Cost Characterizations of Supply Chain Delivery Performance

Transcription

1 Co Chaazaon o Supply Chan Dly oman Ald L. Guda and Rakh Nag* Dpamn o Indual Engnng 34 Bll Hall Uny a Bualo (SUNY) Bualo Nw Yok 460 USA Aa Th pap add ag o mpong dly poman n a al upply han whn dly poman aluad wh p o a dly wndow. Conmpoay managmn ho adoa h duon o aan a a ky p n mpong h oall poman o a ym. odl a dlopd ha nopoa h aaly ound n h nddual ag o h upply han no a nanal mau ha a a nhmak o juyng h apal nmn qud o mpo dly poman whn h upply han o m a agd goal. Ky Wod: Impong Dly oman Juyng Vaan Rduon ap Rd Januay 004 Rd Oo 004 Apd Januay 005 *Copondng Auho: E-mal: [email protected] hon: x. 03 Fax:

2 . Inoduon Co Chaazaon o Supply Chan Dly oman In h pa h dad h laonhp wn uom manuau and uppl ha undgon numou paadgma hang. odn manuaung paadgm uh a h Ju-In-Tm (JIT) phloophy Toal Qualy anagmn (TQ) and agl manuaung adoa h lmnaon o non-alu addng a n poumn poduon and duon. Th pog appoah poud y h paadgm o w nddual aon a pa o an ngad o un unon ha pan ao h n upply han. Th goal o upply han managmn a o du unany and k n h upply han hy poly ang nnoy ll yl m po and ulmaly nd-uom ll (Cha al. 998). E upply han admnaon qu a poa managmn yl oud on long-m onnuou mpomn o h upply han. oman mau ha aualy l upply han opaon a qud o uppo onnuou mpomn whn a upply han. Dong o qu h adopon o poman m ha aualy mau h upply han a a whol and ha ou on maung poman n m o o and unany. Sal ah ha xpd onn gadng lmaon n upply han poman m ( o xampl Gunakaan al. 004). Th onn a h-old. F poman mau a no o ad. Ellam (00) dnd h lak o lan poman mau a a ky a o uul o managmn n h upply han. Th w alo had y Lanon (000) who o ha a h mpoan o upply han managmn gow om n mo mpa o m o mau h o poman o h upply han ym. Lalond and ohln (996) dnd a al nd n upply han managmn o lnkng poman maumn wh o. ang manag n un would ag ha o analy mpoan n h managmn plannng and onol o h oganzaon. Bau h m o o aly undood and ounly wlomd y managmn o-ad poman mau a aa o u n upply han managmn. Co-ad poman mau a ompal ao aou po and ag o h upply han. Coad mau alo pod d npu no h apal udgng po ud o juy nmn n upply han mpomn na. In a a udy o m Ellam (00) ound: ) o onoun a way o l n h oganzaon udd and ) h phloophy wa l and xpnd y all mm o h opoaon om h haman o h oad o h admna a n o h wok on h manuaung loo. Ballou al. (000) h aly o dn and mau o among hannl mm a h p o analyz h upply han o o-ang oppoun.

