Managing Supply Chain Backorders under Vendor Managed Inventory: A Principal-Agent Approach and Empirical Analysis

Transcription

1 nging Supply Chin Bckordrs undr Vndor ngd Invntory: A Principl-Agnt Approch nd Empiricl Anlysis Yuling Yo Collg o Businss & Economics, high Univrsity Emil: yuy3@lhigh.du, Tl: Yn ong Crlson School o Businss, Univrsity o innsot Emil: ydong@csom.umn.du, Tl: rtin rsnr Robrt. Smith School o Businss, Univrsity o rylnd Emil: mdrsnr@rhsmith.umd.du, Tl: Prliminry rt April 4

2 ABSTRACT This ppr xmins th rltionship btwn distributor bckordr prormnc nd its invntory lvls undr Vndor ngd Invntory VI in supply chin tht consists o distributors nd mnucturrs. W construct principl-gnt modl to show tht distributors invntory mngd by mnucturrs cn b usd to induc distributor orts, which r unobsrvbl to th mnucturrs, in convrting lost sls into bckordrs in th cs o stockouts. W us EI trnsction dt collctd rom th lctronic componnt nd truck prt industry to tst our rsults rom th nlyticl modling. Th mpiricl rsults provid strong supports or th proposition tht thr is strong dvrs rltionship btwn th invntory lvl nd bckordr convrsion rt, suggsting th mnucturr could us lowr distributor invntory s n incntiv or th distributors to convrt mor lost sls into bckordrs. Ky Words: Vndor ngd Invntory; Bckordrs; ost Sls; Incntiv; Invntory

3 nging Supply Chin Bckordrs undr Vndor ngd Invntory: A Principl-Agnt Approch nd Empiricl Anlysis. Introduction Introrgniztionl systms IOSs hv bcom prooundly importnt in supply chin mngmnt s irms rliz incrsing nds or collbortions with thir trding prtnrs in ordr to rspond to th st-chnging nvironmnts. IOSs provid n ctiv wy to rduc th inicincis rsulting rom symmtric inormtion in supply chins Bkos 99. As orm o IOSs, with hlp o th rpid dvlopmnt o EI nd Intrnt tchnology, Vndor ngd Invntory VI hs gind trmndous ttntions. Bsids inormtion shring s Kumn nd ohtdi, 3, or xmpl, VI lso turs structurl chng o th rltionships btwn upstrm sy mnucturr nd downstrm sy distributor prticipnts. Th rsponsibility in dciding th timing nd untity or rplnishing th distributor s invntory hs shitd rom th distributor itsl to th mnucturr. Th shit o dcision rsponsibility rdiclly ltrs th contrcting rltionship, thrby providing uniu opportunity or th mnucturr to utiliz VI or grtr bnits. Whil it hs bn widly blivd tht VI my hlp rduc supply chin invntory lvls nd stockouts, thrby gnrting cost svings, th mssgs rom industry rports r mixd t bst. Bsids cost svings rsulting rom VI, incrsing mrkt shrs is nothr importnt ttrctivnss o VI, spcilly whn th distributor crris substitut products rom compting mnucturrs. On wy to incrs mrkt shrs is to convrt lost sls into bckordrs in th cs o stockouts. 3

4 Bckordrs r criticl in msuring supply chin srvic prormnc usmn,. As customr srvic hs incrsingly bcom mjor gol o improving supply chin prormnc, how to mng bckordrs whn stockouts occur hs bgun ttrcting mor intrsts rom both rsrchrs nd prctitionrs or xmpl, u, Song, nd Yo, 3; Song,. With intnsiid comptition in mny industris prsonl computrs, lctronics, utomobils, to nm w, th impliction o bckordrs in mintining nd incrsing mrkt shr in highly comptitiv mrkts hs ld compnis to xplor wys to control nd mng bckordrs. In supply chin whr distributor hs multipl sourcs o supplis, it is to th mnucturr s intrsts to prvnt customr rom switching to its comptitor s products in th cs o stockouts. This, howvr, my not b o th distributor s intrsts, or my b indirnt to th distributor. Th mnucturr nd to ind wys to ssur tht thy do not los customrs nd sls to thir comptitors onc stockout occurs. Th widly doptd VI ors convnint nd ctiv wy to ct supply chin prtnrs rgrding bttr mnging bckordrs. Th ocus o this ppr is to xmin how th mnucturr my us VI to xtrct th bst ort rom th distributor to convrt lost sls into bckordrs in cs o stockouts, i.. incrsd mrkt shrs or th mnucturr. In th xisting VI litrtur, nd supply chin litrtur in gnrl, incntiv contrcts hv bn studid to invstigt mchnisms rgrding inormtion shring, invntory control, cpcity lloction, tc..g. Cchon,, Cchon nd vrir, 999, Tsy,, tc.. Bckordrs in supply chins hv bn nlyzd mostly s n invntory control msur tht is givn with littl strtgic implictions.g., onohu,. tly, bckordrs hv bcom th ocl point o som supply chin rsrch Choi, i, nd Song, 3, 4

