WORKING PAPER. Design Of Extended Warranties In Supply Chains

Transcription

1 WORKING PAPER No MGT July 009 Dsign Of Etn Waantis In Suly Chains By Kunng Li Sa Houston Stat Univsity Suan Mallik Univsity of Kansas Dili Chhaj Univsity of Illinois at Uana-Chaaign Coyight y Autho 009 Th Woking Pas sis is ulish ioially y th Cnt fo Businss an Eonoi Dvlont at Sa Houston Stat Univsity, Huntsvill, Tas. Th sis inlus as y s of th faulty of th Collg of Businss Ainistation oting on sah ogss. Cois a istiut to fins of th Collg of Businss Ainistation. Aitional ois ay otain y ontating th Cnt fo Businss an Eonoi Dvlont. 1

2 DESIGN OF EXTENDED WARRANTIES IN SUPPLY CHAINS Kunng Li Collg of Businss Ainistation, Sa Houston Stat Univsity 181 Avnu I, Huntsvill, TX 770 Suan Mallik Shool of Businss, Univsity of Kansas 100 Sunnysi Avnu, Lan, KS 6605 Dili Chhaj Datnt of Businss Ainistation, Univsity of Illinois at Uana-Chaaign 50 Wohls Hall, 106 South Sith Stt, Chaaign, IL 6180 July 009 Astat W stuy th sign of tn aantis using a suly hain faok onsisting of a anufatu an an innnt tail. Th anufatu ous a singl out an slls it lusivly though th tail. Th tn aanty oul, hov, off ith y th anufatu o y th tail. Th aty offing th tn aanty is th ts of th oliy in its st intst an inus th ai osts at out failus. Un suh a stting, us ga thoti ols to ans th folloing qustions. What a th haatistis of tn aanty oliy isions? Whih snaio las to a high total suly hain ofit, a tail offing th tn aanty o th anufatu? Ho o th otiu i an tn aanty lngth vay un iffnt snaios? W sho that, ning on th ai ost lationshi, ith aty oul ovi tt tn aanty oliis an gnat o syst ofit. W also oa an ontast th to ntaliz tn aanty ovi ols ith a ntaliz syst h a singl aty anufatus th out, slls it to th onsu an offs th tn aanty. W also onsi an tnsion of ou asi ol h ith th anufatu o th tail slls th tn aanty oliis of a thi aty an innnt insuan oany, fo al, insta of offing its on oliy. Ky os: tn aanty, suly hain anagnt, aanty, ga thoy

3 1. INTRODUCTION Slling tn aantis on outs is a aily aning usinss. Etn aantis a off on alost all onsu ltonis an osti alians, anging fo lato outs to ashing ahins an figatos. Slling tn aantis is also a vy ofital usinss. Bn 00 nots that th ofits fo tn aantis aount fo alost half of Bst Buy s oating ino an all of Ciuit City s oating ino fo th ya 00. Bn futh nots that th ofit agins on tn aantis a naly 18 tis high than thos on th outs fo ths tails. An tn aanty is atually a svi lan, un hih th ovi oiss to ai, la, o aintain a out fo f o at a lo i ov a tain io of ti aft th anufatu s oiginal aanty is. Th tn aanty ay also off aitional nfits suh as tun an/o hang ivilgs that a not ovi y th anufatu s oiginal aanty. Etn aantis a sol saatly fo th outs an usually ost ta ony. Gnally, an tn aanty an off y a anufatu, a tail, o y a thi aty Puliation 15, Btt Businss Buau. Th ts of a tyial tn aanty sify th i an th lngth of ti uing hih th out is ov. Th ovi of th tn aanty inus th atual ai osts lat to th aanty. Th iay fous of ou unt sah is to analyz th sign of tn aantis in a suly hain ontt. W stuy a sil suly hain involving a singl anufatu an a singl tail. Th anufatu ous a singl out an slls lusivly though th tail. Hov, th tn aanty oul off ith y th anufatu o y th tail. Th aty offing th tn aanty is th ts of th oliy in its st intst an inus th ai ost hn th out fails. Thus, th ai ost itly influns th ovi s tn aanty isions. Un suh iustans, us ga thoti ols to ans th folloing qustions. Whih snaio las to a high total suly hain ofit, a tail offing th tn aanty o th anufatu? Ho o th otiu i an tn aanty lngth vay un iffnt snaios? Ho is th total suly hain ofit istiut tn th atis in ith snaio? W also oa th to situations ith a ntaliz syst, in hih a singl fi anufatus th out, slls itly to th n onsu, an offs th tn aanty. W also onsi an tnsion of ou asi ol h th anufatu o th tail slls th tn aanty oliis of a thi aty an

4 innnt insuan oany, fo al, insta of offing its on oliy. W thn oa th ofits of th anufatu/tail tn th to iffnt ays of oing usinss: ing an tn aanty ovi o ing a sll. Many anufatus off tn aantis itly to th n onsus. GE Alians, a laing anufatu of ajo alians, ats, an assois offs GE tn aantis on alost all th outs it anufatus. Fis lik Fo, GM, JVC, an Al hav vot hol ivisions solly to anaging an to sving tn aanty ontats Paanahan Manufatus offing tn aantis a also oon fo ainfa outs IBM, fo al an high-n offi ahins suh as ois, fa ahins, an ints. Rtail stos suh as Bst Buy, Ciuit City, an Ho Dot off an oot thi aty tn aantis unittn y insus, an thy at as tn aanty slls. Sas is an al of a tail ho itly ovis tn aantis *. Th ho svi atnt of Sas has ofssional ai sialists ho hanl ost of th ais, aoing to Sas Mast/Rai/Valu Pottion Agnt, hih ovs ost of th outs sol in Sas. Noally, th tn aanty oliy that is sol y th tail is all a svi lan. Oftn, ths lans tn th anufatu s oiginal aanty to a long io, an ay off aitional nfits not ovi y th anufatu s oiginal aanty. Fo al, Bst Buy offs a th-ya tn foan lan fo notook outs in th i ang $ $ Cay-In fo $ An al of a ntaliz syst slling a out as ll as anaging th tn aanty is Dll. A usto an hoos fo a nu of tn aantis hil ustoizing a out at Dll s sit. It is iffiult to fin als of th anufatu ing an tn aanty sll an ill lain th asons in Stion 5. In this a, us ga thoti ols to analyz fou snaios: a tail o a anufatu ing an tn aanty ovi ol R; ol M an a tail o a anufatu ing an tn aanty sll fo a thi aty ovi ol R; ol M. W ol th tn aanty as a f ai svi ov th lngth of th ontat. W fist isuss an oa th tn aanty ovi EWP ols, ol R an ol M. W analyz th total hannl ofit as ll as tn aanty isions. In * Sou:.sas.o/s/ho_svis/svi_agnts.js, tiv on May 1, 006.