3 Sond poman mau on gno aaly. Vaaly nhn n naly all manuaung and duon ym. anagng unany on o h mo mpoan and hallngng polm o upply han managmn (Blakhu al. 004; Sa and Bamon 000). Johnon and Da (998) xpd onn ha un upply han poman m mau au ha uomaly gno h o aaly. Th duon o aan a al ap o a mhodology dgnd o mpo ym poman (Johnon and Da 998; Da 993). Laly h adopon o poman m ha aualy mau h upply han a a whol and ha ou on maung poman n m o o and unany mu ngad no han-wd onnuou mpomn a. Walk and Al (999) no ha upply han poman mau onnu o ly dnd n m ha no only opmz loal opaon u alo wad h nddual poman o han mm. Van Hok (998) onlud ha un poman mau a dgnd o ngl mm whn h upply han and do no ah ao han mm. Coop al. (997) dny ha hoomng n poman maumn lm mpomn poj wn upply han mm. Tho h poman mau ud mu omulad o a ngang ool o ong long m onnuou mpomn wn and whn h aou ag o h upply han. Ap o upply han opaon ha a no maud n undandal poman m uh a o wll laly hnd oopaon wn h aou oalon ound whn h upply han uu. oman analy ha ad on o no an nd n l. Whn ud n omnaon wh non-o ad mau uh a ho ound n h aland o ad mhodology o-ad mau dgnd o mau po lnkng aou ag o h upply han wll po an poman mau o long m mpomn n upply han opaon. Co-ad analy hould wd a an ongong na nopoad no a amwok ha onn unonal aa and oganzaon whn h upply han no a wad ym o n-ndng mpomn. In h ah w onna on on ap o oall upply han poman dly mln o h nal uom n a al upply han ha opang und a nalzd managmn uu. Th oj o h pap a a ollow: ) dlop a o-ad poman m o analyzng dly poman whn a upply han and ) dlop a amwok o ngang dly auay and laly no h onnuou mpomn o upply han opaon. In ayng h ah oj a o-ad poman m o aluang dly poman and laly wll dlopd. Dly lad m dnd o h lapd m om h p o an od y h uppl o h p o h podu odd y h uom. Dly lad m ompod o a o nnal (manuaung and pong) lad m and xnal (duon and anpoaon)

4 lad m ound a aou ag o h upply han. Vaaly n h nnal and xnal omponn o dly lad m modld a ah ag o h upply han and h ulan lad m dly duon o h nal uom dnd. Th dly poman mau dgnd n h ah nopoa h unany no a o-ad poman mau. Dly whn h upply han analyzd wh gad o h uom paon o dly mln a dnd y an on-m dly wndow. To ulll h ond ah oj a mhodology dlopd ha ju h al nd o oganzaon o n apal no h mpomn o dly poman. Th o-ad dly poman mau dlopd hn ngad no a amwok ha dmona h nanal n o dung aaly n dly poman whn h onx o a onnuou mpomn pogam. Th pap oganzd a ollow. In Son an analyal modl ad on h xpd o aoad wh unmly dly dlopd. In Son 3 popoon a nodud o analyz h dly modl n m o ky uual omponn. In Son 4 Lapla anomaon a ud o nopoa h m alu o mony no h modl amwok o pod a mnmum ound n h amoun o nmn qud o mpo dly poman.. odlng Dly oman In oday omp un nonmn uom qu dpndal on-m dly om h uppl. In h ho m dly daon h aln and lan om h agd dly da - mu analyzd a oh aly and la dl a dup o upply han. Ealy and la dl nodu wa n h om o x o no h upply han; aly dl onu o x nnoy holdng o whl la dl may onu o poduon oppag o and lo o goodwll. I omng mo ommon o uom o pnalz h uppl o aly a wll a la dl (Shndman 996). Bu (989) no ha duon n aly dl dud nnoy holdng o a Hwl-akad y $9 mllon. In h auomo nduy Saun l n o $500 p mnu agan uppl who au poduon ln oppag (Fam 99). Chyl n uppl $3000 p hou whn an od la (Rull and Taylo 998). Whn dly mad on m how h o nud y h uppl a ondd o nomal o and no pnaly o nud. Gou (996) omula an analyal modl whn onaual nn a ud o nhan on m dl. To po agan unmly dl upply han manag on nla nnoy and poduon low m u. Cong unmly dl n h ahon pn a a managmn yl ha may nodu addonal ou o aan no h upply han and uh onu o h o h ullwhp. In h long un dly poman an mpoan omponn n h oall onnuou mpomn o upply han opaon. 3