5 u, Song, nd Yo, 3, nd Song,, but ths studis sk to minimiz bckordrs to improv supply chin srvic. Our rsrch tks dirnt pproch nd ttmpts to shd lights on how n upstrm prtnr in supply chin, givn its strongr intrsts in bckordr stockouts thn lost sls stockouts, cn provid incntivs vi VI to inlunc its downstrm prtnr s bhvior in ordr to incrs or mintin its mrkt shrs. Our rsrch intnds to ill th gp through nlyticl modling o th supply chin ordr rplnishmnt procss btwn VI prticipnts, nd mor importntly, through providing mpiricl vidnc rsulting rom conomtric nlysis o th rich dt gthrd rom th EI trnsctions in supply chins o th lctronic componnt nd truck prt industris. Whil mny hv rgud tht th mnucturr undr VI will just lood th loor o th distributor s wrhouss tht th mnucturr mngs, nd othrs,.g., Fry t l., suggst n invntory ciling bing imposd in VI contct, w propos tht, undr VI, thr cn xist n incntiv ord by th mnucturr to lowr th invntory lvls t th distributor s s rsult o inducing ort rom th distributor to convrt lost sls to bckordrs. In this viw, bckordrs bcom mor o strtgic wpon or th mnucturr to nhnc thir mrkt shrs, whrs th distributor njoys lowr invntory lvls rsulting rom mking orts to mng bckordrs. This proposition is supportd by our rsults drivd rom principl-gnt modl cpturing bckordrs, stockouts, nd invntory, undr stochstic dmnd. It is lso supportd by th ollowing mpiricl xmintion tht th distributors with lowr vrg invntory lvl tnd to hv highr prcntgs o bckordr stockouts in totl stockouts. 5

6 Th rst o th ppr is orgnizd s ollows. Sction prsnts litrtur rviw on VI; sction 3 discusss th dvlopmnt o th nlyticl modl; sction 4 prsnts th mpiricl modl; sction 5 provids discussion o th indings rom both nlyticl nd mpiricl modls; nd sction 6 prsnts conclusions, limittions, nd utur rsrch.. itrtur Rviw Thr is rich body o litrtur tht studis VI. Ths pprs cn b summrizd into two strms, ons tht tk VI s givn structur nd study pr vs. post bnits.g., Rghunthn nd Yh ; t l 999; ong t l. nd optiml oprtionl policis.g. Ctinky nd, th othrs tht study th issus on th structurl dsign o VI.g., Fry t l.. Rghunthn nd Yh ound tht th implmnttion o continuous rplnishmnt progrms CRP, supply chin inititiv kin to VI is bnicil to both mnucturrs nd rtilrs in trms o invntory rductions. Invntory rductions r ctd by chrctristics o consumr dmnd; tht is, whn dmnd vrinc incrss, invntory rductions du to continuous rplnishmnt progrms dcrs. In similr pproch, Aviv comprd VI with inormtion shring nd collbortiv orcsting, nd uto rplnishmnt CFAR undr uto-rgrssiv dmnd procss, nd showd tht VI nd CFAR r mor importnt s th dmnd procss is mor corrltd cross priods, nd s compnis r bl to xplin lrgr portion o th dmnd uncrtinty through rly dmnd inormtion. Thy indings rconirm mpiricl vidnc prsntd by t l. 999 in which thy showd invntory turns 6

7 nd stockouts r improvd tr implmnttion o CRP, using dt collctd rom 3 grocry rtil chins. In nothr mpiricl study o just-in-tim prctics, which r otn usd in conjunction with VI, ong t l. ound tht th bnits rom JIT, in trms o invntory rductions, r most likly to low to buyrs rthr thn to supplirs. Ctinky nd prsntd nlyticl modl or coordinting invntory nd trnsporttion dcision in VI. Thy rgud tht th ordr rls policy in us with VI inluncs th lvl o invntory ruird t th vndor, thus dirctly cting supplir s invntory costs. As rsult, th ctul invntory ruirmnts t th vndor r prtly dicttd by th prmtrs o th shipmnt-rls policy. Chung nd lso xmind shipping strtgis in VI, nd idntiid scnrios tht invntory costs my b lowr. Iyr nd Brgn 997 studis nothr similr progrm, Quick Rspons QR, nd ound tht numbr o vribls, such s srvic lvl, wholsl pric nd volum commitmnts, r instrumntl to mk QR proitbl or both th mnucturr nd rtilr. Th scond strm o litrtur xmind VI through lns o contrcting thory. Ths works ocusd on th dsign o th VI. For xmpl, Fry t l. studid VI undr z, Z typ contrct, nd ound th z, Z typ o VI contrct prorms signiicntly bttr thn trditionl rtilr mngd invntory in mny sttings, but cn prorm wors in othrs. Choi t l. 4 discussd numbr o prormnc mtrics tht my b usd to msur VI s prormnc. Thy showd tht th bckordrs should lso b tkn into ccount whil hving considrd invntory lvls. Cchon xmind two-chlon supply chin with on supplir nd N rtilrs, nd ound tht th comptitions mong th rtilrs my ld to substntilly highr costs 7

