PRODUCTION AND INVENTORY CONTROL IN A MULTISTAGE NETWORK

Transcription

1 MITIP6, - Sepembe, Bdape PRDUCTIN AND INVENTRY CNTR IN A MUTISTAGE NETWRK Jean-Clade Henne CNRS, ISA, 6 avene Noe Dame d ac 49 Ange, Fance E-mal: henne@laaf Abac: The dy analye a newok of enepe ha coopeae o manface end podc fom aw maeal The pply chan oganed accodng o he podc ce of he end podc The popoed model h fomally mla o an MRP-ype mlage yem, fo whch effcen conol polce have pevoly been conced The addeed poblem ae o popoe dbed podcon and nvenoy polce fo each manfacng age and o deemne he pefomance of hee polce, compaed wh he globally opmal conol Keywod: Exended Enepe, Manfacng Newok, Spply Chan Inegaon, MRP, Bae-Sock INTRDUCTIN In cona o a mlage yem owned by a ngle podce, a newok of aonomo enepe chaaceed by heeogeney and dbed deconal ce, whch enal he dffcly o effcenly mplemen ono he whole yem, negaed plannng ofwae ch a ERP and APS Newok of enepe ae ypcally chaaceed by poble conflc of nee, andomne and nceany of lead-me and anpoaon delay, conol acon wh lmed mpac Howeve, hey alo have advanage n em of flexbly, placy (eay econfgaon poble) and a qck adapaon o he make, n em of qaly and qany Mlage podcon ofen movae he degn of a pply chan a a val enepe, gaheng n an enepe newok he mo effecve enepe fo each podcon age In a mlage podcon newok, he podc ce dcae he oganaon: podce of pmay podc play he ole of pple, podce of nemedae podc play boh ole of pple and podce, and podce of end podc ae boh podce and eale Spply chan degn hold be opmed no only hogh elecon of he be coalon, negoaon fo ak agnmen and bne conac, b alo hogh oganaon of nfomaon and podc flow Pevo de have popoed an negaed mlage podcon and nvenoy polcy a he m of a feedfowad em, elaed o pedced demand flflmen, and a feedback em, coepondng o mlage a baeock polcy Sch an negaed polcy ha been hown o be opmal wh epec o a pedcve ceon, ob o nceane and dbance and able o gaanee afacon of podcon capacy conan [] The man qeon addeed n h pape "o wha exen he negaed podcon polcy cold be appled o a manfacng newok compoed of aonomo podcon n?" Many de have hown ha local effecvene fa fom aomacally ndcng he global effcency of he whole podcon poce In he mlage cae condeed, he nfomaon avalable a each age manly local, excep fo ome pedcon of demand fo end podc, whch ppoed o be haed among he pane The pape how ha, n pe of he lack of nfomaon a he level of podcon n, poble o bld manfacng polce wh he ame nce popee a he negaed polcy Th el, omewha png and vey neeng n pacce, ake advanage of he neconneced ce of he yem 9

2 MITIP6, - Sepembe, Bdape THE MDE A dynamcal mlage model of a podcon newok The dy conde a plannng model ove a me hoon dvded no wo pa: a ho em hoon wh deemnc demand and a medm em hoon wh ochac demand appoxmaed by a pobablc dbon In h famewok, me geneally dceed n lage bcke whch can be of eqal o neqal daon Sch a me decompoon of he hoon ha been popoed n [], manly o ake no accon wo dffeen nfomaon paen on exenal demand: n he ho-em, ode ae fm and pecely known, and afe he ho-em me hoon, hey ae ncean o andom and can be modelled by pobablc dbon In h dy, an addonal faco of complexy nodced by condeng a podcon newok wh an mpefec anfe of nfomaon along he pply chan End podc manface ae ppoed o decly ell he podc o come They have a pefec knowledge of ho-em demand and know he expeced vale of demand afe he ho-em me hoon Manface of pmay and nemedae podc only know he expeced vale of demand fo end podc They mply eceve ode fom he dec come n he pply chan The manfacng model baed on he mlage ce of podc, nde he ampon of conan lead me clacally ed n MRP-baed appoache Condeed manfacng newok ae ml-age wh conan lead-me θ fo all he podc,n, and wh eoce and oage conan The N podc ae nmbeed n he deceang ode of he level n he mlage podc ce: Tanpoaon delay ae ppoed nclded n lead me ead me ae ppoed ndependen of qane, povded ha capacy conan ae afed A manfacng ode fo podc a peod delveed afe he podcon lead meθ The global yem epeened by a dcee-me lnea mlvaable model wh dbed delay and capacy conan on nvenoe and podcon + [ Dag( ) Π] Fo podc {, N} + d π d wh Dag( ) M, eqaon () decompoe a: M Π π and N π N,, j j () j< Fo {, } n e π N, N, podc an end podc If backode ae allowed, hey can be epeened, clacally, a negave ock Eqaon () hen edce o: M (), +, d nde non negavy conan Fo n e +,,N, podc a componen Eqaon () hen edce o:,, + π nde non negavy conan, I mpoan o j< j j noe ha non negavy of nvenoy vaable fo componen an eenal logcal condon ha deemne feably of a podcon veco p e n denoe he amon of ock p needed o oe one n of podc Fo each of he P oage one, locaed n he dffeen enepe, nvenoy capacy conan ake he fom: In dynamc eqaon, delay ae clacally epeened ng he delay opeao, noed h fo me ee { } h epeen, h : h h By defnon, noaon