5 Rn mpal ah ha dnd dly poman a a ky managmn onn among upply han paon (Lokamy and Comak 004; Vahon and Klan 00; Vma and ullman 998). Gunakaan al. (00) pnd a onpual amwok o dnng dly poman n upply han managmn. Whn h uu dly poman lad a a ag ll upply han poman mau. Dly laly wd a a aal ll upply han poman mau. Th amwok adoa ha o upply han managmn ool dly poman and dly laly nd o maud n nanal (a wll a non-nanal) m. Lokamy and Spn (998) and onzka and ogan (994) no ha aluaon modl al o add dly poman o mau n laon o onnuou mpomn o whn upply han. Hada (996) dnd ha whn o aoad wh md dl a no akn no aoun mo nanally aa o a manuau o hold mo nnoy n. An analy o 50 uppl aluaon modl ound n h opn lau y Guda (999) dnd a alu o h modl o: ) add aly and la dl paaly ) quany dly poman n nanal m and 3) uppo uppl dlopmn and onnuou mpomn pogam dgnd o mpo dly poman. Th naly o anla dly poman no nanal m hnd managmn aly o juy apal nmn o onnuou mpomn pogam whh a dgnd o mpo dly poman. Falu o quany uppl dly poman n nanal m pn oh hom and long-m dul. In h ho m h uy-uppl laonhp may ngaly mpad. Aodng o Nw and Swny (984) a nom alu o pumd poman alhd y daul whn dly poman no omally maud. Th nom ay onan wh m and gnally hgh han h oganzaon aual poman. Ca and aon (999) dmona ha uppl aluaon ym ha a po mpa on h uy-uppl laonhp; uyuppl laonhp ulmaly ha a po mpa on nanal poman. In h long m alu o mau uppl dly poman n nanal m may mpd h apal udgng po whh nay n od o uppo h mpomn o uppl opaon whn a upply han.. Dly Wndow A dly wndow dnd a h dn wn h al apal dly da and h la apal dly da. Whn an od plad h uom ypally gn a xd pom da. Und h onp o dly wndow h uom uppl an al allowal dly da and a la allowal dly da. Sal ah adoa h u o dly wndow n upply han managmn and m-ad manuaung ym ( o xampl Jauphonga al. 004; L al. 00; Faw and Bou 993; Co 99). Johnon and Da (998) no ha m ad on dly (od) wndow apu h mo mpoan ap o h 4

6 dly po: laly. Thy agu ha modlng dly laly.g. aaly h ky o mpong h dly po. Whn h dly wndow a dly may lad a aly on-m o la. Fgu llua a dly wndow o nomally dud dly. Dly lad m X a andom aal wh poaly dny unon X ( x). Th on-m poon o h dly wndow dnd y. Idally 0. How h xn o whh > 0 may maud n hou day o wk dpndng on h ndual uaon.. odl Dlopmn <In Fg. aou h> Cond a upply han n opaon o a m hozon o lngh T ya wh a dmand qumn o a ngl podu o D un wll m wh a onan dly lo z Q. A ngl uppl pod a uy wh h dly o a mak-o-od podu. L X pn h dly m o Q; h lapd m om h p o an od y h uppl o h p o h dly lo z y h uy. Hn h dly m on o h nnal manuaung lad-m() o h uppl plu h xnal lad m aoad wh anpong h lo z om uppl o uy. Fo a wo-ag upply han h xpd pnaly o p pod o unmly dly Y Y QH a ( x) X ( x) dx K ( x ) ( x)dx wh Q onan dly lo z H uppl nnoy holdng o p un p un m K pnaly o p m un la (ld y h uy). a paam dnng h dly wndow dly lad m omponn a ag W ( x) dny unon o dly m X. X W W Th nddual lad m omponn a ah ag o h upply han a modld ung h nomal duon and ndpndn wn ag aumd. Nomaly and ndpndn among ag on aumd n h lau ( o xampl Elah and Sngh 999; Tywoh and O Nll 997). I uh aumd ha dly poman al nough o ha h modal dly m whn h onm poon o h dly wndow. Fo uaon nang h nd o una h nomal dny o pn nonnga dly m o l oh dny unon dnd o only po alu o h dly m Guda (999). X () 5

