IMPACT OF THE OPERATIONS MANAGER S DUAL ROLE ON INVENTORY POLICY *

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1 Woking Pa 7-66 Businss onomis is tmb 7 atamnto d onomía d la msa Univsidad alos III d adid all adid Gta ain Fax IPA F H PRAIN ANAGR UAL RL N INVNRY PLIY JÉ ALFAR JP A. RIBÓ Abstat In modn ooations t ations anag s ol in dining o im s statgy is boming mo imotant. In tis a w dsib ow ims an us tis tndny o ations anags to mak statgi disions as a manism to vnt invntoy mismanagmnt. s manags av inntivs to sulat wit invntoy ost dutions tby avoiding sa dutions in a singl iod baus it would ind ut dutions in t utu. Rmakably ims may vnt su bavio by stimulating t ations anags statgi ointation witout losing sigt o invntoy-iint managmnt. Kywods: ations anag bavio omnsation modl Invntoy oliy. Businss atmnt. Univsity o Navaa. amus Univsitaio 38 Pamlona. ain. -mail: jalao@unav.s Businss atmnt alos III / adid 6 Gta mail: joatibo@m.u3m.s autos wis to tank aía José Álvaz aía Gutiéz as wll as smina atiiants at t Univsidad alos III adid 5 o ti usul ommnts. Finanial suot ovidd by t ojt o t omunidad d adid Gant # s-55/ti/3 om t gant # J6-94 and om t Fundaión Ramón As is gatully aknowldgd. W a sonsibl o any os.

2 / INRUIN ations disions a laying an inasingly imotant ol in a im s ovall statgy to aiv omtitiv advantag. is is not suising as Wild 979 masizd a long tim ago ations manags' disions inlun t nti oganization t jobs witin it and t mann in wi t wol is managd. Wit and Waton 99 suvys 9 U manuatuing ims and givs a so o 5.39 o odution on a sal om to 7 tus onsiding it as a signiiant lmnt in a ooat statgy. s atus lad Amistad and as 99 to onlud tat oations manags' ols a likly to b mo ousd on ooat tagts tan on oman masus o manuatuing. A onsqun ollows: ts manags sould mov ti ous om odution lanning sduling and ontol Gwin 993 to oodination tasks i. onnting odution and makting Ni and Young 997; o to dsign and oodinat ntwoks o knowldg ak and Ramaasad 3. Howv tis oss o gaining mo managial skills akland and oal 989 is a om a ality. As Ntto and oal 999 its t UK s oations manags w sn as manis wit dity ing nails at tan gntlmn and ti ointation is mainly ost ousd at tan statgi ointd Hum and Low 99. Intstingly tis is in sa ontast to t otntial aabilitis o ts manags. Ntto and oal 999 sows making us o a saml o Austalian ims tat unt ations anags a aadmially wll-qualiid in od to undtak sta suvision untions. is lads ts autos to agu tat ations anags in t utu sould av a gat ol to lay in stting t statgi dition o t omany and dining ioitis. Along tis lin ou main objtiv in tis a is to invstigat wt ations anags involvmnt in ativitis not ditly latd to oational managmnt lik t dinition o a ims statgy may at dtimntally ti tim and ot dvotd to managing invntoy in a ontxt w ts manags av inntivs to bav ootunistially. As a onsqun invntoy oliy may not b otimum. W intnd to ov tat tis is not tu. W aoa tis oblm by dvloing a siml modl w ations anags a omnsatd wn ty aiv two omlmntay goals. Fist wn t is a dution in invntoy osts. And sond wn ty ddiat ots to ot ativitis not ditly latd to oations. s ots a dvotd o xaml to dsigning a knowldg suly ntwok. is is a ntwok tat intgats manuatuing distibution ngining tnology dloymnt makting and ustom svis. s a sially abl to oodinat ts dint sous o knowldg as t oational outins ndd a quit amilia to tm. is inos a im s statgy by nsuing iint dlivy o nd oduts and svis to makts ak and Ramaasad 3. Also ts ots an b snt in analysing outsid inomation lik dmand stivs o a im s oduts and omtitos oliis. is analysis will ailitat t oodination task btwn