5 aition, onsi onsu s lfa in ts of th i unit lngth of ovag of th tn aanty. Ou sults sho that, ning on th ai ost lationshi, ith ol R o ol M an ovi high hannl ofit an off tt tn aanty. W also isuss ho th total hannl ofit is istiut tn th anufatu an th tail in th to ols. In aition, oa th foan of th ntaliz ols ith thos of a ntaliz syst an sho that th ntaliz syst alays has th highst hannl ofit, ut os not nssaily off th st tn aanty. W nt analyz th tn aanty sll EWR ols, ol R an ol M. Ou fous is in oaing th EWP ols ith th EWR ols. W intify th onitions an ovi guilins fo oth th anufatu an th tail onning hn it is tt to an tn aanty ovi o sll. Ou a ovis insights aout th influn of tn aantis on suly hain isions an foan. It also hls to unstan so of th uniqu fatus of th tn aanty, its i an uation, as ll as th nny of th tn aanty an on th iay out an. Not that tn aantis itly sol y thi atis to onsus, though oon in ati, is not a fous of ou unt ok. Suh oliis an ol as insuan oliis, th sign, iing, an analysis of hih hav n ll stui in onois, insuan an isk anagnt litatu.g., Lutz an Paanahan 1998, Manov 198, Shlsing 198, an Taylo Th tn aanty ovi in ou a not only slls an ainists th oliy, ut also influns th out tail i itly in ol R o initly though th out holsal i in ol M, an th tn aanty holsal i in ol R an ol M. Ou ol thus allos us to stuy th intations of th out isions an th tn aanty isions in a suly hain. Th ain of th a is oganiz as follos. Th nt stion vis th lat litatu. W snt ou asi ols ols R an M an th solution ous in Stion. In Stion, analyz th sults an vlo insights. Mol R an ol M a isuss in Stion 5, hil Stion 6 suaizs an onlus th a.. LITERATURE REVIEW 5

6 Th sah on sign an analysis of tn aanty oliis is liit. Hov, thois of out failu an aantis hav iv tnsiv attntion in oth onois an oations sah litatu..1 Eonois/Makting Litatu Th istint thois hav n oos in onois litatu to lain th istn of out aantis: th insuan thoy, th signaling thoy, an th inntiv thoy. Ou a lats losly to th insuan thoy fist ass y Hal, 1977, hih assus that onsus a o isk-avs than slls, thfo aantis a ovi to onsus as a fo of insuan against out failu. Th onois an akting litatu tyially tats aantis as ash onsation ai to onsus in as of a out failu. This also alis to th sas litatu on tn aantis. Th insuan ont ay th sult of onsu htognity, as ntion y Hollis 1999 an as osv y Eons 1989 an Paanahan Slf-sltion is usually aot to al ith th onsu htognity. Tyial als of suh ok a Paanahan 1995 an Lutz an Paanahan Waantis a also tat as ontay onsation in th iial stuy y Paanahan an Rao 199. Although aantis a a fo of insuan, in ati, aanty ontats a usually sifi y th ti uation of ovag ath than y th aount of ontay aynt. Ou a atus this fatu of aantis an ols th tn aanty as uation of ti, hih istinguishs ou ok fo ost tn aanty litatu. Although Hollis 1999 ols aanty as ti uation, unlik ou ok, his ok als ith onsu htognity an slf sltion. Th a that os losst to ou ok is Dsai an Paanahan 00. Thy isuss th ols of tn aanty in hannl i ooination fo a anufatu, ho slls a ual out though a tail. Thy ol th tn aanty as a u onsu liaility hn a out fails. Th tn aanty is off to th onsus itly ith y th anufatu o y an innnt ovi. Thy also onsi a as h th anufatu slls th tn aanty though th tail. Ou sah iffs fo this as follos. 6

7 Dsai an Paanahan 00 only ol snaios h ith th anufatu o th innnt aty is th tn aanty ovi. Ou ol allos th ossiility of a tail offing th tn aanty ol R. As si in Stion 1 of ou a, ajo tails oftn ovi tn aantis on vaious goos. By oaing ol R an ol M, ou ok liitly onsis ofit iliations of tn aantis in a suly hain ontt. Whil onsiing th thi aty tn aanty ols, iv ou sults an insights y oaing ols M an R. Ou a fouss on th sign of th tn aantis. Both th i an th lngth of th tn aanty a ision vaials. Thi ok onsis iing ols only. Consistnt ith ou osvation in ati, ol th tn aanty as uation of ti, an onsi th nu of out failus as ll as th osoning ai osts. Thi a follos th insuan thoy in onois an ols th tn aanty as u ontay loss at a on-ti out failu.. Oations Rsah Litatu Th oations sah litatu on aantis fouss on athatial ols ith onsial so an tails in th sition of aanty osts. Th out quality is usually ol in onjuntion ith th out failu. Pout lif-ti istiution an failu at funtion a iotant oonnts of th foulation of th aanty ost ol. Sahin an Polatogu 1998 ovi an llnt vi of vaious aanty oliis an out failu ols. Wa 1987 analyzs th ta-off tn aanty an quality, an illustats th snsitivity of aanty osts to nvionntal vaials. Anson 1977 vlo a ision ol fo th otial hois of th aanty io an th out i. Bal an Sahin 1986 iv total out lant ost un oth o ata an f lant aanty oliis y assuing that th sussiv failu tis fo a nal oss. O t al. 00 onsi a ost iniization ol of outsouing aanty svis to ai vnos un stati alloation. Thy vlo an ffiint otial algoith an onstat that th otial algoith an hanl inusty-siz ols an fos tt than oon stati alloation huistis. Hs 008 onsis th snaio h to oting anufatus sll thi outs though a oon tail. If th tail slls its on tn aanty, th anufatus fa 7

8 a ila in stting thi as aantis. Whil thy hav inntivs to ovi a tt aanty to ak thi out attativ to th usto, th tail ight f slling th lo aanty outs to nhan th sals of tn aantis. Hs vlos a ol to tin an analyz otial anufatu an tail statgis in this stting an shos that this ynais ts ona ssu on anufatu aantis. H futh shos that a tail an nfit fo inuing ustos to siultanously onsi out an tn aantis ath than ithing th tn aantis at hkout. Anoth uniqu ok lat to aantis is y Cohn an Whang 1997, ho vlo a out lif-yl ol in hih aanty ost is inooat in th ofit funtion of a fi sking to aiiz total lifyl ofit fo a out. Thy assu that th aanty ill un fo a fi intval an that th aanty ost is lina ith th anufatu s quality of aftsals svi. Hov, th sign o th anagnt of th aanty is not th fous of thi ok. W stuy th sign of tn aantis in a suly hain stting, hih allos us to stuy out iing isions an tn aanty sign isions ithin a unifi ontt. To th st of ou knolg, th sign of th tn aantis in a suly hain ontt has not n stui fo.. THE EXTENDED WARRANTY PROVIDER MODELS In this stion, intou th tn aanty ovi EWP ols, h ith th anufatu o th tail offs th tn aanty itly to th onsus an inus all assoiat osts. W a ostly intst in oaing an ontasting ths to snaios in ts of th total suly hain ofit an its ivision tn th anufatu an th tail. W also oa an ontast th otial tn aanty lngths an is tn th to ols an iv insights fo thos. Consi a suly hain onsisting of a singl anufatu an a singl tail. Th anufatu ous a singl out.g., TV, ioav, out, o ovn an slls it lusivly though th tail at a holsal i. Th tail slls th out to th n onsu at a tail i. Th anufatu offs th oiginal out aanty, hos lngth, ithout loss of gnality, is noaliz to zo. This assution nals us to fous lusivly on th analysis of th tn aanty. 8

9 W onsi to ols fo tn aanty. In ol M, th anufatu ovis th tn aanty itly to th onsus, hil in ol R, th tail is th tn aanty ovi. In ith ol, th anufatu sts th holsal i of th out hil th tail sts th tail i. Th sifiation of th tn aanty involvs to oonnts, hih a th ision vaials fo th aty offing it: th lngth of th tn aanty in units of ti, not y ; an its i, not y. Duing th lifti of th tn aanty, th ovi oits to off f ai svi fo a fail out an inus th assoiat ai osts. W ill oa an ontast th to ntaliz ols ols R an M ith a ntaliz syst, ol C, in hih th anufatu ous th out, slls itly to th n onsu, an offs th tn aanty. Figu 1 shatially sis th th ols along ith thi lvant ision vaials. Th soli lin is assoiat ith out isions, hil th ott lin is fo tn aanty isions. Manufatu Manufatu Manufatu, Rtail Rtail,, Custos Custos Custos a Mol C Mol R Mol M Figu 1: Th EWP Mols Th Costs W assu that th anufatuing ost fo th out is onstant an is noaliz to zo, so that th holsal i is also th anufatu s out ofit agin in th ntaliz ols. Th aty offing th tn aanty hooss th tn aanty lngth i, its, an inus ossil ai osts uing th tn aanty ti io. W assu that th nu of out failus inass quaatially ith ti. Th litatu Anson 1977, Mnk 1969, an Patanka an Wo 1981 oftn assus that th nu of failu 9