8 thn optiml. urthr showd tht chng o control, i.. implmnttion o VI contrct, could ld to optiml supply chin prormnc. Plmbck nd Znios 3 considrd VI in principl-gnt stting tht th principl motivts th gnt to control th production rt in mnnr tht will minimiz th principl s own totl xpct discountd cost by mking pymnts contingnt on th invntory lvl. Finlly, rynn t l. xmin rtilr nd supplir undr nwsvndor stting. Th rtilr crris substitutbl products rom othr supplirs, thrby rsulting in dirnt stockouts costs or th supplir nd rtilr. Thy drivd conditions undr which stocking dcision should b trnsrrd rom rtilr to supplir, i.. n implmnttion o VI. Thr r numbr o rlvnt pprs tht hv xmind incntiv mchnism in supply chins in gnrl, though not in VI stting prticulrly. For xmpl, Chn xmins th dsign o compnstion pckgs to th sls orc in ordr to induc thm to xrt ort in wy tht ctully smooths th dmnd procss. rivir nd Portus dmonstrt th pric cn b n ctiv contrct trm to chiv supply chin coordintion in th nwsvndor stting. 3. Anlyticl odl 3. odling Frmwork W modl th VI in principl-gnt stting whr th mnucturr cts s principl nd th distributor cts s n gnt. u to inormtion shring in VI, th mnucturr hs ull knowldg bout dmnd distribution s wll s distributor invntory costs nd policy. Th mnucturr mks dcision on th rplnishmnt 8

9 untity to th distributor undr VI, nd implmnts production policy o kto-ordr. Without loss o gnrlity, w ssum singl itm mngd in th VI btwn th mnucturr nd th distributor, nd th distributor lso crris substitut products ord rom compting mnucturrs. Th slling pric or th itm t th distributor is p, purchs cost i.. th mnucturr s slling pric is w, nd mrginl production cost or th mnucturr is v. In VI, lthough th mnucturr mngs th distributor s invntory, it is still th distributor who intrcts dirctly with thir customrs. In th cs o stockouts, th customrs hv thr options, plc bckordr, purchs substitut itm rom th distributor supplid by compting mnucturr, or to purchs products rom dirnt distributor. Th irst scnrio rsults in bckordr stockouts, whrs th scond nd third scnrios rsult in lost sls stockouts to th mnucturr. I products rom dirnt mnucturrs hv similr mrgins, th distributor gnrlly is indirnt btwn bckordr stockouts nd lost sls stockouts, s long s th lost sls r substitutd by othr purchss t th distributor. Th mnucturr, on th othr hnd, prrs bckordr stockouts to th lost sls stockouts Cchon ; Nrynn t l.. Sinc dircting xtr orts in ssuring customrs is costly or th distributor, th mnucturr would hv to provid incntivs or th distributor whn stockouts occur. Whn th mrgins r substntilly dirnt, th distributor nds vn mor incntivs rom th mnucturrs who contribut smllr mrgins so s to not divrt its customrs to th othr products. Th xtnt to which lost sls stockouts r convrtd into bckordr stockouts dpnds on th distributor s ort. For xmpl, whn stockouts occur, i th 9

10 distributor s sls rprsnttivs could spnd crtin lvl o orts in ssuring th customr on th mnucturr s product ulity, gurntd st rplnishmnt, or r on-sit dlivry, it would incrs th possibility tht th customr dcids to plc bckordrs, rthr thn buy substitut. W dnot th distributor s ort s, nd th ort is not obsrvbl to th mnucturr. Thr r two lvls o ort, igh nd ow. Tht is, [ ] ;. W dnot th prcntg o bckordr stockouts to totl stockouts s,, which dpnds on th ort th distributor mks nd is unknown x nt. W ssum tht ollows conditionl distribution, nd this distribution is common knowldg. W urthr ssum tht th distributor o stisis irst ordr stochstic dominnc, suggsting good rsults r mor likly to hppn undr high orts. Th distributor incurs n incrsing cost or xrting th ort, c, nd c > nd c >. Accordingly, c > c. Th dmnd is stochstic with distribution o gx. Both bckordr stockouts nd lost sls stockouts incur pnlty costs or both th mnucturr nd th distributor or th distributor, only whn th sls r lost to compting distributor. Th unit pnlty costs or bckordr stockouts is normlizd to ul its gross mrgin or both th mnucturr nd th distributor or computtion convninc without loss o gnrlity. Tht is, or vry unit in bckordrs, th mnucturr nd distributor hv to xpdit thm with zro proits. W ssum th mnucturr hs lrg nough cpcity so tht it cn ulill ny mount o bckordrs immditly. Th unit pnlty costs or lost sls stockouts r l nd s or th mnucturr nd th distributor, rspctivly, nd l >s sinc th mnucturr is pnlizd mor svrly thn th distributor s th distributor my sll substitut product. Finlly, w ssum th ovrstockd products r disposd

11 t costs o nd h or th mnucturr nd distributor, rspctivly, nd h to nsur th distributor will not sll th ovrstockd products bck to th mnucturr or proits to th mnucturr. Ths ssumptions r consistnt with thos in Cchon. Thror w cn writ th xpctd proit unctions or th mnucturr nd distributor: x g x dx l x E w v g x dx E x [ px w h x ] g x dx [ p w s x ] g x dx c x Undr VI contrcting, th sunc o th gm is s ollows. First, th mnucturr ors VI mnu contrct,,, to th rtilr, nd th distributor dcids to ccpt it or rjct it. I th contrct is rjctd, th distributor s proits r normlizd to zro. I ccptd, th distributor dcids whthr to mk n ort. Thn, rplnishmnt ordr is plcd nd th contrct is xcutd. Finlly, th dmnd is rlizd. Th mnucturr dos not obsrv th distributor s ort dirctly, nd cn only contrct on th x post bckordr rtio, which dpnds on, nd rlizs whn n ordr is plcd, nd ordr untity. Sinc th distributor is risk vrs with rgrd to th rplnishmnt untity nd its ort is not obrsrvbl, morl hzrd problms my xist, nd th mnucturr nd to provid incntivs to motivt th distributor to xrt highr lvl o orts. Th incntiv mchnism is sttd s ollows: x, x x E E, d 3 subjct to