agnts witin t im lik woks Haltiwang and aini 994 o btwn dint divisions lik makting and odution Ni and Young 997 in od to din a wll-goundd statgy. onsiding only t ist at o t omnsation sm invntoy ost dutions in t sot-tm annot b dasti baus tis would ind t aivmnt o lvant dutions in invntoy osts in t utu ootunisti bavio. Howv t omnsation o managial ots not dvotd to oational ativitis would justiy dasti dutions in invntoy osts. is is baus t latt anings may ost t xtd utu losss tat an initial dasti invntoy ost dution bings about. o aiv su an ougout t a w a going to to ts ots as managial ots tat a onsidd not ditly latd to invntoy managmnt. 3

3 outom an ations anag sould ombin intnsiv ots to du invntoy osts wit low managial ots in t ist iod. is allows a gat ossibility o utu omnsation linkd to imovmnts in ts latt ots tat an ost t dution in utu omnsation latd to invntoy osts dution. us toug tis manism t im s own an us monitoing o ations anags bavio in imlmnting ts noninvntoy latd ots dution in agny osts as a way to inlun invntoy ost dutions. Paadoxially by inooating omnsation om inass in ts managial ots w ind tat invntoy osts a dud and a stady-stat invntoy lvl is ad in a sot iod o tim tan by omnsating only on invntoy ost dutions. W an xtat sval onlusions om ou a. Fistly ims an ty to stimulat t managial ol o ti ations anags witout giving u invntoy-iint managmnt. ot dsign o t omnsation akag an mak bot objtivs omatibl. Intstingly ou oint is tat tis sm also woks wn ts altnativ tasks av vn no lationsi wit invntoy managmnt and wn ations anags av lag inntivs to bav ootunistially. ondly long-sving ations anags wit additional non-invntoy sonsibilitis may ix invntois at ti otimal lvl in a sot iod o tim tan ntly-aointd manags witout ts sonsibilitis. n tat invntoy lvl as bn ad t is no ut invntoy vaiability. onsquntly tis vaiability in t mdium-tm is smoot in tos ims wit long-sving ations anag in omaison wit tos ims wit nwly aointd manags Alao and ibó 3. idly ims wit xtis in monitoing manags sould andl invntois mo iintly. Lastly i w onsid t managmnt o manow lvls as an ations anag s sonsibility w an onlud tat ations anags may maniulat woko lvls as a omlmntay manism to aiv low invntoy vaiability tan by only managing invntois. is is in aodan wit ot studis Haltiwang and aini 994. is a is dividd into six stions. In t sond stion w build u t modl wi is solvd in t tid stion. W disuss t main totial indings in t out stion. tion iv insts ossibl xtnsions o t modl. a onluds wit som inal maks. / H L is is a two-iod modl wit an ations anag not o a sntativ im diding invntoy oliy as wll as imlmnting som non-viiabl managial ots. Fim s own monitos ts ots to omnsat t ontingnt on tm. modl is basd on t ollowing assumtions: Assumtions / im as dmand t t and to w [ ] { } avoid a ngativ dmand tat is is lag noug. s a dviations om t man and a known at t nd o a iod. y a indndnt and uniomly distibutd wit a zo man valu. s dviations allow us to abstat om issus latd to t dmand stutu and its imat on ims invntoy oliy. imila dmand onsidation an b ound in Kan 99 altoug tis a dos not siy t distibution o dmand soks. adotion o a non-uniom but symmti distibution would av gnatd qualitativly t sam ty o sults. main din is tat t omaativ stati analysis would av bn mo dndnt on t initial onditions ov total invntoy osts. 4