7 Th pnaly o K an oppouny o du o lo poduon. Don al. (99) pod ha puhang manag w h poduon dupon aud y dly okou o mo wdpad and mo oly han h lo al ha okou au. Hn K ha n dnd a an oppouny o du o lo poduon a dd y Fam (99) and Rull and Taylo (998). Smplyng () and nodung ( ) and ( ) Φ a h andad nomal dny and umula duon unon ply yld h oal xpd pnaly o o nomally dud dly m Y QH ( ) Φ K ( ) Φ. () 3. Sag o Impong Dly oman Th a h p ap o h xpd pnaly o modl ha managmn an u o dmn h ponal o mpomn n dly poman. opoon wll pnd o pod an analyal analy o h xpd pnaly o modl a a unon o: ) h wdh o h on-m poon o h dly wndow ) h man o h dly m duon and 3) h aan o h dly m duon. Th nx on xamn h dynam o h h appoah on h xpd pnaly o modl whn h dly duon nomally dud. 3. Th Dly Wndow Rdung aly and la dl a dal mpomn goal. Th oj only ahal whn managmn ha no only dnd h au() o unmly dly u alo ha akn uqun aon o mo h au o unmly dly om h upply han. On y managmn d h on-m poon o h dly wndow dud n od o ndu mo mly dly. opoon dmona h ponal polm aoad wh dung h on-m poon o h dly wndow whn no aon akn o al h man and aan o h dly duon. opoon. Fo a xd man and aan dung h on-m poon o h dly wndow na h xpd pnaly o. oo. Wh no lo o gnaly l h on-m poon o h dly wndow dnd uh ha. Rdnng () and dnang wh p o g ( QH K ) Φ Y. (3) 6

8 Y o all 0. Hn o a onan man and aan aaly dung h wdh o h on-m poon o dly wndow wll ul n an na n h xpd pnaly o. Examnng (3) < 0 Fo a onan man and aan h pnag na n h xpd pnaly o o dung h wdh o h on-m poon o h dly wndow y α pn Y Ψ ({ α} ) Y ( ) Y ( ) 00. Rmak. Fo 0 < α < h maxmum na n h xpd pnaly o o dung h wdh o h on-m poon o h dly wndow oundd y Ψ max ( x ) xp < xr R x w h x and ll Rao. x (4) (5) 3. an o h Dly Duon Th on wll ouln an analy o h xpd pnaly o wh p o h man o h dly duon whn h dly wndow and aaly o dly a hld onan. opoon. Fo a xd dly wndow and onan aan dung h man o h dly duon wll da h oal xpd pnaly o whn Y > Y aly. la oo. Th da o h xpd aln and xpd lan omponn o h xpd pnaly o wh p o h man a ply Y aly ( ) QH Φ and Y la ( ) K Φ. (6) Dang h man o h dly duon lad o a da n h oal xpd pnaly o whn Y <. Th ondon ahal only whn Y > Y ( ). 0 aly la Rmak. Fo a xd dly wndow and onan aan dung h man o h dly duon wll na h oal xpd pnaly o whn Y < Y aly. la 7

9 oo. Dang h man o h dly duon lad o an na n h oal Y >. Th ondon ahal only whn xpd pnaly o whn 0 Y < Y ( ). aly la 3.3 Vaan o h Dly Duon Th on wll nga h o aaly on h xpd pnaly o whn man o h dly duon and h dly wndow a hld xd. opoon 3. Th oal xpd pnaly o a monoonally nang non-onx unon o h aan o nomally dud dly. oo. Th and ond da o Y wh p o h aan a and Y () QH K (7) QH Y 5 / 4 ( ). (8) () ( ) ( ) 4 K Examnng (7) h oal xpd pnaly o an nang unon o h aan n Y () > 0 o po alu o Q H K and. Th oal xpd pnaly o no a onx unon o h aan n h gn o no ha Y () > 0 whn mn ( ) ( ) u Y < 0 whn {( ) ( ) } max. 5 / { } Y hang. Examnng (8) w { } Rmak. Th xpd pnaly o qual zo whn mn ( ) ( ) { } oo. Whn mn ( ) ( ) Smlaly Φ( 4) Φ( 4) D uuon o h alu o h odna and umula duon unon no () yld Y o and ( 4 ) Rmak. Th xpd pnaly o a monoonally nang onx unon o h aan podd < mn{ ( ) }. () 0 oo. Examnng (8) Y > whn < < { } 0 mn ( ) ( ). 8