12 4 IC: Ex d c c 5 IR: E x d c Th objctiv unction is th mnucturr s xpctd proits. Th individul rtionlity constrint IR rlcts th minimum lvl o proits tht th distributor would ccpt th contrct. Th incntiv comptibility constrint IC stts tht th distributor will choos igh ort tht rsults in highr proits or th distributor. 3. odl vlopmnt nd Anlysis W irst nlyz th conditions undr which th optiml contrct xists. W thn dvlop th irst bst nd scond bst rsults, which ld to th min rsult rgrding th VI contrct. in th prtil drivtivs with rgrd to or th mnucturr nd distributor s xpctd proit unctions s: w l [ l ] G p w sb s [ p h p w sb s ] G Sinc both proits unctions r concv in, ths unconditionl irst ordr prtil drivtivs ld to both prtis prrrd ordr untitis. in whr, nd * whr. Th ollowing rsult shows th condition * undr which sibl contrct is lso optiml. mm. For ny sibl contrct, it is optiml i nd only i. This rsult indicts ncssry condition undr which n implmntbl contrct is optiml. Sinc th mnuctur is th prty to mk th dcision on, h will choos

13 * i * lso stisis ll th constrints, rsulting in th unconstrind irst bst contrct. owvr, i th IR constrint is violtd by *, th mnucturr hs to chng th so tht th distributor s proits incrs until th IR binds. I nd only i, th mnucturr my incrs whn incrs th distributor s proits. < or dcrs whn * * > th to * * It cn b shown tht or >, * * p w s * G p h s 6 w v l * G l 7 Sinc G. is cumultiv dnsity unction, G. is incrsing in. Thror, * * > suggsts G > G. Compr 6 with 7, nd collct trms, w cn * * dduc suicint nd ncssry condition tht dscribs th rltionships btwn nd *. This lds to th lmm. mm. Whn * * p w p h w v > w v s h w l, > ; nd whn * * p w p h w v < w v s h w l, <. Considring w v s h w l >, suicint not * ncssry condition or > cn b dducd: * * < p h w v. Sinc <h<p, it cn p w b urthr simpliid to: <. 5. This rsult indicts tht p h > stisis s long * * s th proit mrgin or th mnucturr w-v rltiv to th distributor s proit mrgin p-w is lrg nough, i.. lrgr thn 5%. 3

14 Whil both situtions my occur givn combintions o dirnt pric nd cost prmtrs, w ocus on th sitution whr >. W ssum this rltionship * * bcus o th prsnc o incrsing dgr o scl conomis moving up supply chins in mny industris. W obsrvd in our dt tht th numbr o distributors downstrm supply chin, 89, is substntilly grtr thn th numbr o mnucturrs upstrm supply chin, 4, lding to this ssumption. It pprs mor pproprit to ocus on th > scnrio lthough this rducs th pplicbility o th rsults. Furthrmor, our * * mpiricl nlysis uss dt collctd rom lctronic componnt nd truck prt industry. Ths numbrs to crtin xtnt vlidt >, t lst in th lctronic componnt * * nd truck prt industry. To ollow th bov discussions, w hv nd, corrsponding to >. For th sk o convninc, w urthr rstrict our nlysis to > nd * * <. W rgu tht mintining or or ny is nithr rlistic nor ncssry, lthough w rcogniz th ct tht this my ct th xtnt to which our rsults r gnrlizd. Th ollowing scond ordr drivtivs provid urthr chrctristics o th optiml contrct. [ l ] g < R b [ p h p w s s ] g < 4

15 Thror, w cn dtrmin tht is incrsing in, nd is dcrsing * * in,,, bcus >. W now dvlop th irst bst solution nd th scond bst solution o th modl. Th irst bst solution is obtind by substituting th IR constrint into th objctiv unction nd ignoring th IC constrint, whrs th scond bst solution is obtind by substituting both th IR nd IC constrint into th objctiv unction. W introduc th ollowing lmm on th irst nd scond bst solutions. in: w v l [ p h s ] B. solution, G A ; [ l ] A ; B p w s ; Proposition : In th irst bst solution, G A µ B FB A µ. In th scond bst B SB A µ B A µ B B λ. B λ From this rsult, th importnc o ordr untity, s n incntiv instrumnt to xtrct high ort rom th distributor, dpnds on th conditionl distribution o th bckordr convrsion rtio givn ort. Th ollowing rsults urthr xplor th rltionship btwn th conditionl distributions nd solutions to th problm. or ny sibl 5

16 SB mm 3: *, FB i > SB FB * ; nd, i <. As hving shown rlir tht > nd < in ordr to stisy <, ll sibl in th uilibrium solutions, including th irst bst FB nd th scond bst SB, * * should b in th rng tht,. nc, w cn dduc tht th irst bst FB * * solution should b lso in th rng tht,. Sinc t th irst bst solution, FB IR constrint binds, suggsting tht. Considring < tht highr lds to lowr rtilr s proit i..,, w cn conclud tht ~ <, or ny ~ FB, * > FB, which violts th IR constrint tht th rtilr only prticipts whn its proit is ul to or grtr thn. Thror, ny sibl scond bst SB nds SB to b in th rng tht *, FB. Bsd on th possibl rng in which th scond bst SB my rsid nd lmm 3, w cn dtrmin tht or ny scond bst solutions, th inulity o > should lwys b stisid. Furthrmor, w ssum onoton iklihood Rtio Proprty RP holds. RP is proprty tht nsurs highr production lvl is clr vidnc tht th gnt hs md highr ort ont nd rtimort,, pg65. In our cs, it suggsts highr ort lvl incrss th liklihood o high convrsion rt mor thn th liklihood o low convrsion rt. 6