4 / otal Invntoy ost iod is dind as t sum o t osts assoiatd wit illing ustoms ods t ost o aying invntois and t stokout osts 3. An xssion o tis untion 4 is: W: Filling ost od; otal dmand iod; Unitay invntoy olding ost; Unitay invntoy stokout ost; Invntoy lvl; Lot siz; Planning iod i w tak it as w aommodat lanning iod wit dmand on. In a iod a im as a dmand tat aivs at a ontinuous at and at t nd o t iod total dmand oms out to b t. Bsids w assum in od to simliy tat dmand is attndd wit onstant lots wit a siz. W an tink o t xistn o som tnologial onstaints to justiy tis assumtion 5. 3/ An is isk nutal and as a two-iod tmoal oizon 6. omnsation is dind as ollows w imliitly assum a zo disount at: wt t t k t t By notation w t is t iod-t wag tat it is omosd o two ats: a ixd at wi is ig noug 7 and a vaiabl at. vaiabl at as two tms. Fist tm t t masus t das in t total invntoy osts btwn iod t- t and iod t t. sond tm t t masus t inas in t obsvd managial ot s nxt assumtion btwn iod t- t and iod t 8 t. Wit tis kind o sm t im s own givs s inntivs to du invntoy osts as wll as to inas managial ot 9. 3 Invntoy aying ost is t avag ost o olding invntois btwn dint lots o odution onsiding a uniom dmand. tokout ost is t ost o not attnding a uniom dmand ngativ invntoy btwn dint lots o odution. 4 W av didd to wok wit baus altoug t dmand inluds a stoasti at t andom nois is uniomly distibutd and on avag total ost untion an b aatizd by tis untion on w substitut t dmand o its man valu. 5 o onsid an ndognous lots siz dos not bing about lvant nw insigts. 6 I w ad addd an additional iod t main din would av bn tat t ist iod solution would av bn mo omlx and in gnal t dution in invntoy osts would av bn lss dasti. In gnal t lag t numb o iods in t modl t smoot t invntoy oliy. 7 is sould b ig noug to avoid situations o ngativ wags i t as not aivd an invntoy ost dution and as not inasd managial ot. 8 Not tat tis managial ot is not obsvabl and an only b ind om a signal tat an b masud in adinal tms at t imlmntation o som monitoing -s nxt assumtion. is signal is t outut gnatd wi is a standad assumtion in agny toy ilgom and Robts 99. oov w av assumd o simliity tat tis outut is ootional wit a ato K to t ot. lag t ot t mo skilld is t manag in dining a sussul statgy gnating tangibl sults. Not also tat aamt k ontols t lativ wigt o t s omnsation o managial ot in omaison wit invntoy ost dution wi will allow us to ondut som omaativ stati analysis in lat stions. 9 An altnativ inntiv sm to omnsat ovall ot in a iod instad o t dins in ts ots intodus an asymmty wit gad to t oosd sm tat omnsats t dution in invntoy osts. In any as tis altnativ inntiv sm would odu mo onound ositiv ts o managial ots on invntoy ost dution. 5

5 4/ wns only obsv managial ot i ty imlmnt a monitoing intnsity. In atiula w ollow wat is stablisd as standad in t agny toy litatu.g. iamond 99; monitoing intnsity dins t obability o dtting ot ind om t outut tat tis ot gnats. Finally o t sak o simliity w assum tat tis monitoing intnsity is xognously givn wit t sam valu in bot iods. 5/ an imlmnt managial ot wit a ost givn by t untion [] tat satisis ' ' and ''. oov w saat t ost latd to ts ots om tos ots dvotd to oational ativitis. Hn w do not o x-ant t intation btwn oational and managial ots by assuming omlmntaitis/substatibilitis in t ot ost untion. oov t ots dvotd to t dinition o an invntoy oliy a obsvabl s ootnot and an b ixd x-ant in a ontat. is justiis ti xlusion om t maximization ogam solvd by an. 6/ An an b id at t nd o t ist iod i o s as not atd nt valu. In tis as to simliy iing osts a assumd to b zo. us t x-ant obability o an s ontinuation quals t obability o obsving tat an as atd valu. is an b aivd by duing o by inasing managial ot. o is dind as: ob k ob is is t sum o two tms. Fist t obability o knowing ot tims t obability o an inas in t obsvd valu gnatd by t inluding. ond