3 MITIP6, - Sepembe, Bdape N p n N p e m denoe he amon of eoce needed pe peod o podce one n of podc I ppoed ha he ame amon of eoce eqed dng he lead me Podcon capacy conan hen ake he followng fom: θ N l m, l M fo,r,, (4) Model (), (), (4) decbe he yem evolon ove he whole plannng hoon (wh poble ecalng f he e of he me bcke vae) nly he ampon on demand and ode change fom he ho em o he medm em hoon Eqaon () mple: T ( ) (5) wh max ( ) [ ( θ T Dag ) Π] whch can be decompoed a follow: T ( ) T + T + + (6) θ Tθ De o he ce and delay em of max T (), T ( ) cly ancpave e δ be he maxmal degee n of polynomal max T ( ) ne can we: δ T ( ) Q( ) whee max Q (), whch polynomal n δ Qδ, decompoed a follow: Q( ) Q + Q + (7) Mace, {,δ } Q ae lowe angla wh nonnegave coeffcen The yem delay δ hen coepond o he longe me pah n he podc ce gaph fom aw maeal o end podc If capacy conan (), (4) ae afed by he aonay olon, a nomally he cae f he newok ha been coecly degned, condon (5) may be acheved by: T ( ) ˆ (8) d Eqaon (8) can hen be e-wen: δ Qk + k k Eqaon (9) can be ed n he dbed a well a n he cenaled famewok, povded ha all he podce n he newok know he podc ce and e he ame demand pedcon fo end podc n he ohe hand, naal o ame ha, n a decenaled podcon newok, each afey ock level, comped ndependenly In he cae of aonomo n, eqaon () hold be ed ahe han eqaon () o conc dbed podcon and nvenoy conol polce { }{, }) baed on he nfomaon locally avalable ( A pedcve model fo medm em demand Afe he ho em me hoon, exenal demand fo end podc ( {, n e }) ae decompoed no a pedced componen and a dbance: d d ˆ + e () and e, ha mean vale and andad vaaon σ I amed ha hee no exenal demand fo pmay and nemedae podc: d N fo n e +,,N () (9)

4 MITIP6, - Sepembe, Bdape Demand dbance fo end podc ae known eveal peod n advance by end podce b npedcable fo pmay and nemedae manface: d d k,, ˆ fo { } ˆ,, k De o non negavy of demand eqence ( d, ), dbance on ode fo end podc can be amed bonded fom below I alo ealc o ame hem bonded fom above Then, f an end podc ( {,n e }), ω e ω, wh ω, ω, {, n } (), e If he pobably dbon of e, nfom n ( ω, ) ω, hen mean andad devaon : ω σ In he eqel, demand fo end podc a each peod wll be ppoed nfomly ω, + ω dbed on [,, ] PRDUCTIN AND INVENTRY CNTR PICIES The medm em pedcve conol The popoed podcon conol polce combne he bae ock appoach, o manan conan he nvenoy poon (nvenoy level + ode no ye delveed) n aonay condon, and he MRP appoach o ode componen and manface podc n ageemen wh he expeced demand fo end podc In he medm-em ange, exac demand ae no ppoed known by advance In ode o lm podcon flcaon de o andom demand and he o-called bllwhp effec, manface bae he podcon polcy on acally emaed mean demand ahe han on he acal ode fo componen eceved fom he dec come Sch a polcy combne open-loop wh cloed-loop popee I eglae he yem owad efeence level fo podcon and nvenoy a each age of he pply chan Accodngly, podcon level, ae decompoed no wo pa: + v () whee he go podcon level fo podc a peod, v he nvenoy eplenhmen nde he bae ock polcy, he nomnal afey ock level, ppoed conan ove he condeed me hoon Accodng o he eleced bae-ock polcy fo podc, he ncemenal ock level a peod defned by: y () In aonay condon, ˆ ˆ, + Ung Hadley-Whn' appoxmaon [] of nvenoy level fo each podc,,n, can be clacally choen o a o gaanee ome qaly bond on he ocko pobably: Pob(pplemenal demand dng θ ) ε The no ocko lm pobable can be acheved wh baeock level gven by he clacal newboy fomla (ee eg Refeence[]): h Φ + c ( ε ) wh ε (4) h + b whee Φ () he cmlaed PDF of pplemenal demand fo podc dng lead me θ, c he n podcon co fo podc, h he n holdng co pe me n fo podc, b he n backode co pe me n fo podc Unde nfomly dbed demand dbance fo fnal podc, n e