10 inass onntially ith ti. Ou quaati failu assution atus th inasing at of out failu ith ti, hil taining th analytial tataility. A siila assution has also n us in Hs 008. Lt i i =, snting th tail an th anufatu, stivly not th avag ai ost failu fo aty i. Thus, th ost of oviing an anaging th tn aanty of lngth is, i =,. i Dan Funtions To an funtions a involv in ou ol, th out an an th tn aanty an. Fist, onsi th out an. W assu that th an is linaly asing in i an is givn y: q = 1, 1 h is th tail i of th out, q is th out an, an is th i snsitivity of th onsus. W nt iv th an funtion fo th tn aanty. Not that only thos onsus ho ought th out a otntial aniats fo uhasing th tn aanty, i.., th aiu an fo th tn aanty is liit y th out an 1. Ho shoul th an fo th tn aanty, not y q, hav? Aong th iotant haatistis, this an shoul asing in tn aanty i, an inasing in tn aanty lngth. In ati, tn aantis fo th sa out vay in i an uation of ovag; onsus onsi oth hil valuating an offing. Thus, i unit lngth of ovag, /, is an fftiv ay to oa iffnt tn aantis an atu ho an is afft. Finally, if no tn aanty is off, its an shoul qual to zo. W us th silst fo of an funtion that satisfis ths otis an aintains tataility of th ol. Lt fin as th snsitivity of /, th i unit lngth of ovag of th tn aanty. Thn, th an fo th tn aanty is q = 1, if 0, if = 0. > 0; 10

11 It is asy to s fo that th aiu alloal an fo th tn aanty is sily 1, an that th an funtion satisfis th sial otis si aov. Dsai an Paanahan 00 iv a an funtion fo th tn aanty y onsiing out failu oaility an th utilitis of isk-avs onsus. Thi sulting an funtion is lina an is of th folloing fo Equation 8 in thi a: q q k1 k =, h, k 1 an k a onstants. Siila to that of Dsai an Paanahan 00, ou an funtion fo th tn aanty is lina in its i. Hov, unlik thi ok, th lngth of th tn aanty is also a ision vaial in ou ol. Ou non-lina an funtion atus th fft of th lngth of tn aanty on its an. Latini an Osini 001 us a siila non-lina an funtion to ol th fft of out quality on its an. W also not that hav int analytially o nuially hn analytial ok as not ossil ith sval oth fos of an funtions inluing a lina an funtion. Th sults fo ths an funtions a qualitativly siila to thos fo ou unt an funtion iniating that th onations of ou ol a quit oust. Stion 5. of th a futh laoats on ths altnativ an funtions. This stion also los th tnsion of ou ol to th snaio h th an of th tn aanty is itly influn y th out i. Fo al, hil any onsus hoos to uy tn aantis on outs suh as as an flat sn tlvisions, f hoos to uy tn aantis on outs suh as tlhons o sing ahins. W assu that th is no infoation asyty in th hannl an that th anufatu ats as a Staklg la in th ga. Th anufatu, thfo, an look aha an antiiat th tail s out iing ision, as ll as his tn aanty isions, if alial. W ill us susits an susits to failitat th ssion of th ol vaials. Th susits ill not a ol C, R, o M; th susits,,,, an sys. ill not th tail, th anufatu, th thi aty, th tn aanty, an th syst, R stivly. W ill also us th susit * to not otial valus. Fo al, is C th otial ofit of th anufatu in ol R, hil sys. is th syst ofit in ol C. 11

12 .1 Mol C: Th Cntaliz Syst A ntaliz syst aiizs th total suly hain ofit y siultanously onsiing th out an tn aanty ans. C Ma = 1 1,, Mol C an solv y using stana otiization thniqus. Tal 1 snts th otial solutions to ol C an th folloing to ntaliz ols, along ith th otial valus of all ision vaials.. Mol R: Rtail Povis Etn Waanty In ol R, sis th tail i, th tail also is th tn aanty oliy y sifying an. In th fist stag of th ga, th anufatu hooss th holsal i that aiizs h ofit. Th otiization ol of th anufatu is givn y: R Ma Π = 1. In th son stag, taking th holsal i as givn, th tail aiizs his on ofit. Th tail s ol is as follos. R Ma = 1 1 5,, W solv th ol stating ith th tail s ol an oking akas. Noting that th son o onitions fo th aiization ols a satisfi, th th fist o nssay onitions of th otiization ol in 5 an solv siultanously to yil th tails tail s st sons tail i * in ts of th anufatu s holsal i. Th otial holsal i of th anufatu an thn foun y sustituting this st sons funtion into th anufatu s ofit aiization ol in an otiizing ith st to th holsal i. On th otial holsal i is knon, th otial valus of all oth ision vaials an iv fo th fist o onitions of th otiization ol in 5. 1

13 . Mol M: Manufatu Povis Etn Waanty In th fist stag of th ga, th anufatu hooss th holsal i, an th tn aanty oliy,. In th son stag, th tail taks th anufatu s isions as givn an sts th tail i. Th anufatu s otiization ol is as follos. M Ma = 1 1 6,, In th son stag, givn th anufatu s isions, th tail solvs fo : M Ma Π = 1. 7 Th solution ou fo ol M is siila to that of ol R.. RESULTS AND ANALYSIS This stion is ivi into to su-stions. Stion.1 isusss th otial sign of th vaials fining th tn aanty. W also laoat on th intations tn th out akt an th tn aanty akt. Stion. analyzs th ofits of iffnt atis offing th tn aanty. Th sults ans an iotant qustion: hih ol ovis a high suly hain ofit? Ou analyss a as on th otial valus of th ision vaials suaiz in Tal 1..1 Etn Waanty Dsign Osvation 1: Th tn aanty snsitivity aat,, ust high than tain thshol valus fo th fasiility of ah of th th ols, C, M, an R. Th onition fo th fasiility fo th th ols, C, M, an R, a / 9, 6 /, an / 1, stivly. Ths onitions ios aitional stitions on th fasil valus of th ol aats. Siila quints an foun in Guta an Loulou 1998, an Savaskan t al. 00. Thus, vy lo snsitivity to tn aanty is not a onuiv nvionnt fo offing it. Osvation 1 has intsting iliations. Th th fasiility onitions a ha to satisfy hn th out i snsitivity is high an 1

14 th ai ost is lo. Suh ight th as ith outs suh as tlhons, sall kithn alians, t. As a sult, an tn aanty is aly off on suh outs. On th oth han, th th fasiility onitions a asily satisfi hn th out i snsitivity is lo an th ai ost is high. Th als of suh outs a flat sn tlvisions, as, high-n aos, t., fo hih tn aantis a ath oon. Fo any fi valu of th out i snsitivity, th thshol valus fo offing tn aantis ass as th out ai ost inass. This ilis that a onutiv nvionnt fo offing tn aantis quis th out ai ost to high than tain thshol valu, hih ss to onsistnt ith th osv atis. This hov os not ily, as th folloing oosition shos, that a high ai ost ill sult in a long lngth of ovag fo th tn aanty. Poosition 1: Fo th th ols, C, M, an R, th otial i an th otial lngth of th tn aanty a a asing in th ai ost i, an th snsitivity aat. inasing in th out i snsitivity aat. Th oofs of all sults a inlu in th Ani. Ou ol assus quaati ost of tn aanty. Thfo, fo a givn i, as th ai ost inass ass, th ovi us inas th lngth of ovag of th tn aanty. Intstingly, th otial tn aanty i is also asing ith th ai ost. Whn th ai ost inass, Poosition 1a, it is otial to as th lngth of th tn aanty. This, in tun, us th an fo th tn aanty. To ount this fft an th fft of shot tn aanty, th ovi us th i of th tn aanty. Aoing to Th Wall Stt Jounal, DailChysl u th tn aanty on its vhils fo 006 aus of high ai osts sulting fo high lao osts an oliat thnology Saano 005. Th finings of ou ol itly suot this ation. As th ai ost ass, Poosition 1a, th lngth of th tn aanty an its i inass. Hov, hn th ai ost os too lo, th fasiility onitions si in Osvation 1 a violat, an offing tn aantis a no long fasil. Poosition 1 togth ith Osvation 1, thus, suggsts that all ls ing qual th is a ang 1