10 3.4 Jon Opmzaon o h Expd naly Co Bad on h an and Vaan o ly l a aly o wll dnod y up. h Han D Fo noaona da o h xpd pn H max o Y T dnd a K QH K QH H K QH K QH 5 / 5 / 4 4. Th H o dn o ay h onxy u Claly an mu p ondon o a mnm m. > 0 Y H how h omp nau o lad Y Y Y H plud a d analy o dmn 0. Th onx ly > H y ana an mpld y nodung and analyzng Y. a onx unon o h wdh o h dly wndow and h aan o dly whn opoon 4. Th xpd pnaly o QHK QH K >. oo. Whn h on-m poon o h dly wndow ymm h Han H { } K QH QH K QH K K QH 5 / 3 / 3 / / 4. (9) Th pnpl mno laly po. Th ond pnpl mno po podd QHK K QH >. (0) L K QH η hn (0) η η >. Th onan lluad o ld alu o η n Fgu. <In Fg. aou h> 9

11 Rmak. Y ( ) mnmzd whn. Y mu ay h od oo. Th opmal ondon Whn pa ha mnmz Φ ( QH K ) ( QH K ) 0 and () 0. () / ( ) 0 and Φ ( ). 0 onxy qumn o mnmzng Y and h od ondon and a ad. Th ul uppo nu judgmn. Fo a xd ll o h aan a h wdh o h on-m dly wndow na. Wdnng h ymm dly wndow o a xd aan lad o low xpd pnaly o du o unmly dly. Conly o a xd on-m dly wndow a h aan appoah zo. Dang h aan whn h dly wndow xd wll alo du xpd pnaly o. 3.5 A Summay o Dly Impomn Sag Fgu 3 ummaz h pu managmn opon o dung h o o unmly dly. In addon al mxd ag a alo dnal ad on omnaon o h h pu ag. <In Fg. 3 aou h> A hown n popoon dung h on-m poon o h dly wndow whou alng h man and/o aan o h dly duon no a o al agy. Inang h wdh o h on-m dly wndow wll low h xpd pnaly o; how h a lad o a dad onol o h dly po a ul ha any ompany uly o dad wh. A lluad y popoon hng h man o h dly duon hang h magnud o oh h aln a wll a h lan o omponn whh ha nly o a man h. Dang h man wll na xpd aln o and da xpd lan o; nang h man wll da xpd aln o and na xpd lan o. Th n laonhp wn h don o h man h and h ulan on h magnud o h aln and lan o omponn would nd o mak a pu man h agy dul o mplmn. 0