t obability - o not knowing ot tims t obability o an inas in t valu gnatd by t du to t dution in invntoy osts. knows t obability wi mans tat t monitoing intnsity imlmntd by t own is known. W justiy su an assumtion baus t an in om t ssus xtd by t inial in od to dtmin managial ot. im-lin o t odl / simultanously dtmins ist-iod invntoy lvl as wll as istiod ot. o do so o s taks into onsidation is o xtation o utu dmand alizations as wll as t own s monitoing intnsity. / Fist-iod dmand alization is known at t nd o tat iod. ivs t wag and ontinus in t im i noug valu is gnatd. I not t is id and a nw on is id. / dins sond-iod invntoy oliy as wll as sond-iod ot. o do so o s taks into onsidation ist-iod total invntoy osts ist-iod ot as wll as is o xtation o sond-iod dmand alizations. 3/ Last-iod dmand is alizd and t ivs is o aymnts. lak o obsvability o tis ot onoms to t ida tat ty a not oational and tat ty a mbddd in t dinition o t ovall omany statgy. Givn t intangibl natu o ts ots wi is in sa ontast wit t manial natu o t oational ons it is quit natual to assum tat managial statgi ots a not obsvabl witout monitoing was oational ons a. om autos lik Rullo and uaz 4 onsid tat t obability o knowing ot dnds not only on monitoing intnsity but also on ot. W abstat om ts issus givn tat ou ous is not on t intation btwn monitoing ots and statgi ots but on t t o t latt on invntoy managmnt. By allowing to b ndognous would av intodud tnial omlxitis witout giving nw insigts into t onntion btwn ot and invntoy ost dution. 6

6 3/ LVING H L W solv t modl bakwads. us w ist aatiz sond-iod disions. n w mov to t ist iod. ond-iod Poblm At t an dtmins sond-iod invntoy lvl as wll as sondiod managial ot. maximization oblm to solv is t ollowing: ax{ } [ ] [ [ ] w k 3 [ [ ] i i i Wit and i { } i W an only b obsvd wit a obability wi is givn by own s monitoing intnsity. Fist d onditions F o t vious oblm lads to 3 : { w } s 4 { w } ' [ ] ' [ ] 4 W an s tat inass in and/o k lad to inass in sond-iod ot du to. Not also tat ot dnds on ato. it an inas in t inntiv intnsity and/o in t monitoing intnsity an b usd as substitut manisms to stimulat sond-iod ots. In wods o ang and Lai 999 t is a tad-o btwn t wag aot inntiv and t suvision stik inntiv. Fist-iod Poblm At t dtmins ist-iod invntoy and ist-iod ot taking into onsidation t otimal solution ound in t sond iod. oblm t solvs is t ollowing stands o iod-zo xtations: ax{ } [ [ ].t. [ ] and ' [ ] By -aanging tis xssion and nglting onstant tms w an tansom t vious maximization oblm into minimization o t ollowing objtiv untion : in{ } { } [ ] 5 W 4 us k 3 ond od onditions a satisid staigtowadly. 4 xssion o is obtaind using t assumtion mad tat o tm ollows a uniom distibution. 7

7 Fist od onditions lad to s oint in t Andix: k ' 6 { } { } 7 w and solution o tis oblm lads to an quilibium tat dnds on t valu o: Wit and givn in 4 and 4 stivly. Poosition otimal invntoy oliy is dind in tms o givn in 8: a I < k ' w b I in tat as t quilibium is givn by: ' ' k wit Poo oint in t Andix. 4/ IUIN Poosition sows tat quilibium invntoy lvl Ŝ as wll as its assoiatd is aivd in a singl iod wn t imlmnts som managial ots in t ist iod. n t ontay wn o s xiss no ot in t initial iod t stadystat quilibium is not aivd until t sond iod. bviously in t om situation in omaison wit t latt t is no invntoy vaiability btwn iod on and iod two. Also om tis quilibium w obtain tat on t stady-stat invntoy lvl Ŝ is aivd t is a dasti inas o managial ots om to. Rmakably wnv is ig imotant dutions in a quid and t omnsation sm must avo managial ots in od to mak t outom