15 of ai ost fo hih offing th tn aanty is otial. It is instutiv to highlight hat hans at th lo an u ouns of th fasil valus of th ai ost. Whn th ai ost is at th u oun of th fasil ang, th ovi isontinus offing th tn aanty aus of th high ost. On th oth han, hn th ai ost is at its lo oun, th tn aanty snsitivity of th onsus is so high as si in Osvation 1 that it is no long onoial fo a ovi to off th tn aanty. This ight th as fo outs suh as sall kithn alians, tlhons, t. Th fft of a hang in th aat is siila to that of th ai ost. As inass, th an fo tn aanty gos on. A lo tn aanty i is nssay to ount this fft. Consquntly, th sult is a shot tn aanty lngth. It is asy to sho that an inas in o th ai ost also sults in an inas of th out holsal an tail is. Un this snaio, a ovi attts to offst th lost vnu fo tn aanty though aitional vnu fo th out sals. What is th fft of hangs in th out i snsitivity aat? In asn of an tn aanty akt, oth out i an an oul asing in. But ith tn aanty, as inass, th out tail i ass an this as is lag nough to ou an inas in th out an. This, in tun, inass th siz of th otntial akt fo th tn aanty. Thus, a high i an hag fo th tn aanty ith a long lngth of ovag. Th otial tn aanty is a not itly oaal aoss th th ols as th otial lngths of th tn aanty a iffnt in ah ol. W thfo oa th i unit lngth of ovag, /, aoss th th ols. Th folloing oosition sis ou sult. Poosition : Mol M has th lost tn aanty i unit lngth of ovag, unlss >, in hih as ol R has th lost i unit lngth of ti. In atiula, hn th ai osts of th anufatu an th tail a qual, th tn aanty i unit lngth of ovag is highst fo ol C an is lost fo ol M. It is iotant to hasiz that i unit lngth of ovag, /, is sily a onstut that allos us to oa th th ols. This atio is not a ision vaial fo any ovi 15

16 of th tn aanty. This lus th ossiility of offing an infinitsial aanty to aiiz this atio. It an thought of as on asu of th valu of th tn aanty to a onsu. As Poosition stats, oth ol M an ol R a otntial aniats fo th lost i unit lngth of ovag. Consus gt th st valu in ts of i unit lngth of ovag hn th tn aanty is ovi y th anufatu, unlss th tail s ai ost is sustantially high than that of th anufatu. Why os this han? Th tail in ol R itly influns th an of th out an th tn aanty y hoosing th stiv is. Thus, unlss th tail has a sustantial isavantag in ai ost i.., >, h an aniulat th to is, an, siultanously to hag a high i unit lngth of ovag to th onsu. Mol C, ing a ntaliz ol, allos th ovi to hag th highst i unit lngth of ovag, an onsquntly ovis th ost valu to th usto. Un ost iustans, th ai ost of th tail is unlikly to th tis lag than that of th anufatu, ilying that ol M is oftn likly to hav th lost tn aanty i unit lngth of ovag. Dit suot of this fining an also foun in th oula usinss ss; A Businss Wk atil Astong 00 stats that th ltoni tail CoUSA hags $69.99 fo a th-ya tn aanty lan on a Toshia Satllit lato out, hil th anufatu Toshia Co. hags only $199 fo a tt lan. Consu ts oftn on uying an tn aanty itly fo a anufatu. Poosition suots this onation. Ho o th out is oa aoss ol R an ol M? Using th ssions fo Tal 1, it is asy to iv that th ntaliz syst offs th lost out tail i. Futho, th out tail i in Mol R is high than that in ol M i.., R* M * > if an only if >. This ilis that hn th ai osts of th anufatu an th tail a qual, th out tail i ill highst hn th anufatu offs th tn M * R* C* aanty an lost hn th suly hain is ntaliz > >. Thus, th out an th tn aanty is unit lngth of ovag hiit oosit lationshis aoss th th ols. Th intuitiv lanation fo this is as follos. A lo out i sults in a high an fo th out an a high otntial akt siz fo th tn aanty hih allos a ovi to hag a high i fo th tn aanty unit ovag. Whn th anufatu offs th tn aanty, th tail, in stting th 16

17 out i, is not onn aout th otntial an fo th tn aanty an thus i is high.. Pofit Analysis In this su-stion, oa th syst ofit fo th th ols, an ain th ivision of total ofits tn th anufatu an th tail ithin th ols. W fin th syst ofit o th suly hain ofit of any ol as th su of ofits of th tail an th anufatu. Oviously, th ntaliz ol C yils th highst syst ofit aongst th th ols, as an vifi using th ssions fo Tal 1. As a sult, ill stit ou attntion to only ol R an ol M in this su-stion. Tho 1 lo stats ou fist sult. M Tho 1: Th otial syst ofit of ol M is high than that of ol R > R sys. sys. if an only if th ai ost of th tail,, is high than a thshol valu s, h s is lag than. In atiula, hn =, R > sys M sys... Th oof of Tho 1 ovis th analytial ssion fo th thshol valu s. Tho 1 vals an intsting suly hain ynais. P ou tho, hn th ai osts of th anufatu an th tail a qual, th tail offing th tn aanty yils a high syst ofit oa to th snaio h anufatu offs th tn aanty. Why? Whn th tail slls th tn aanty, h ontols th iing an hn th an of oth th out an th tn aanty. H, thus, has stong inntiv to sll o outs an hn ks th out tail i lo. As a onsqun, th oul aginalization in th out akt is u an th ovall syst ofit iovs. Fo a oling stiv, in ol R, th tail is, an, hil th anufatu is th holsal i. Thus, th tail an siultanously aniulat all th vaials to aiiz ofits. Ths th vaials allo hi to itly influn th out an as ll as th tn aanty an. On th oth han, hn th anufatu offs th tn aanty ol M, th tail still tins th out tail i. Th out i, in tun, tins its an an aiu otntial fo th tn aanty. Un this snaio, th tail has no inntiv to ontol th oul aginalization in th hannl 17

18 an th anufatu has no hanis to ontol it. This sults in a lo total suly hain ofit. Tho 1 futh shos that a tt syst ofit an otain if th tn aanty is off y th tail, insta of th anufatu, vn hn th ai ost of th tail is high than that of th anufatu as long as th lationshi < hols. Ou tnsiv nuial int iniats that as th out i snsitivity aat inass, so os s. This ilis that as th ustos o o i snsitiv, an tn aanty off y th tail ill gnat high syst ofit vn if th ai ost of th tail gos u. Whn th ai ost of th tail inass yon th thshol valu of s, th ost avantag of ol M outighs th stutual avantag i.., u oul aginalization of ol R an hn, ol M gnats a tt syst ofit. W nt look at th ivision of ofit tn th anufatu an th tail ithin a ol, as ll as tn th to ols. Th folloing oosition snts th sults. s Poosition : a Coaison tn ol R an ol M: i Manufatu s ofit: R M if an only if. ii Rtail s ofit: R M if an only if is gat than a thshol valu, h is lag than. iii In atiula, hn =, hav an. R > M R > M Coaison ithin ol R an ol M: i In ol R, th ofit of th anufatu is high than that of th tail hn < 11.8, an is lo than that of th tail hn < < ii In ol M, ofit of th anufatu is high than that of th tail hn <.75, an is lo than that of th tail hn < < Th analytial ssion of an foun in th oof of th Poosition a. Th oosition shos that unlss th anufatu has sustantial avantags ov th tail in ts of th ai ost, oth th tail an th anufatu a tt off ith th tail offing th tn aanty. In atiula, hn th ai osts of th to atis a qual, 18