12 A ndad n popoon 4 h xpd pnaly o und an ondon a onx unon o oh h wdh o h on-m dly wndow and aan o h dly po. nmzng h xpd pnaly o dpndn on h ao o h wdh o h dly wndow and h aan. Th ao o h wdh o h on-m dly wndow o h andad daon o dly an n aually qual po nny. Th ugg ha a qunal (a oppod o a mulanou) agy nolng jon duon o h dly wndow and aan may uul. 4. odlng Impomn n Dly oman Idally h xpd pnaly o o unmly dly Y hould qual o zo. Th mpl ha o h unly dnd dly wndow all dl a whn h pd dly wndow and ha wa n h om o aly and la dl ha n lmnad om h ym. Inang mpomn n upply han dly poman qu apal nmn. Th xpd pnaly o modl dlopd hn wll pod a uul ool o ang h nanal nmn qud o mpo dly poman. Y o m hozon T pod an ma n un dolla o o nud du o unmly dl. Th pn woh ma pod a nhmak om whh managmn an juy h apal nmn qud o mpo dly poman. Th pn woh o an nmn n a Th pn woh o h o am pogam o mpo dly poman hould no xd h pn woh o Y. L Ω pn h onanng h paam n h xpd pnaly o modl ha a hangd y managmn n an mpomn pogam o du unmly dly. odl paam no nludd n Ω a aumd xd. Th xpd pnaly o modl und h mpomn pogam dnd y Y ( Ω ). Fo any p modl paamω Ω mpomn o m aumd o ak a unonal om wh ( ω ) < 0 and ( ω ) > 0. Th om mpl ha whn mpomn n dly mln a mplmnd h paam wll da a a dmnhng a. Th unonal om ha nu appal n gnally om had o gan addonal nmnal po mpomn on uh nhanmn ha alady n mad. Th om ha n wdly adopd n al po mpomn ud ( o xampl Tuno and Su 000; Cho 994; Ghak and ala 99). 4. Dly Vaan Rduon In h on h xpd pnaly o modld a a dang m-dpndn unon o h dly aan Ω { }. Hypol and xponnal om a ud o pn a dang m-dpndn dly aan. Th umula m pod wh h xpd pnaly o qual zo und ah aan om alo dnd. Th ul pnd n h on a dd n Appndx A.

13 Hypol Dly Vaan Rduon Hypol duon n h aan o dly dnd a ( ) wh h paam pn h ll o aan n h dly duon po o h adopon o an mpomn pogam o du dly aan. Th xpd pnaly o und hypol aan duon π ( ) QH xp( k ) ( ) Φ( z ) Y π ( k ) ( )( Φ( z )) K xp (3) wh: k ( ) and z () ( ) o. Th umula m pod whn h xpd pnaly o qual zo an ound y ng and olng o. Lτ mn. Fo hypol 0 { } 4 aan duon. τ Exponnal Dly Vaan Rduon Exponnal duon n h aan o dly dnd a ( ) wh h paam and pn h ll o aan n h dly duon po o h adopon o an mpomn pogam o du dly aan and h aan day a ply. Th xpd pnaly o und xponnal aan duon Y ( ) QH xp( ( k ) ( ) Φ z π K xp π ( ( k ) ( ) Φ z ( ) (4) wh: k ( ) and z () ( ) o. Und xponnal aan duon h umula m pod whn h xpd τ pnaly o qual zo ln. 4

14 4. Dly Wndow Rduon In h on h xpd pnaly o modld a a dang unon o h wdh o h on-m poon o h dly wndow Ω { } o. Hypol and xponnal om a ud o pn a dang on-m dly wndow a a unon o m. Th ul pnd n h on a dd n Appndx B. Hypol Dly Wndow Rduon Hypol duon n h wdh o h on-m poon o h dly wndow dnd a ( ) o. Th xpd pnaly o und hypol dly wndow duon Y QH xp Φ (5) π K xp π Φ. Exponnal Dly Wndow Rduon Exponnal duon n h wdh o h on-m poon o h dly wndow dnd o day a a ( ) ( ) o. Th xpd pnaly o und hypol dly wndow duon Y (6) π K xp Φ. π ( ) QH xp ( ) Φ 4.3 Jon Rduon n Vaan and Dly Wndow In h on hypol and xponnal modl a pnd o jon duon o h aan o dly and h wdh o h on-m poon o h dly wndow Ω } o. { Jon Hypol Vaan and Dly Wndow Rduon An xpon o jon hypol duon n h dly aan and h wdh o h on-m poon o h dly wndow ound y uung h hypol om no 3