mo likly. A natual way to aiv tis is by aising k t lativ wigt o t managial ot in t omnsation sm. iially xssion 8 sows tat wn t is an imotant dution in ist-iod total invntoy ost ig t is also a signiiant das in t valu wi in tun also dass -by 6 and - ist-iod ot. logi o tis sult is tat a makabl dution o gnats limitd sond-iod gains baus o dutions in a mo diiult to aiv wn is low. A way to ost ts diminisd vnus is by duing ist-iod ot baus tis ons t ossibility o substantial sond-iod gains linkd to managial ot k may b ig wn is low. us inasing ot omnsation wit a ig k avos t ossibility o st invntoy ost dution in t ist iod. is is statd in t ollowing Poosition

8 Poosition omnsation o managial ots allows o signiiant dutions in invntoylatd osts so as to aiv t otimal long-tm invntoy lvl in a sot iod o tim. is gnats in utu iods a dud vaiation in a im s invntoy lvl. Poo Follows ditly om Poosition. is sult may justiy a im s oliy o omoting t managial ol o s. In tat as s ty to du to aiv t otimal lvl in a singl iod and at tat ty ous on inasing managial ots. is dsibs a attn o s bavio tat sould b tstd miially. Intstingly ts ots as w statd in t intodution may b omltly unlatd to invntoy managmnt. In at w a assuming tis to b tu otwis t omnsation sm ivd by s would ly xlusivly on dutions in an amliid total invntoy ost untion as w disuss in t nxt stion. Not also tat by quiing som monitoing o viiation w assum imliitly tat ts managial ots a o a dint natu to tos imlmntd in t dinition o invntoy managmnt ts latt ots do not qui any monitoing. An xaml o ts managial ots altoug to som dg latd wit invntoy managmnt is labo iing. om autos sow tat in as o ig dmand soks vaiability an wit bot sonsibilitis may did to us wok tunov to smoot invntoy vaiability Haltiwang and aini 994. In ou modl ig dmand vaiability ig maks t outom in 9 mo obabl. is lads to t quilibium wit non-null managial ot i.. labo iing ot and smoot invntoy oliy. Poosition also allows dsibing tos snaios wit ig invntoy vaiability in t mdium tm as w din it. is is t din btwn sond-iod invntoy lvl and t ist-iod on. Basially tis analysis lis on t instion o t xssion o wn < 5 wi an b aangd s oint 3 in t andix as: [ ] [ ] us a mo ngativ mans an inas in t din btwn ist-iod invntois and Ŝ sond-iod invntois. is will lad to an inas in invntoy vaiability 6. Also xssion in 9 and allows making a omaativ stati analysis wit gad to stutual aamts lik k. is dins t ollowing Poosition. Poosition 3 Wn t ixd otion o t omnsation is lag tan t vaiabl at ig; and/o t own s monitoing intnsity is lag noug lag; and/o ot inntiv sm is ig noug k ig and/o t initial invntoy osts a not vy ig low t onsquns ollow. Fistly t is a sa dution in invntoy and t stady-stat lvl is aivd in a singl iod. ondly invntoy oliy is quit stabl in t mdium tm and lastly imlmnts managial ots duing t initial iod. 5 as o lads to null invntoy vaiability. 6 o ty to smoot tis vaiability is lvant baus at a maoonomi lvl u to 87% o GP vaian duing sot-tm ssions is linkd wit dasti invntoy dutions Blind and aini 99. 9

9 Poo itly by insting and making us o t sult o Poosition. is oosition dsibs dint manisms tat an lad to a mdium-tm invntoy vaiability tat is low wn an own tis to du invntoy osts. Fistly t dsign o omnsation sm tat ombins a ig ixd at wit lag aymnts o managial ot ig k. ond an intnsiv monitoing ig o managial ots. is lads to som tstabl ditions lik a low invntoy vaiability in tos ims ownd by banks ognizd as sialists in monitoing in omaison wit tos ownd by non-banks ibó 6. is modl also dits tat wnv initial is ig and vntually a nw is id to dal wit tis situation an