19 Poosition aiii shos that oth atis a tt off hn th tail offs th tn aanty. Thus, un oaal ai osts, an tn aanty off y a tail not only gnats a high syst ofit Tho 1, ut also aks oth tail an anufatu tt off than thy oul if th anufatu to off th tn aanty. Why os this han? Whn th tail offs th tn aanty, as isuss aft Tho 1, th oul aginalization in th hannl is lo than that hn th anufatu offs th tn aanty. This sults in a high an fo th out an th tn aanty fo ol R. Using th ssions fo Tal 1, it is asy to vify that fo R* M * q =, R* M * q q an q. It an futh shon that hn th to ai osts a qual, th anufatu s holsal i is lo in ol R oa to ol M. Poosition aiii, thus, shos that th nfit of uing th oul aginalization in th hannl is so signifiant that th anufatu s ofit fo th out alon at a lo holsal i ol R is o that of slling th out at a high holsal i an slling th tn aanty ol M. Th tail too njoys a high ofit un ol R aus of high ans fo th out an th tn aanty oa to ol M. Ths insights an sv as a usful qualitativ guilin fo th atitions sonsil fo stting u o unning tn aanty usinsss. It also ilis that th tn aanty an us statgially to u th oul aginalization is a suly hain. A th finings in Poosition a onsistnt ith osv atis? Waanty Wk, a ajo ta uliation fo th inusty ofssionals, not in its Oto 5, 005 issu that on an agggat asis, ost tn aantis in th Units Stats a sol y tails Sou: htt://.aantyk.o/ahiv/ htl, tiv on May 17, 009. Waanty Wk futh not in its Januay 19, 005 issu that th anufatus aount fo only 7.% of th total akt of th tn aanty ainistatos in th USA Sou: htt://.aantyk.o/ahiv/ htl, tiv on May 17, 009. Ths osvations, on again, suot th asstion in Poosition a. Looking fo aitional als, on of th authos visit th n autooil alshis Toyota, Hona, an Nissan stivly osing as a ostiv uy. In ah of th th visits, th autho as tol aout th tn aantis only aft th sal i of th n a as ag uon an that ah of th th als off to sll an tn aanty unittn y a onsotiu of a 19

20 als. Th als tol aout th anufatu s tn aanty only hn th autho sifially ask fo altnativ tn aantis. Ths als sho a a al s inlination fo slling a tail s tn aanty ov that of th anufatu s. This havio, if ivn y ofit onsiation, ill onsistnt ith Poosition a. Nvthlss, th a anufatus, suh as Dll an Al, ith highly ofital tn aanty usinsss. What aks an iniviual fi sussful in th tn aanty usinss is yon th so of ou oling faok. Ou ok, hov, os ily that oth th anufatu an th tail ay nfit y valuating th ision of a anufatu offing th tn aanty. Poosition stats that in ols M an R, th anufatu s ofit is high than that of th tail fo lo valus of th out i snsitivity aat. Th anufatu is th Staklg la in ou ol. Sh otiizs h ofit y antiiating th tail s isions, an is al to otain a high sha of th total suly hain ofit. Hov, hn os lag, th ustos o o i snsitiv an a lag at of total ofit is iv fo th out sals, giving th tail o ofit. To ovi o not to ovi th tn aanty Duing th 1980s tn aantis off only on lag an nsiv its. Toay tn aantis a oon on alost all ual goos inluing a sil onsu ltonis its. What a th ofit iliations of offing an tn aanty? W lo th ans to this qustion nt. To aolish ou ojtiv ill oa ou ol ith a as as h no tn aantis a sol i.., th anufatu ous th out an slls it to th tail at holsal i an th tail slls th out to th onsu at tail i. Un suh a snaio ols R an M a intial an that th syst ofit, th tail ofit, an th anufatu ofit a stivly, 1,, an 1. Th syst ofit fo ol C is 1. W fin th at of ofit iovnt of a ovi o that of th syst u to th tn aanty to th iffn tn th ofits of th ovi o 0

21 th syst ofit un th tn aanty an un th as as ss as a fation of th as as ofit. Th folloing oosition stats ou sults. Poosition : a Fo th syst ofit, ol C has th highst at of ofit iovnt u to th tn aanty. Mol R has th sallst at of ofit iovnt u to th tn aanty if an only if is gat than a thshol valu s, h s is gat than. In atiula, hn =, ol M has th sallst at of ofit iovnt u to th tn aanty. In oth ols M an R, th tail s at of ofit iovnt u to th tn aanty is high than that of th anufatu. Th analytial ssion fo s has n ovi in th oof. Poosition a shos that, oviing an tn aanty iovs th syst ofit o hn it is sol y th tail ath than th anufatu unlss th tail s ai ost is sustantially lag than that of th anufatu. Whn th tail offs th tn aanty, h ks th out i lo to an th otntial akt fo th tn aanty, hih in tun, us th oul aginalization in th hannl sulting in a high at of ofit iovnt fo ol R. Poosition shos that this ution in oul aginalization an vn ovo so ai ost isavantag fo th tail. Hov, hn th tail has a sustantial ai ost isavantag, ol M offs tt at of ofit iovnt. Un th as as, th anufatu s ofit is to tis that of th tail. Hov, ith an tn aanty, th tail s ofit inass at a fast at than that of th anufatu. In, as Poosition iniats, hn th i snsitivity aat is suffiintly lag, th tail s ofit an vn suass th anufatu s ofit. This iniats that a tail stans to gain o ith an tn aanty than a anufatu. This ight lain hy tails a so ativly involv in th tn aanty usinss aoss vaious inustis. 5. EXTENSIONS Ou isussion thus fa has fous on th tn aanty ovi ols, h ith th anufatu o th tail as th unit of th aanty an inu osts 1

22 assoiat ith out failu. Th ojtiv of this Stion is to-fol: to lo an tnsion of ou oiginal ol to allo thi aty tn aantis, an to stuy th oustnss of ou ky finings un altnativ an funtions. To aolish ou fist ojtiv, ill lo an tnsion of ou asi ol, h th anufatu o th tail sily slls th tn aanty oliis of a thi aty unit. W ill all ths ols th tn aanty sll ols EWR as oos to th tn aanty ovi ols isuss thus fa. As isuss in Stion 1, Bst Buy, CoUSA, an oth tails a oftn th slls of th tn aantis fo thi aty units suh as AIG, GE, an Aian Ho Shil. Stion 5.1 ill isuss ths ols. To aolish ou son ojtiv, ill sho in Stion 5. that th ky finings of ou a ontinu to hol un vaious altnativ an funtions an vn hn th an of th tn aanty ns on th out i. W ill also isuss th liitations of ou ol. 5.1 Th Etn Waanty Rsll Mols In analyzing th EWR ols, k th asi stutu of ou ol unhang, ilying that th anufatu still ous a singl out an slls it lusivly though th tail an that th anufatu sts th out holsal i hil th tail sts th tail i. Hov, th anufatu o th tail in th EWR ols uys th tn aanty unittn y a thi aty, an slls th oliy to th n onsu at a tail i. Th thi aty is sonsil fo anaging th tn aanty, an is its lngth an holsal i in its st intst. Th anufatu o th tail, on th oth han, sts th tail i of th tn aanty. W ill onsi to EWR ols, ol R, h th tail slls th thi aty tn aanty; an ol M, h th anufatu slls th thi aty tn aanty. Ou ojtivs in this su-stion a to-fol: to oa th EWP an EWR ols an to oa th to EWR ols. Th fist oaison yils insights aout hth it is o ofital fo a anufatu o a tail to a ovi ov a sll of th tn aanty. Th son oaison ovis stutual insights aout th M an R ols. W ol th EWR snaios as a th-stag ga. In th fist stag, as th Staklg la, th anufatu is th out holsal i. In th son stag, th thi aty aks th tn aanty isions th lngth an th holsal i of th tn