15 (A-) and (A-3). Th xpd pnaly o o jon hypol duon n dly aan and wdh o h on-m poon o h dly wndow Y Φ (7) π ( ) QH xp K xp Φ π. Jon Exponnal Vaan and Dly Wndow Rduon An xpon o jon xponnal duon n h dly aan and h wdh o h on-m poon o h dly wndow ound y uung h xponnal om no (A-4) and (A-5). Th xpd pnaly o o jon xponnal duon n dly aan and wdh o h on-m poon o h dly wndow Y ( ) ( ) ( / ) QH xp ( ) Φ (8) π K ( ) xp π ( ) Φ ( / ) wh: day a o aan day a o on-m wndow and o. 4.5 Fnanally Juyng Inmn o Dly Impomn () Th pn woh o Y pod managmn wh a nhmak o juyng apal nmn o mpong upply han dly poman. Und onnuou ompoundng h pn woh o h onnuou o low Y an aluad ung Lapla anomaon (Guöm 967; Buk and Hll 975). Th Lapla anomaon map h o low unon ha onnuou n h m doman o a pn woh unon onnuou n h n a () doman. Th Lapla anomaon o h xpd pnaly o o a onnuou mpomn pogam dnd o a n m hozon 0 T [ ( Ω ) ] Y ( Ω ) d L Y T 0. (9) An analy o h pn woh o Y ung (9) pnd o h a o mdpndn duon n dly aan Ω { }. Expon o L [ Y( ) ] und 4

16 hypol and xponnal om o m-dpndn aan duon a dd n Appndx C. 5. Conluon Th pap addd on ap o upply han plannng y modlng dly poman ung a o-ad mau. A modl ha n pnd ha nanally alua h o unmly dly. Th modl pod a amwok o modlng h onnuou mpomn o dly poman wh a al upply han. Th modl nopoa h m alu o mony no h aluaon po and pod a man o juyng h ou qud o nng n a onnuou mpomn pogam o uppl dly poman. Th modl ha n dmonad und hypol and xponnal unon o dly aan. Oh a an xplod n a mla mann. Th a al ap o h ah ha ould xpandd. An opmzaon modl ould ud o dmn and alloa aan duon houghou h omponn ag o h upply han uj o an nmn onan. Sond oh podu and non-podu dny unon ould ud o modl h nddual omponn m o h aou ag n h upply han. Laly h aumpon o ndpndn among h ag ould ngad. 5

17 Appndx A. Hypol and Exponnal Rduon o Dly Vaan. Th xpd pnaly o an xpd a a m-dpndn unon o h aan a Φ QH Y Φ K. (A-) Und a hypol duon o dly aan. Suung h hypol om no (A-) and mplyng yld (3). Two ky p o h daon a: Tm (o ): xp π (A-) and Tm (o ): { } Φ Φ dx x. (A-3) Und xponnal duon o dly aan. Suung h xponnal om no (A-) and mplyng yld (4). Two ky p o h daon a: Tm (o ): { } xp π (A-4) and Tm (o ): Φ Φ dx x. (A-5) Appndx B. Hypol and Exponnal Vaan Dly Wndow Rduon. Th xpd pnaly o und m-dpndn duon o h on-m poon o h dly wndow { } Φ QH Y 6

18 K ( ) ( ) { ( ) } Φ (B-) wh: o. Suung h hypol om ( ) o no (B-) and mplyng no (B-) yld (5). Smlaly uung h xponnal om and mplyng yld (6). Appndx C. n Woh Expon o Tm-Dpndn Dly Vaan Rduon. Hypol Vaan Rduon Th pn woh o Y ( ) o h plannng hozon angng om 0 o T und hypol aan duon [ ( k k ) ] QH Φ( z () ) K ( Φ( z () )) d L Y T π π o (C-) wh: k ( ) and z () ( ) o. Th a wo ky m n (C-) whh lad o h aluaon o [ Y( ) ] ) h Lapla anomaon ak h om L. Fo m (o L T k k d π π π o T 0 ( k ) d. (C-) Ealuang h ngal dnd n (C-) yld Gadhyn and Ryzhk : p.37). π k [ γ ( { T ( k ) })] ( ) ( 7