17 Proposition : Assum RP holds, dcrss in, i.. <, *, FB. Proposition shows tht in th optiml contrct, th bckordr convrsion rt is ngtivly ssocitd with th rplnishmnt untity, which dtrmins th distributor s invntory lvl dirctly. Th lowr th invntory lvls th highr th bckordr stockouts convrsion rts. This rsult suggsts tht th mnucturr my us lowring invntory lvl s n incntiv to th distributor to spnd highr orts whn intrcting with thir customrs in th cs o stockouts to convrt grtr lost sls stockouts into bckordr stockouts. 4. Empiricl odl 4. thodology W dvlop n mpiricl modl bsd on th proposition drivd rom th nlyticl modling in th lst sction. Proposition shows tht thr is ngtiv rltionship btwn stockouts convrsion rt nd th rplnishmnt untity i.. distributor s invntory lvl. Invntory lvls hv ggrgt cts on totl stockouts i.. bckordr stockouts lost sls stockouts tht th lowr th invntory lvls th highr th totl stockouts. Proposition suggsts, howvr, tht th mnucturr my b bl to provid th distributor with som invntory rductions s n incntiv to induc th distributor s high orts in crting highr convrsion rts i.. grtr bckordr stockouts nd wr lost sls stockouts givn crtin lvl o totl stockouts. This ct is bov nd byond th ggrgt cts. For xmpl, suppos th totl stockouts r units with 5 o ch or bckordr nd lost sls stockouts 5%. I 7

18 th mnucturr dcids to rduc th rplnishmnt untity i.. distributor s vrg invntory, thn th totl stockouts my incrs to units but with combintion o 7 nd 5 units or bckordr nd lost sl stockouts, rspctivly 58.3%. Th ovrll two-unit incrs rlcts th ggrgt cts, whrs th convrsion rt incrs rom 5% to 58.3% rlcts th cts rsulting rom th distributor s high ort. Our mpiricl modl is constructd to tst th xistnc nd mgnitud o th lttr cts. In th mpiricl study, w tst th high ort cts using n intrction trm o totl stockouts nd invntory with proprly controlling or totl stockouts nd othr xognous vribls. Our gol is to show tht th mrginl chngs o bckordr stockouts with rgrd to totl stockouts r highr whn invntory lvls r lowr, othr things bing ul. Th rson tht w do not dirctly tst th chngs o on invntory is bcus th diicultis in clculting whn th sum o bckordr stockouts nd lost sls stockouts is zro s dnomintor. Our mpiricl rsults r imd t providing prtil vidnc tht th incntiv mchnism is t work, nd th mnucturr cn improv its bckordr stockouts with lowr lvls o invntory. Thus, w ormult our min mpiricl rsrch ustion s: Invntory lvls INV hv ngtiv impct on th numbr o bckordr stockouts BS or givn lvl o totl stockouts TS. Empiriclly, w ocus on th ution BS g TS; TS * INV, Exognous Vribls, nd th dtils r discussd in th ollowing sction. 4. t Firm lvl dt wr collctd rom Entrpris t ngmnt E, 3 rd prty logistic solution providr spcilizd in VI. E hlps supplirs nd distributors 8

19 mng thir invntory by intgrting thm through VI procsss. istributors shr thir invntory sttus, dmnd, nd sls inormtion with thir mnucturrs through stndrd EI protocol, EI 85, nd in rturn, th mnucturrs dcid th tim nd th untity to rplnish distributors invntory. t o 4 mnucturrs mnging 89 distributors invntory ws collctd. Among 4 supplirs, o thm r in th lctronic componnt industry with on mnging 65 distributors nd th othr mnging 4; th rst o r in th truck prts industry with on mnging 6 nd th othr mnging 4. Th sourc dt contins wkly inormtion or th most rcnt 8 wks t th tim th dt wr collctd, i.. rom th wk o y, to th wk o Jun 3, nd or th oldst 8 wks which is two yrs go sinc only two yr s dt ws kpt in thir systms, i.., rom th wk o July 3, to th wk o Sptmbr 7,, on invntory lvl, bckordr stockouts, lost sls stockouts, totl itms mngd, nd sls t distributor s. Annul sls or ch distributor r lso collctd. t wr ggrgtd ovr 8 wks or both most rcnt nd th oldst priod, rspctivly, so tht it bcoms two priod cross sctionl dt st. Among 89 distributors, o thm strtd VI prctic btwn th oldst priod nd th most rcnt priod. Th obsrvtions or th oldst priod wr not usd in our nlysis s w ocuss on th distributors undr VI prctics. nc, th dt st contins 68 89*- obsrvtions. Bckordr stockouts r th numbr o dys pr wk tht bckordrs occurrd, nd bckordr stockouts occur whn rustd untity is grtr thn on hnd invntory nd th customr grs to plc bckordr. ost sls stockouts r th numbr o dys 9