imlmnts no managial ots and ouss mainly on duing invntoy. n t ot and wn a long-tnu is in ag gnally /s is also involvd in non invntoy-latd ativitis. s s av dvlod t quid skills to ay out ot sonsibilitis not ditly latd to invntois. In tat as ou modl sows tat by iving good inntivs ts s a abl to: du invntoy to a gat xtnt; nsu a onvgn to t stady-stat invntoy lvl in a sot iod o tim; and din a smoot invntoy oliy. is sult is onsistnt wit som miial studis tat oma invntoy vaiability btwn ims wit long-tnu s and tos wit ntly-aointd ons Alao and ibó 3. As a inal ommnt w an intgat in ou analysis atos latd to im s makt stutu as wll as t aatistis o t goods tat a im odus. As a ist aoximation w an onsid tat a ig low valu o may snt mainly omtitiv monoolisti makts wil a ig low valu o may b linkd to isabl nnial goods. iml instion o in 9 vals tat and. us om tis oint o viw t mo omtitiv t makts and/o t mo isabl t goods tadd t mo likly a tos atus linkd to t quilibium: dasti dution in t sot-tm and low invntoy vaiability in t mdium tm. Howv tis sult lis also on t valu o wi dnds not only on t initial onditions o t im but also on t makt stutu and t ty o goods. 5/ XNIN is modl an b xtndd in two ways in od to ino ou onlusions. o n ossibility is to onsid tat as to aiv an objtiv total ost. Fom tat lvl is omnsatd nalizd o any ut dutions inass. o b mo alisti w an assum tat t inial ntnu dos not know xatly wat t otimal lvl to b aomlisd by t sould b asymmti inomation. In tis as a solution o t inial is to udat tis otimal lvl taking as n t dutions in tat as aivd in t vious iod. Fomally: o o o i i δ i i w δ 7. In tis as δ mans tat t dution in t total ost aivd by t is a omlt indiation o wat t objtiv untion sould b in t nxt iod t is a ull inomation udating. n t ontay δ mans tat t objtiv is t sam o bot iods. Intstingly wn t is inomation udating δ t omnsation sm oinids wit tat o t modl. Not tat o as δ. In tis as omnsation is: 7 By nalizing aoiatly inass in t om t objtiv lvl w vnt om baving ootunistially by stting a ig in t vious iod in od to indu t ntnu to ix an aivabl objtiv untion in t snt on.

10 o o wi iδ ii i i i i i i i o siially t xists a tsold valu < δ < su tat o δ δ t quilibium in invntoy and ot lvls is o t ty givn in Poosition and all t analysis mad tougout t a alis. Howv wn δ < δ only t quilibium wit low invntoy vaiability and signiiant dution xists. Intstingly in tis latt situation stong ist-iod dutions do not lud om imlmnting signiiant ist-iod ot as w av ound in ou modl. onvsly lag ist-iod ots do not ind ist-iod dutions tat aatiz t so-alld goodquilibium. In tis as t bniial ts o managial ots a vn gat tan in ou modl as t is lss nd to giv u substantial ist-iod managial ots to aiv a stong ist-iod invntoy dution. In atiula t maginal loss in t omnsation o invntoy ost dution is ootional to δ. Wn δ is low imlmnting ig managial ots as a limitd dtimntal t on t s omnsation o dutions aivd in invntoy osts. Anot xtnsion is to onsid tat managial ots a xlusivly linkd to invntoy managmnt. Fo xaml in t JI aoa t imlmnts ots to ontinuously imov t aamts o t xisting ost untion. In tis as t a dint modling ossibilitis. n t on and w an onsid tat ts managial ots du untion in an additiv way tat is i i i i K. In tis as omnsation basd on duing i t ovall om an objtiv lvl δ tansoms to an quivalnt untion to xssion o t modl: wi i ki i ki i i k i i. Hn t analysis mad tougout t a alis. n t ot and t is an altnativ tat is to intodu ts managial ots in a multiliativ way; o xaml by duing by a ato -. In tis as t manag will imlmnt low managial ots in t ist iod in od to mak t objtiv untion in t sond iod aivabl. n in tis latt iod t will imlmnt su ots to nsu st dution in t and as tm in aodingly. Hn tis dynami is quit simila to tat dsibd in ou modl but in tis as ts managial ots a lss bniial o stimulating dutions. 