5 MITIP6, - Sepembe, Bdape q Φ ( q) + a wh a [( I Π) ] Ω θ and: a b h c h + b In he decenaled famewok, each podcon n aocaed o podc ( { ne +, N} ppoed o have nfomaon on local nvenoy and podcon vaable (, k ), and ( ) on demand pedcon fo end podc: ˆ, {,δ } d + k k,,, k ) Addonally, he podcon n eceve ode fom downeam age, ealy enogh o delve podc on me Unde hee ampon, he mlage podcon poce may be coodnaed hogh he choce of mla b locally defned podcon polce ha combne a pedcve pa and a baeock feedback em on he nvenoy poon: Q ( ) + v whee Q () denoe he h ow of Q(), p, +δ v +, (5) and he oal addonal (eplenhmen) ode fo podc a peod comng fom downeam podcon n: N j π v j j The feedback pa of eqaon (5) doe no meely apply he baeock feedback polcy o he nvenoy level,, b ahe o he nvenoy, poon, p, clacally defned a he m of he nvenoy level and pendng ode:, p +,, θ v k k Th expeon, ogehe wh (5), lead o expeon (7) n veco fom: ˆ Q( ) d +δ ( I Π) ( p ) (7) The podcon veco hen afe: wh θ + δ + F( ) + l l l F ( I Π) ; G ( I Π) U Q( ) G v (8) + T ( v ) e,,,n, and he cloed-loop yem can be wen: Conol law (8) he ame a he one popoed n [] fo he negaed famewok I man advanage ae opmaly wh epec o he nfne hoon mean vale ceon, obne by opmal dbance aenaon and conan afacon nde ome bondng condon on dbance And conveely, he negaed pedcve MRP polcy (8) can be mplemened n a dbed manne, a he m of a pedcve em (em Q ( ) + δ ), an ode-baed em ( ), and a baeock nvenoy poon eglaon em: Q ( ) δ + p + () +, Towad a mooh accebly o he age ae The f objecve of he ho em conol polcy o dve he yem o a age ae fom whch he dbed MRP polcy () can be mplemened wh ably and obne In he ho-em anen phae, no exenal demand eved (d()) and coneqenly, he yem flly deemnc The econd conol objecve o mnme he daon of h phae, o ha he yem ge eady o eve he demand a oon a poble n opmal nnng condon Fom (9), he mnmal daon of he anen phae δ degee( T ( )) The yem ppoed o be naled a peod wh all pevo vaable nll: (), () fo (6) (9)

6 MITIP6, - Sepembe, Bdape Amng ha capacy conan allow he yem o each nomnal egme n he mnmal nmbe of peod,δ, he age ae can be chaaceed by d, {,δ } and fo >δ Addonally, bae ock hold be bl fo all he podc, o oban δ + δ The j-nme mnmal me ajecoy can be mplemened: n a dbed way n he fom: δ Qδ ( ) + Q + k d ˆ δ δ + k k fo,,δ () The f em n expeon () coepond o he bldng of nal nvenoe The aocaed podcon of componen may be ancpaed fo moohng podcon 4 AN EXAMPE The example aken fom Refeence [] The ac valaon n he gono gaph of Fg coepond o he bll of maeal Podc 5 podced by pple Podc and 4 podced by pple 5 4 Podc and podced by podce Aveage demand ae d e Aveage demand ae d d The np-op max Fge A 5-podc mlage example T ( ) and h T ( ) h example, he mnmal daon of he anen phae δ 5 Tanen ajecoe ae comped fom expeon (), ng he moohng mechanm, and eady ae ajecoe fo podcon and nvenoy vaable ae comped by expeon () Smlaon how no gnfcan devaon fom he yem behavo n he negaed famewok 5 CNCUSINS Tadonal podcon yem wee geneally oganed nde he lgh of Compe Inegaed Manfacng, amng a fll coodnaon and global opmaon of he yem Nowaday, he new pevalng paadgm ae Spply Chan Managemen and Enepe Newok, focng on oganaonal adapably and local deconal aonomy Sch dbed ce ae ceanly moe ealc and manageable, b hey ofen nvolve he mpobly o mplemen he globally opmal managemen polce Th dy ha hown ha fo mlage yem nde ome mld ampon, ome local podcon and nvenoy polce may pefom a well a he opmal negaed polcy Th el, omewha png, ae he e of deemnng he mnmal nfomaon neceay o locally mplemen a globally comped polcy 6 REFERENCES [] Hadley, G, Whn, T, 96 Analy of Invenoy Syem Pence-Hall, Englewood Clff, NJ [] Henne J-C, A bmodal cheme fo ml-age podcon and nvenoy conol, Aomaca (9),, pp [] Poe, E, 99 Sochac nvenoy heoy, Handbook n peaon Reeach and Managemen Scence, vol Sochac Model Noh-Holland, Amedam In 4