20 pr wk tht lost sls occurrd, nd lost sls stockouts occur whn rustd untity is grtr thn on hnd invntory nd th customr ithr purchss prtil rustd untity, or dcids not to purchs t ll. In ordr to bttr undrstnd how th two typs o stockouts occurrd nd rcordd by th distributors, w prsnt hypothticl cs in th ollowing tbl. Tbl : Bckordr Stockouts nd ost Sls Stockouts Assum: Rustd Quntity ; On nd Invntory Scnrio. Th customr wnts th whol units bckordrd.. Th customr tks units on hnd, nd wnts th rst o units bckordrd. 3. Th customr tks th units on hnd nd thn buys th rst o units rom comptitor. 4. Th customr buys ll o units rom comptitor. Bckordr Stockouts ost Sls Stockouts istributor s Rcord Ys No Bckordr Stockouts Ys No Bckordr Stockouts No Ys ost Sls Stockouts No Ys No It cn b sn rom th tbl tht th distributor s dt corrctly rcordd scnrio -3, but ild on scnrio 4, mning tht rportd lost sls stockouts would b lowr thn ctul lost sls stockouts. W ssum tht unrcordd lost sls stockouts hppns rndomly cross th distributors, so tht th ct o undr ccountd dt my wsh o. 4.3 Estimtion nd Rsults Th rgrssion modl spciid in sction 4. is stimtd in two stgs du to th ndognity btwn invntory nd totl stockouts. Th irst stg is n stimtion o invntory s n instrumntl vribl. Th scond stg stimts th bckordr stockouts ution with ittd vlu o invntory gnrtd rom th irst stg instrumntl

21 stimtion. Sinc bckordr stockouts r th countd numbr o dys tht bckordring vnts occur during wk, it ollows Poisson distribution. Ordinry st Surd OS stimtion is not pproprit, nd Poisson mily rgrssions, such s Poisson rgrssion or ngtiv binomil rgrssions, r considrd Grn 997. Thror, th stimtion utions cn b urthr ormultd s ollows: INV α α ITES α SAES α 3 SIZE α 4 TIE α 3 i i F i BS β β TS β TS*INV β 3 ITES β 4 SAES β 5 TIE β 3 i i F i Whr: Totl Stockouts TS is th countd dys o totl stockouts or ll itms mngd, including bckordr stockouts nd lost sls stockouts, during wk. Bckordr Stockouts BS is th countd dys o bckordr stockouts or ll itms mngd during wk. Invntory lvl INV is th vrg on-hnd untity or ll itms during wk, vrg ovr 8 wks. Wkly Sls SAES is th totl untity sold or ll itms during wk, vrg ovr 8 wks. Totl Itms ITES is th totl numbr o itms mngd by mnucturr t distributor s loction, vrg ovr 8 wks. Annul Sls SIZE is th dollr mount o nnul sls or distributor. Tim ummy TIE is th dummy vribls with indicting th most rcnt dt, nd indicting th oldst dt.

22 nucturr ummis F is th dummy vribls crtd to control th ixd cts o dirnt mnucturrs. α, β, α, nd β r prmtrs to b stimtd. Tbl prsnts th dscriptiv sttistics. Tbl : scriptiv Sttistics N68 n S.. in x Totl Stockouts,5.66,38. 5,89 Bckordr Stockouts ,47 Invntory $ 48, , ,49,75 Wkly Sls $ 3, , ,4 Totl Itms ,98.5 Annul Sls x 6 $ Th two utions r stimtd in two stgs using STATA. Th irst ution is stimtd using OS. Th scond ution is irst stimtd using Poisson rgrssion. Th ollowing goodnss-o-it tst o th rgrssion is signiicnt Goodnss-o-it chi 84.7; Prob > chi59., suggsting n ovrdisprsion o th dpndnt vribl so tht Poisson rgrssion is inpproprit. Poisson rgrssion ssums tht th xpctd mn should b ul to th xpctd vrinc, which is violtd in our cs. Thror, mor lxibl orm o Poisson mily rgrssion, ngtiv binomil rgrssion, is usd. Tbl prsnts th stimtion rsults. In th irst ution, th coicints or totl itms α nd or wkly sls α -3.3 r positiv nd signiicnt p<.. Th rsults show tht th highr th numbr o totl itms in VI nd th highr th wkly sls, th grtr th

23 invntory lvl t th distributors. Th djustd R-surd o.8 indicts trriic it in prdicting instrumntl vribl o invntory. In th scond ution o bckordr stockouts, th intrction trm, clcultd by multiplying ittd vlu o invntory rom th irst ution with totl stockouts, is pluggd in to tst high ort cts. Th coicint or th intrction trm β is ngtiv nd signiicnt p<., indicting tht invntory hs dvrs cts on th mrginl chngs o bckordr stockouts with rgrd to totl stockouts. Th coicints or totl stockouts β.54 is positiv nd mrginlly signiicnt p<., indicting tht chngs o totl stockouts r positivly ssocitd with bckordr stockouts. Plugging th stimtd coicints into th irst ordr drivtiv o th bckordr stockouts rgrssion with rspct to th totl stockouts, w hv: BS 9 9 TS INV TS 9.4 TS BS igh BS low W cn conclud tht INV < INV TS TS INV. Th rsult shows tht distributors with lowr invntory hv highr mrginl chngs o bckordr stockouts with rgrd to totl stockouts. In ddition, Chi-surd sttistic or th scond ution is highly signiicnt. Th og iklihood Indxs, which r uivlnt to R surd in OS, r., indicting rsonbl it or th ngtiv binomil rgrssion nlyss. 3