6/ NLUIN In tis a w sow tat an ations anag wo dvots som ots to din a im s statgy may outom an xlusivly dvotd to invntoy managmnt baus t latt as mo inntiv to bav ootunistially. is is aivd by imlmnting a omnsation sm tat wads invntoy ost dutions as wll as t inas in ot valu-gnating managial ots. Wit su a sm an as inntivs to du signiiantly invntoy osts in t sot-tm altoug tis lows t ossibility to ut invntoy osts in t utu. us an will only av inntivs to mak su dutions i ts utu losss a ost wit ot gains. s may b aivd by wading managial ots adquatly. Aoding to t oosd inntiv sm w onlud t ollowing s bavio. In t ist iod s dvot mo ots to du invntoy osts tan to ti managial sonsibilitis. Howv wn t stady-stat invntoy lvl is ad t managial omonnt o t ots linkd to statgi tasks is mo imotant. us aadoxially by ombining bot tys o ots t is an intns invntoy ost dution

11 in t sot-tm tat divs t im s invntoy lvl to its stady-stat valu. is may not b tu wn an only manags im s invntoy. In tis as o s bavs statgially and avoids sa dutions in invntoy osts in t sot-tm baus tis would ind utu dutions in ts osts. u analysis also igligts dint atus. Fistly in an iintly dsign ontat amwok wn w oma ims wit long-sving s wit tos ntly aointd a smoot mdium-tm invntoy vaiation is xtd in t om in omaison wit t latt. ondly ou modl as som lationsi wit tos modls tat oma ntalizd vsus non-ntalizd invntoy dision-making. An wit managial and oations sonsibilitis oms at o a igly ntalizd dision-making amwok. In tat as ou sult o low invntoy vaiability valu in omaison wit lss ntalizd amwoks oinids wit atsuua and subon 993. idly tos ims wit an involvd in an inasing amount o additional sonsibilitis nd not b onnd about ti lak o ous. aoiat dsign o t omnsation akag basd aadoxially on lvant aymnts o tos non-invntoy latd ativitis ould ovom all ts oblms. is sult is onsistnt wit som ommon atus o bavioal toy: In a ontxt wit inomation asymmtis du to untainty invstmnt vaiability may b dud on w av dsignd an iint omnsation sm tat wigts vaiabls tat a suiintly inomativ in atuing managial bavio non-invntoy latd ots. is is a la mssag tat an b xtatd om tis a: it is ossibl to sa t natual tndny o s to at as statgi manags in a way tat dos not damag a im s invntoy oliy and vn vnt tm om baving ootunistially on invntoy managmnt. u modl as som limitations tat on nw avnus o utu sa. is is a two-iod stati modl tat dos not allow us to analyz t dynamis o t ol witin t im. A dynami modl would on u t ossibility to study issus o latd to a onns. W xt tat in su a modl t would intnaliz ti omotion ossibilitis wi in tun would ovid ut inntivs to xt managial ots. Hn w xt t sults o ou modl to b inod wn dynami ts a inooatd. ustions o inomation asymmtis a also uld out o t sak o simliity. Howv altoug siml ou modl onlusions a obust to dint modling altnativs. Also a st o miial ditions onning ims invntoy vaiability mgs om ou totial sults. W xt low invntoy vaiability in tos ims wit: long-sving s wo ay out ts managial ots; lag ix-at managial omnsation; and iintly monitoing i.. wit banks as saolds. Also om ou modl w ind tat omnsation is basd mainly on invntoy ost dution in t sottm and on managial ots in t mdium-tm. Finally on w inooat som additional qustions o makt miostutu w gt tat in monoolisti makts wit low unitay olding ost invntoy vaiability is sially ig. miially tst ts totial outoms will b t subjt o utu sa.