23 aanty aft osving th out an valuating th avag ai ost. W ill lt not th ai ost of th thi aty aanty ovi. Finally, th tail is of th out an th tn aanty a tin siultanously. Th tail is th out tail i hil th tail i of th tn aanty is tin y ith th anufatu Mol M o th tail Mol R. W si ou ol foulations lo. Mol R In th fist stag of th ga, th anufatu otiizs h ofit y iing th out holsal i : R Ma Π = 1. 8 In th son stag, th thi aty aiizs h ofit y siultanously iing th holsal i an th lngth of th tn aanty R Ma Π = [1 / ] 9, In th last stag, taking th lngth of th tn aanty, an th holsal is of th out an th tn aanty as givn, th tail siultanously hooss th tail i of th out, an th tn aanty tail i ol is as follos. to aiiz his ofit. Th tail s R Ma Π = 1 [1 / ] 10, W solv fo th ol using stana thoology y oking akas, stating fo th tail s ol in th last stag. Mol M ill hav a siila foulation an solution thoology, an hn, a oitt. Th otial solutions of th to ol M an R a snt in Tal. Bing a Povi vs. Bing a Rsll W ill oa th otial ofits of Mols M an R ith thos of Mols M an R stivly. This givs us insights aout hth it is o ofital fo a anufatu o a tail to a sll of th tn aanty insta of ing a ovi. Th folloing oosition sis out sult.

24 Poosition 5: a Th anufatu gts a high otial ofit y ing a ovi of th tn aanty if an only if <. Th tail gts a high otial ofit y ing a ovi of th tn aanty if an only if <, h is a funtion of. Th analytial ssion fo an foun in th oof. Poosition 5a shos that a anufatu is tt off ing a ovi of th tn aanty vn hn h ai ost is qual to that of th thi aty. In fat, sh is tt off ing a ovi unlss h ai ost is sustantially high than that of th thi aty. A anufatu is likly to hav tt knolg of h out, ilying h ai ost is likly to lo than, o oaal to, that of th thi aty. Thus, th lationshi < is likly to hol in ati. Thfo, ing a ovi is oftn th f ay of offing tn aanty fo a anufatu. This is usually th as ith th auto anufatus, as isuss in Stion 1. As afo ntion, it is iffiult to fin an al h a anufatu slls thi aty tn aantis. Poosition 5a an ou isussion aov ight lain hy this is th as. Poosition 5 si th nssay an suffiint onitions fo th tail to a ovi of th tn aanty. Ou nuial intations iniat that th valu of falls in th ang of 1. ~.5 fo a i ang of valus of th ol aats. W int ith 100 snaios y vaying th i snsitivitis an fo 0.1 to 1 ith a st of 0.1. Th lagst valu of is.9, an th sallst is 1.0, ith ost of th valus aov. Not that th onition fo ing a sll of tn aanty in Poosition 5 is lss stitiv than that in Poosition 5a. In aition, a tail ight not hav tis in aiing th out fo a anufatu. Poositions 5a an 5 thus iniat that in ati, a tail is o likly to th sll of an tn aanty than a anufatu is. Ou als in Stion 1 stongly suot this. Poosition 5 ovis gnal guilins fo atitions in hoosing th ays of anaging th tn aanty usinss: to an tn aanty ovi o a sll. W onlu this stion y noting that th snaio h a thi aty offs tn aanty itly to a

25 onsu is yon th so of ou a. Suh a snaio an asily ol as an insuan oliy an is ll stui in th litatu of isk an insuan anagnt.g., Lutz an Paanahan 1998, Manov 198, Shlsing 198, an Taylo Nuial Stuy: A Coaison of th to EWR Mols In this stion, snt a nuial stuy to oa th to EWR ols ith st to otial i, an, an ofit. As th a ill s, th lationshis tn ols M an R a qualitativly siila to thos tn ols M an R, ilying that th sn of a thi aty unit os not hang th stutual otis of ou ol. Th otial solutions of th ols R an M a suaiz in Tal. It is ha to oa th otial solutions of ths to ols analytially. As a sult, nuially otain th otial solutions of th to ols un vaious sntativ valus of th ol aats. W hoos th thi aty s ai ost = 5 oth fasil valus of ai ost yil siila sults an lt th i snsitivitis an vay fo 0. to 1 at a st of 0.. Ou nuial finings a suaiz in Figus a g. In ah of ths figus lot th iffn tn th otial solutions of th ols R an M fo iffnt valus of th an snsitivity aats an. Ths figus a staightfoa. As a sult, sily suaiz ou finings in th folloing to osvations. Osvation : a Th otial tail i of th out in ol R a alays lo than thos in ol M i.., R < M. Th otial tn aanty is unit lngth of ti in ol R a alays high than thos in ol M i.., R M * * >. Osvation : a Th otial ofits of th tail, th anufatu, an th thi aty aanty ovi a high in ol R than thos in ol M, ilying ol R givs is to a tt R R M syst ofit than ol M i.., >, >,. M sys. M R > M, an > R sys. 5

26 In th to ols R an M, th otial ofit of th anufatu is alays high than R R M M that of th tail i.., > an >. Th lationshis tn ols R an M in Osvations an a siila to thos tn th ols R an M fo = not that th ai ost fo th ols R an M a intial an quals to that of th thi aty. Thus, th sn of th thi aty os not signifiantly hang th stutu of ou ol. Th intuitions hin ths sults hav n isuss in tail in Stion. 5. Snsitivity of Rsults ith st to Altnativ Dan Funtions W isuss sval altnativ an funtions in this su-stion. Fist onsi th as h th an of th tn aanty ns on out i. Thn snt fou oth an funtions. Dan of th Etn Waanty Dns on Pout Pi In this stion, tn ou asi ol into a o ol snaio, h out i not only influns th aiu otntial an of th tn aanty 1, ut also has a it iat on th tn aanty an. Many onsus hoos to uy tn aantis on nsiv outs suh as as, flat sn tlvisions t., hil f onsus uy tn aantis on outs suh as tlhons o sing ahins. This osvation suggsts that th an fo th tn aanty lativ to th out an shoul inasing ith th out i. Ou an funtion in quation aily aooats suh as tnsion y ltting th aat to a funtion of th out i, i.., q = 1, 0, > 0. W hoos = /, h is a onstant, an it th an funtion fo th tn aanty as q = 1, fo > 0. Not that this an funtion satisfis th si haatistis isuss in Stion. 6