24 Tbl 3: Two-Stg Rgrssion Rsults Stndrd Errors in Prnthss Intrcpt Totl Stockouts TS* ittd INV x -9 Totl Itms Wkly Sls Annul Sls TIE nuctur nuctur nuctur 3 pndnt Vribls Invntory Bckordr Stockouts *** *** ** ** 3.5.4*** ***.35 3.*** ***.9.77*.8 odl Sttistics N F Sttistics 5.*** og iklihood Chi-Surd 63.9*** Adjustd R.8 Psudo R RI. p <.; * p <.5; ** p <.; ***p<. 4. Scnrio Anlysis 4

25 W prsnt scnrio nlysis to bttr illustrt th dvrs ct invntory hs on bckordr convrsion rt bsd on th stimtd coicints in tbl 3. W ssum it is th old tim, mnucturr # i.., Tim; nucturr ; nucturr ; nucturr 3, nd totl itms nd wkly sls r t thir mn vlus. W idntiy 9 scnrios rprsnting ll possibl combintions o 3 dirnt vlus o totl stockouts nd invntory. 3 dirnt vlus o totl stockouts rprsnt high, mdium 6, th mn o totl stockouts, nd low 5, nd 3 dirnt vlus o invntory rprsnt high 34975, th mx vlu o th invntory, mdium 483, th mn o invntory, nd low 97, th min vlu o invntory. Tbl 4 prsnts th scnrio nlysis. It cn b sn rom th tbl tht bckordr convrsion rt is ngtivly ssocitd with invntory lvl or givn lvl o totl stockouts. For xmpl, in th cs o totl stockouts o 6 units, th bckordr convrsion rtio rducs rom 45.% to 4.4% whn invntory lvl incrss rom 97 to 483, nd to % whn invntory lvl urthr incrss to This rsult provid urthr vidnc in supporting our proposition tht th mnucturrs r bl to us lowr invntory to induc th distributors to xrt highr ort in convrting lost sls stockouts into bckordr stockouts, s msurd by stockouts convrsion rts. It is lso intrsting to not tht bckordr convrsion rt is lso dcrsing in totl stockouts or givn lvl o invntory. For xmpl, bckordr convrsion rt rducs rom 69.5% whn totl stockouts r 5 units, to 45.% whn totl stockouts r 6 units, nd to 39.4% whn totl stockouts r units. 5

26 Tbl 4: Numricl Exmpls Totl Stockouts Units Invntory $ Bckordr Stockouts Units Bckordr Convrsion Rt % % % % % % % % % 5. Concluding Rmrks In this ppr w xmin n incntiv mchnism dsign in VI tht th mnucturr cn us to incrs its mrkt shrs. In prticulr, w show tht th mnucturr cn us VI s mchnism nd us lowr mngd invntory s n incntiv to induc th distributors to xrt thir bst orts in incrsing th mnucturr s bckordrs in th cs o stockouts. Our modl ollows th notions usd in Cchon nd Nrynn t l. tht bckordr stockouts nd lost sls stockouts hv dirnt implictions in costs or th mnucturr nd th distributor. ost sl stockouts hurts th mnucturr mor thn th distributor s th distributor usully crris substitut products rom othr compting supplirs. This cost impliction gp motivts th mnucturr to dsign contrct o incntiv with th distributor in ordr to mitigt th problm. W irst construct n nlyticl modl in th principl-gnt stting to show tht th mnuctur cn or mnu o combintion o rplnishmnt untity i.., vrg invntory lvl nd bckordr convrsion rt tht inducs th distributor to choos high orts in incrsing th convrsion rt. W thn tst th proposition w gnrtd rom 6

27 th nlyticl modling through mpiricl modling o irm dt collctd rom th industry. Our mpiricl rsults provid strong supports or our proposition. W dmonstrt thr r strong dvrs rltionship btwn th invntory lvl nd bckordr convrsion rt, suggsting th distributors with lowr invntory mngd by th mnucturrs work mor diligntly in convrting lost sls into bckordrs, i.. incrsd bckordr convrsion rt nd mrkt shrs. This ppr contributs to th VI litrtur, nd supply chin litrtur in gnrl, by pproching VI dirntly in idntiying potntil morl hzrd problm tht xists btwn prticipnts. Th rsrch shds lights on how n upstrm prtnr in VI, givn its strongr prrncs in bckordr to lost sls, cn provid incntiv vi VI to impct its downstrm prtnr s bhvior in ordr to mitigt th morl hzrd problm, thrby incrsing its mrkt shrs. or importntly, th rsrch is on o vry w pprs tht mpiriclly tstd drivd proposition using industry dt in th VI litrtur. Th rsults provid strong mpiricl vidnc tht VI cn b usd s n incntiv mchnism or th upstrm prticipnts to cpitliz mny bnits, such s incrsd mrkt shrs. 7