12 RFRN Alao J. and ibó J. 3. ations manag tunov and invntoy lutuations. Intnational Jounal o Podution onomis 8-8: Amistad.G. and as J. 99. anging ol o suly ain oations manags. Logistis Inomation anagmnt 5 : -7. Blind A.. and aini L.J. 99. aking stok: A itial assssmnt o nt sa on invntois. Jounal o onomi Pstivs 5 : ang J. and Lai aots o stiks? A soial ustom viwoint on wok ot. uoan Jounal o Politial onomis 8 : iamond. W.. onitoing and Rutation: oi btwn Bank Loans and itly Plad bt. Jounal o Politial onomy 99 4: Ntto B. and oal A angs in t odution manag s job: ast snt and utu tnds. Intnational Jounal o ations and Podution anagmnt 9 : Gwin anuatuing lxibility: A statgi stiv. anagmnt in 39 4: Haltiwang J.. and aini L.J Invntois and multi-iod labo ontats: Imliations o businss yl analysis. Invntoy yl and ontay Poliy: Nw Yok: ing-vlag. Hum. H. and Low L. H. 99. tion o t statgi ol o manuatuing amongst oations manags: An miial study basd on a nwly industializd onomy. Intnational Jounal o ations and Podution anagmnt : 5-3. Kan J. 99. Wy is odution mo volatil tan sals? oy and vidn on t stokout-avoidan motiv o invntoy-olding Woking Pa Hoov Institution. ak K.. and Ramaasad A. 3. Knowldg suly ntwok. Jounal o t ational Rsa oity 54 : atsuua H. and subon H A omaison o ntalizd and dntalizd ontol uls in us-ty odution oding systms. uoan Jounal o ational Rsa 7 : 99-. ilgom P. and Robts J. 99. onomis ganization and anagmnt Pnti Hall d. Ni W. and Young A study o oations and makting goal onsnsus in t banking industy. Intnational Jounal o ations & Podution anagmnt 7 8: akland J.. and oal A duation taining and a o odution manags in Bitis industy. Intnational Jounal o ations and Podution anagmnt 9 8: Rullo R. and uaz J. 4. Vntu aital Finan: A uity sign Aoa. Rviw o Finan 8 : ibó J. A. 6. wnsi tutu and Invntoy Poliy. Intnational Jounal o Podution onomis in ss. Wild R ganization sign nology and t Inlun o ations anagmnt. Psonnl Rviw 8 3: 5-5. Wit.. Waton. J. 99. unt anuatuing Aoas: inion and Pati. Podution and Invntoy anagmnt Jounal

13 4 APPNIX / { } [ ] ' A. { } s A. Wit and Aanging t vious xssions w gt in: { } ' ' k k A.3 { } A.4 Wit and / By insting A.3 and A.4 w an distinguis two situations: a I ' k and om wit In tis as t otimal invntoy and ot valus a ' k. W: ' wit Not tat [ ] [ ] ' ' and joint wit < nsus an intio solution o ot s A.3. ond od ondition o A.4 o nsu tat: { } and as us tis is a minimum. oov as Ŝ is a minimum o tn t ondition nsus tat o any. is atu nglts as a minimum. Finally not tat t Hssian is also ositivly dinit as { } { } { } ; k k and b I <. In tis as ' ' wit in A.3 nsus tat { } w a minimizing. oov A.4 sows tat Ŝ annot b otimal as { } <

14 5 wi is t ondition o a maximum. us t solution o { } annot b but satisis tat : 8 us by oosing t oot o t vious olynomial wit Ŝ w an nsu tat { } Fo { } ' wit { } ' k. oov and is a minimum as t Hssian H is ositivly dinit: 9 { } { } { } [ ] k H as is lag noug Assumtion. Not also tat [ ] k H w is minimum o 3/ [ ] I w us t dinition o in 9 and t at tat [ ] w obtain: [ ] [ ] 8 is is a sond-od olynomial wit a al solution wn <. is is t as baus and inass wit o Ŝ. us it will xist a Ŝ su tat 9 assumtion 5 o t ost untion.