial -.97 in g2 Long lr must attach to top of scal, so lngth of lr is limitd by scal width (Pythagoran) 0.00 in g3 Rack shortr than bas whn piot is rotatd 90 dg in g4 Lngth of short lr has to b lss than bas lngth in g5 Lr joint occurs at a position on th long lr, must not b largr than th lngth in g6 Dial diamtr must b lss than bas width -.64 in g7 Dial diamtr must b lss than bas lngth minus spring and plat 0.00 in g8 Long lr must b a minimum distanc y3 away from cntrlin at bas connction Paramtrs (y) Enginring Modl Minimiz diation from targt product charactristic alus in Nam Dscription Valu Units y Gap btwn bas and cor 0.30 in y2 Minimum distanc btwn spring and bas 0.50 in y3 Intrnal thicknss of scal.90 in y4 Minimum pinion pitch diamtr 0.25 in y5 Lngth of window 3.00 in y6 Width of window 2.00 in y7 Distanc btwn top of cor and window.3 in y8 Numbr of lbs masurd pr tick mark.00 lbs y9 Horizontal distanc btwn spring and piot.0 in y0 Lngth of tick mark + gap to numbr 0.3 in y Numbr of lbs that numbr lngth spans 6.00 lbs y2 Aspct ratio of numbr (lngth/width).29 - y3 Min. allowabl dist. of lr at bas to cntrlin 4.00 in ( ) 2 M E 2 ( )( ) ( ( ) ( )) x2 x8 ( x4 2 y ) + y7 x7 y9 x x5 2y ( x+ x2) ( x4 2 y x7) + 2 x7 + y9 + x+ x8 x4 2y x + x x 2y ( ) x5 x+ x2 x2 x5 2y x x 2y x y ( x y x ) y ( x x ) x 2 (dial diamtr) x 3 x 4 x 6 (spring constant) x 7 x 8 (rack lngth) x 9 (pitch diamtr) x 2 x 5 x x 3 x 0 (piot horizontal arm lngth) x (piot rtical arm lngth) x 4 AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING

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