28 Rrncs Avid, Y.. Gining Bnits rom Joint Forcsting nd Rplnishmnt Procsss: Th Cs o Auto-Corrltd mnd. nucturing & Srvic Oprtions ngmnt 4: Bkos, Y. J. 99. Inormtion inks nd Elctronic rktplcs: Th Rol o Introrgniztionl Inormtion Systms in Vrticl rkts. Journl o ngmnt Inormtion Systms 8: 3-5. Cchon G.. Stock Wrs: Invntory Comptition in Two-Echlon Supply chin with ultipl Rtilrs. Oprtions Rsrch 495: Cchon G.. Supply Chin Coordintion With Contrcts ndbooks in Oprtions Rsrch nd ngmnt Scinc: Supply Chin ngmnt. Editd by Stv Grvs nd Ton d Kok. North-ollnd. Ctinky, S. nd C. Y.. Stock Rplnishmnt And Shipmnt Schduling For Vndor-ngd Invntory Systms. ngmnt Scinc 46: 7-3. Chn, F.. Sls-Forc Invntivs nd Invntory ngmnt. nucturing & Srvic Oprtions ngmnt : 86-. Chung, K.., nd... Th Invntory Bnit o Shipmnt Coordintion nd Stock Rblncing in Supply Chin. ngmnt Scinc 48: Choi, K.S., J.G. i, nd J.S. Song. 4 On suring Supplir Prormnc undr Vndor-ngd Invntory Progrms in Cpcittd Supply Chins. Working Ppr. Gorgi Institut o Tchnology. ong, Yn, Crig Crtr nd rtin E. rsnr, JIT purchsing nd prormnc: n xplortory nlysis o buyr nd supplir prspctivs. Journl o Oprtions ngmnt 9: Fry,.J., R. Kpuscinski, nd T.. Olsn. Coordinting Production nd livry Undr z, Z-Typ Vndor-ngd Invntory Contrct. nucturing & Srvic Oprtions ngmnt 3: Grn, W Economtric Anlysis. Sddl Rivr, Nw Jrsy, Prntic ll. Iyr, A.V. nd.e. Brgn 997. Quick Rspons in nucturr-rtilr Chnnls. ngmnt Scinc 434: Kumn, R.J., nd. ohtdi 3. Anlyzing Intr-orgniztionl Inormtion Shring Strtgis in BB E-Commrc Supply Chins. Working ppr. 8

29 rivir,.a. nd E.. Portus. Slling to th Nwsvndor: n Anlysis o Pric-Only Contrcts. nucturing & Srvic Oprtions ngmnt 34: 93-35,. G., T. Clrk nd K. Y. Tm 999. Rsrch Rport. Cn EI Bnit Adoptrs? Inormtion Systms Rsrch : u, Y., J. Song, nd.. Yo 3. Bckordr inimiztion in ultiproduct Assmbl-to-Ordr Systms. Working ppr. Nrynn, V., A. Rmn nd S. Krislburd. Contrcting or Invntory in istribution Chnnl with Stochstic mnd nd Substitut Products. Working Ppr, rvrd Businss School. Plmbck, E.. nd S.A. Znios 3. Invntiv Eicint Control o A k-to- Stock Production Systm. Oprtions Rsrch 53: Rghunthn, S. nd A. B. Yh. Byond EI: Impct o Continuous Rplnishmnt Progrm CRP Btwn nucturr nd Its Rtilrs. Inormtion Systms Rsrch 4: Song, J.. Ordr-Bsd Bckordrs nd Thir Implictions in ulti-itm Invntory Systms. ngmnt Scinc 484:

30 3 Appndix Proo o Proposition Substituting th IR constrint into th objctiv unction nd ignoring th IC constrint, w hv: c d d µ µ, A- Tking prtil drivtiv with rgrd to pointwis, w obtin th irst ordr condition, nd st it to zro, w hv: µ A- Sinc <, µ>, indicting IR is binding. Thror, rom A- w cn solv th t uilibrium: B A B A G FB µ µ. Th scond bst solution is obtind by substituting both th IR nd IC constrint into th objctiv unction. Thus, w hv: [ ] c d c c d d µ λ µ λ,, A-3 Tking prtil drivtiv with rgrd to pointwis, w obtin th irst ordr condition, nd st it to zro, w hv: µ λ A-4

31 3 Sinc > µ d E, indicting th IR binds. Insrting µ d E into A-4, nd multiplying it by, w obtin: [ ] E λ A-5 Intgrting A-5 ovr [ ],, w hv: [ ] λ d E d A-6 From th slcknss condition o 7, w know tht: [ ] [ ] c c d λ λ A-7 Substituting A-7 into A-6, w hv: [ ], Cov d E c c λ A-8 nc, λ sinc nd vry in sm dirction ovr. Also, λ only i SB is constnt, but in this cs th IC is ncssrily violtd. As rsult, w hv > λ, indicting IC binds. Thror, rom 4 w cn solv th t uilibrium: SB B B A B B A G λ µ λ µ A-9

32 3 Q.E.. Proo o mm 3 Rmmbr FB is th tht stisis FB FB µ. Insrting this into A-4, w hv: SB SB FB FB λ A- W know tht is incrsing in. I >, thn > SB SB FB FB λ. nc,, * FB SB. It is sy to s th proo or th rst. Q.E.. Proo o Proposition St A-4, w hv: µ λ t s writ:, F µ λ Using implicit unction thorm: λ µ λ µ d d F F / /

33 33 Whr: < F l l [ ] < F s s w p s s w p b b [ ] < l [ ] < s s w p h p b R R From corollry, w know tht >. Sinc RP holds, w hv d d. Thror it is sy to s tht <. Q.E..