27 W solv th th ols nuially an oa th insights ith ou oiginal ol. W hoos th snsitivity aat qual to 0. an 0.7, an lt th i snsitivity vay fo 1.05 to 1.5 in sts of 0.05, hil th ai ost i vais fo 0.05 to.0 in sts of 0.1. W sk th otial solutions un th oinations of th aats isuss. Ou ain finings a snt in Figus a. Figu a shos ho th tn aanty i unit lngth of ovag, /, vay aoss th th ols C, M, an R hn th ai osts of th tail an th anufatu a qual. This fining is onsistnt ith that in Poosition. Siilaly, Figu valiats Tho 1 fo th o gnal oling faok hil Figus an valiats Poosition a. This suggsts that th finings of ou ol a quit oust an that th ky insights of ou oiginal ol ain unhang vn hn lt th an of th tn aanty n on th out i. Altnativ Dan Funtions Whil hav us th silst fo of an funtion that satisfis th sial otis an aintains analytial tataility, to hk th oustnss of ou ol, hav at ou alulations an analyss analytial o nuial hn analytial alulations not tatal fo ah of th folloing altnativ an funtions: q = 1 f, 11 q = 1 f /, 1 q = 1 f, an 1 q = 1. 1 Eah of ths an funtions satisfis th sial otis of th tn aanty an si in Stion. Unlik ou an funtion in, ah of th an funtions in 11, 1, an 1 allos iffnt snsitivitis fo th i an th lngth of th aanty. W also tst fo oth lina quation 11 an non-lina quations 1-1 lationshis an allo ol lationshi tn th an an lngth of th tn aanty y inting ith fou iffnt -1.0, -0.5, 0.5, an 1.0 onnts of. W not that Dsai an Paanahan 00 us a lina aitiv an funtion to stuy tn aanty. Ou hois allo th gnalization of thi an funtion to o ol an alisti 7

28 snaios. Ths analyss using ah of th aov fou an funtions yil siila qualitativ sults as thos of ou oiginal ol isuss in Stion. Ths alulations, on again, suggst that th onations fo ou ol a quit oust. 6. SUMMARY AND CONCLUSION In this a, hav vlo ga-thoti ols to sign tn aantis an oa iffnt tn aanty shs in a suly hain ontt. Sifially, onsi a suly hain involving a singl anufatu an a singl tail, ith of ho an a ovi o a sll of th tn aanty. W fist analyz to EWP ols ith th tail an th anufatu, stivly, ing th ovi of th tn aanty. W oa th to ols in ts of syst ofits, tail ofits, anufatu ofits, out iing isions, an tn aanty isions. W also nhak th foans of th to ols ith that of a ntaliz syst. Ou ain sults a as follos. Th tn aanty lngth an i a asing in th ai ost of th aty ho ovis tn aanty. Noally, th anufatu ovis th st tn aanty ith st to th lost tn aanty i unit lngth of ovag, unlss th tail s ai ost is sustantially high than that of th anufatu. Th tail, ith a high at of ofit iovnt, nfits o fo th tn aanty usinss than th anufatu, unlss h has sustantial ai ost isavantag. Dning on th valu of th ai ost, ith ol an gnat tt syst ofit. Hov, hn th ai osts of th to ols a qual, ol R not only gnats a high syst ofit ut also aks a Pato iovnt ov ol M. This fat aiss u to th u oul aginalization in th suly hain. Hov, hn th ai ost avantag fo th anufatu sustantially outighs th stutu avantag in ol R, ol M is al to gnat o syst ofit. W thn stui to EWR ols h a thi aty off th tn aanty, hil th anufatu o th tail sily at as th tn aanty sll. Ou sults sho that aing a thi aty ovi os not hang th ynais of th syst. By oaing th osoning ofits of th anufatu an th tail tn EWP an EWR ols, 8

29 outlin so gnal guilins fo atitions, on hn a fi shoul hoos to a ovi vsus a sll of th tn aanty. Ou a aks th folloing ontiutions to th oations anagnt litatu. Fist, it ovis a uniqu an funtion fo th tn aanty, hih liitly taks into aount out an, out failu, an ai ost. In lin ith ou osvation in ati, ol th tn aanty as a svi out ith i an ti uation fo ovag. Son, hil a ajoity of th litatu in tn aantis fouss on onsu oal haza an htognity issus, ou ok asss its sign issus an its ol in th hannl foan. By aoting a ga-thoti aoah, stuy th statgi intation tn th anufatu an th tail as ll as th intation tn th out sals an th tn aanty sals. Th ain sults of ou ols a al to qualitativly lain so osv atis. Fo al, hy o onsu ts alays on th anufatu s tn aantis? Why is Chysl shotning th tn aanty on its n vhils? Thi, ou ol ovis a n stiv in istinguishing th tn aanty slls on th akt: a ovi o a sll. W also ovi guilins fo hling ak th ight hois. Fouth, ou ol ilis that th tn aanty is not ly a sou of vnu. Baus of th uniqu haat of its an, hih is nnt on out an, th tn aanty oul us statgially in hannl hois to iov syst ofits an out iing isions. Ths sults ovi usful insights as ll as qualitativ guian to atiing anags involv in signing, stting u, an anaging an tn aanty usinss. Lik any oth ol in oations anagnt litatu, ou ol is as on a st of assutions. Fo siliity, stui th tn aanty usinss using a onoolisti stting. This allo us to isolat th iat of th tn aanty on total suly hain ofits. An iotant tnsion of ou ol oul to inlu otition, ith tn anufatus o tn tails. Inooating an untaintis ight anoth usful tnsion. Ou ol assus no infoation asyty. In ati, a tail ight hav ivat infoation aout onsu an. In suh a snaio, th tail ight us this infoation statgially to iov his ofit. W hav assu a on-si akt h th an fo th tn aanty is influn y th out an ut not th vi-vsa. This assution ss to hol in ati fo a i ang of onsu uals anging fo 9

30 osti alians to onsu ltonis. Rtails suh as Wal-Mat an Sa s Clu tyially o not vn ith th sal of an tn aanty until th hk out. In th authos on ins, ajo alian tails suh as Sas, Ho Dot, an Los o not ing u tn aanty hil hling a otntial usto hoos fo iffnt ans of osti alians. Suh als hav vn ot sahs to stuy hth th tn aanty shoul ith to a onsu alongsi a out? Hs 008 ots that ajo onsu ltonis tails suh as Bst Buy os not ith outs an tn aantis siultanously an vlos a ol to onlu that a tail ill tt of ithing oth siultanously. Fo ths als, it is la that un any situations in ati, th an of th tn aanty is influn y th out an ut not th vi-vsa. Ou a ols suh snaios. Aittly, th ight snaios h th availaility of an attativ tn aanty ill influn th out an as ll. Stuying tn aantis un suh to-si akts ains on ou agnas fo futu sah. Aknolgnt Th authos thank th anonyous snio ito an th to fs fo thi valual inuts. REFERENCES Anson, E. 1977, Pout Pi an Waanty Ts: An Otiization Mol, Oational Rsah Quatly, Vol. 8, No., Astong, L. 00, Whn Svi Contats Mak Sns, Businss Wk Onlin, D 0, Issu 91, Bal, Y. an I. Sahin. 1986, Rlant Costs Un Waanty: Cost Monts an Ti Vaiaility, Oations Rsah, Vol., No., Bn, R. 00, Th Waanty Winfall, Businss Wk Onlin, D 0, Issu 91, Cohn, M. an S. Whang. 1997, Coting in Pout an Svi: A Pout Lif-Cyl Mol, Managnt Sin, Vol., No.,

31 Dsai, P. an P. Paanahan. 00, Dual Goo, Etn Waanty an Channl Cooination, Rvi of Makting Sin, Vol., Atil, 1. Eons, W. 1989, On th Liitation of Waanty Duation, Th Jounal of Inustial Eonois, Vol. 7, No., Guta, S., an R. Loulou. 1998, Poss innovation, out iffntiation, an hannl stutu: statgi inntivs in uooly, Makting Sin, Vol. 17, No., Hal, G. 1977, Guaants an Risk Shaing, Rvi of Eonoi Stuis, Vol., Hs, S. 008, Suly Chain Dynais un Etn Waanty Sals, Woking Pa, Iniana Univsity. Hollis, A. 1999, Etn Waantis, Avs Sltion, an Aftakts, Th Jounal of Risk an Insuan, Vol. 66, No., 1. Latini, L. an R. Osini. 001, Ntok Etnalitis an Th Ovovision of Quality y A Monoolist, Southn Eonoi Jounal, Vol. 67, No., Lutz, N.A. an V. Paanahan. 1995, Why Do W Osv Minial Waantis?, Makting Sin, Vol. 1, No., Lutz, N.A. an V. Paanahan. 1998, Waantis, Etn Waantis, an Pout Quality, Intnational Jounal of Inustial Oganization, Vol. 16, 6 9. Ma, J. 1987, Disount an P Unit Costs of Pout Waanty, Managnt Sin, Vol., No. 7, Manov, M. 198, Povi Insuan, Th Bll Jounal of Eonois, Vol. 1, No., Mnk, W. 1969, Dtination of Waanty Rsvs, Managnt Sin, Vol. 15, No. 10, O, M., I. Aan, V. Kulkani, an J. Sainathan. 00, Outsouing Waanty Rais: Stati Alloation, Woking Pa, Univsity of Noth Caolina, Chal Hill. Paanahan, V. 1995, Usag Htognity an Etn Waantis, Jounal of Eonois & Managnt Statgy, Vol., No. 1, 5. Paanahan, V. an R.C. Rao. 199, Waanty Poliy an Etn Svi Contats: Thoy an An Aliation to Autooils, Makting Sin, Vol. 1, No.,

32 Patanka, J. an G. Wo. 1981, Pition Intvals fo Waanty Rsvs an Cash Flos, Managnt Sin, Vol. 7, No., 7 1. Sahin, I. an H. Polatogu. 1998, Quality, Waanty, an Pvntiv Maintnan, Klu Aai Pulishs. Saano, J. 005, DailChysl Gos in Rvs on Waantis, Th Wall Stt Jounal, May 6, 005, D. Savaskan, R., S., Bhattahaya, an L. Van Wassnhov. 00, Clos-loo suly hain ols ith out anufatuing, Managnt Sin, Vol. 50, No., 9 5. Shlsing, H. 198, Nonlina Piing Statgis fo Cotitiv an Monoolisti Insuan Makts, Th Jounal of Risk an Insuan, Vol. 50, No. 1, Taylo, G. 1995, An Equiliiu Mol of Insuan Piing an Caitalization, Th Jounal of Risk an Insuan, Vol. 6, No., Tiol, J. 1988, Th Thoy of Inustial Oganization, MIT Pss. Waanty Wk. 008, Ciuit City s Etn Waantis, Waanty Wk, Jan. 16.

33 R* - M* =0. =0.6 =1 / R* - / M* =0. =0.6 = Figu a: Coaison of Otial Pout Rtail Pi Btn Mols R an M Figu : Coaison of Otial Etn Waanty Pi P Unit Lngth of Ti tn Mols R an M R* - M* =0. =0.6 = R* - M* =0. =0.6 = Figu : Coaison of Otial Pofit of Rtail Btn Mols R an M Figu : Coaison of Otial Pofit of Manufatu Btn Mols R an M =0.6 R* - M* =0. =0.6 =1 R* - R* Figu : Coaison of Otial Pofit of Thi Paty Btn Mols R an M Figu f: Coaison of Otial Pofit Btn Manufatu an Rtail in Mol R

34 =0.6 M* - M* Not: W hav oitt th uvs fo = 0. an = 1 fo Figus f an g as th y-ais valus a sustantially high fo ths uvs. Th qualitativ natu of all uvs, hov, is siila. Figu g: Coaison of Otial Pofit Btn Manufatu an Rtail in Mol M

35 * / * Mol C Mol R Mol M s M* - s R* / Figu a: Coaison ith Poosition, EW Pi P Unit Lngth of Covag =0.5, =0. Figu : Coaison ith Tho 1, Coaison of Otial Syst Pofit tn Mols R an M =0., =1.01, =0.5, angs fo 0.05 to M* - R* / M* - R* / Figu : Coaison ith Poosition a, Coaison of Otial Manufatu s Pofit tn Mols R an M =0., =1.01, =0.5, angs fo 0.05 to Figu : Coaison ith Poosition a, Coaison of Otial Rtail s Pofit tn Mols R an M =0., =1.01, =0.5, angs fo 0.05 to 5

36 6 APPENDIX: PROOFS OF RESULTS Poof of Poosition 1 W ov oosition 1 fo Mol R. Th oofs fo oth to ols a siila. Using th ssions fo Tal 1 gt: a 1 1 = < 0; 1 ] 1 [6 = < 0; 1 ] 1 [ = < 0; 1 ] 1 [ 8 = < = > 0; 1 ] [6 = > 0. Poof of Poosition Th tn aanty lngth is fo ol C, ol R, an ol M a: = C ] [, = R ] [, an = M ] [. Whn =, = M R. An M is asing in, aus M / = <. So if inass fo to, M ass an os sall than R, i.., hn =, > M R.

37 In aition, hn suay, hav lag than =, C R > 9 > 0 C R > > = M hn M as th to ols hav th sa ai ost Also, as ovn aov, hn <, R has th lost lngth i., hih shos C R >. In. This also shos. C is alays R M <, hih shos th onition hn ol Poof of Tho 1 Fist, ov that hn =, R > sys M. sys.. R > sys M sys > < 0, hih hols hn 0,7.6 ; o > 0, hih hols hn [7.6,1 ]. Fo any valu of, hav R > sys M sys.. < s, h s is qual to th valu of 1 [ δ, h δ =

38 Nt, ov > : s Whn =, ol R has high syst ofit than ol M. In aition, R* sys. = [ ] < 0. As inass, ol R s syst ofit ass. Whn <, ol R s syst ofit is lo s than that of Mol M. Oviously s is qui to lag than. Poof of Poosition a i R M. ii R M, h 680 = δ, h δ = [ 6 6 ] [ Siila oof as in Tho 1 fo is lag than. In ol R, R > R 189 < 11.8 ; 16 M In ol M, > M 15 < =.75. Poof of Poosition Coaing th inasing at of th syst ofit tn ol R an ol M, otain 16 > 16 R M sys. sys ] R > sys M sys.. < s. Th valu of s an foun in th oof of Tho 1. Th st of th oofs a staightfoa. Poof of Poosition 5 8

39 M a > M < Ma[, ]. Fo any valu of 1, , so th final onition is <. R < [ R ] < R, <, h = [ 7 R* R* R* R* ]. R Not that = 8 y 9 y 9 [ y 6 y 6 16 y 6 16 ], an y = 1 Φ Φ Φ 8 117, h Φ =

40 0. Tal 1: Otial solutions fo ol C, ol R, an ol M Mols Mol C Mol R Mol M Pout isions N/A Etn aanty isions Dans q q Otial ofits: Mol C Pofit C sys. ] [ Mol R Pofits R sys. 9 ] [ R 9 ] [ R ] [ Mol M Pofits M sys. ] [ M ] [ 9 M ] [

41 1 Tal : Otial solutions fo ol R an ol M Mols Mol R Mol M Pout isions Φ Φ Φ Etn aanty isions 7 9 ] 1 88 [ ] 1 88 [ 8 9 ] 1 [1 Dans q ] 1 [1 6 q Pofits sys. * * * * * q q ] 1 88 [ 108 * * * * * * q q ] 1 88 [ 6 * q * ] [18 * * * q ] [ Not: Th ssions fo otial solutions fo ol R a ath oliat. W hav only ovi th ssion of th otial holsal out i R* in Tal, h Φ = Th otial valus of oth vaials hav n ss in ts of R*.