19 Fo m (o ) h Lapla anom ak h om Lapla dny T ( z () ) d Φ. Th 0 Φ x o x > 0 ud o alua m. To uppo h L[ ] L[ ( x) ] nonnga on o h dny l Whn L Φ z z ( z ) ( u) du ( u)du z > 0 h Lapla dny an appld dly. Th yld T 0 [ Φ( z () )] d L[ ( z )] T T z d xp π 0 0 T d xp π 0 d T 0 ( { k } ) d xp π k ( { k } ) 0.. (C-3) Whn z < 0 and h nonnga on n h Lapla dny an manand du o h ymmy dnd y Φ ( z ) Φ( z ). Th ul dnal o ha o (C-3) wh ud n pla o k. k Ung h ky p oulnd ao h pn woh o h xpd pnaly o und hypol dly aan duon [ ( ) ] L Y QH π k { γ ( ( ))} ( ) T k ( ) T T π k ( k ) K T T { ( )} γ T k π k π k ( k ). (C-4) Exponnal Vaan Rduon Th pn woh o Y ( ) o h plannng hozon angng om 0 o T und xponnal aan duon 8

20 T 0 π Φ z () [ ( ) ] QH xp ( k ) L Y K ( ) xp π ( k Φ z () ( ) d wh: k and z () ( ) o. Th a wo ky m n (C-5) whh lad o h aluaon o L [ Y( ) ]. Fo m (o ) h Lapla anomaon ak h om (C-5) L xp π π o T ( ( k ) xp ( k ) ( d π T 0 d k wh. To alua (C-6) l u hn Und h uuon (C-6) an wn a T 3 u L[] u du π du d and u u. (C-6) 3 u u du u π 3 u du. (C-7) Ealuang h ngal dnd n (C-7) yld L[] Γ Γ π T (C-8) ( Gadhyn and Ryzhk :3 p.37). Th uu o h ond m n (C-5) mla o m o h hypol a and ollow dly om h p oulnd n (C-3) ha o 9

21 () [ ] [ ] 0 T z L d z L Φ T d 0 xp π. (C-9) Th ngal n (C-9) an aluang ung h uuon dnd n h aluaon o (C-6). Th yld [] Γ Γ T T L π. (C-0) Ung h ky p oulnd ao h pn woh o h xpd pnaly o und xponnal dly aan duon [ ] Γ Γ T QH Y L π Γ Γ T T π Γ Γ T K π Γ Γ T T π. (C-) 0

22 Rn Ballou R. H. Gl S.. ukhj A Nw managal hallng om upply han oppoun. Indual akng anagmn Blakhu J. Wu T. O Gady Nwok-ad appoah o modlng unany n a upply han. Innaonal Jounal o oduon Rah 4(8) Buk J. R. Hll T. W Addon o h Lapla anom mhodology o onom analy. Th Engnng Eonom 0(3) Bu D. N anagng uppl up o pd. Haad Bun Rw July- Augu Cha R. B. Aqulano N. J. Jao F. R oduon opaon managmn manuaung and 8 h Edon Iwn/Gaw Hll Boon. Ca A. aon J Sagally managd uy-uppl laonhp and poman ouom. Jounal o Opaon anagmn 7(5) Cho J-W Inmn n h duon o unan n ju-n-m puhang ym. Naal Rah Log Coop. C. Lam D.. agh J. D Supply han managmn: mo han a nw nam o log Innaonal Jounal o Log anagmn 8() -4. Co L Dly wndow a nw way on mpong manuaung lxly and on-m dly poman. oduon and Innoy anagmn 33(3) Da T E upply han managmn. Sloan anagmn Rw 38() Don.. A. Hay L.. Don. C. Lundkn J. 99. Conqun o nnoy okou. Indual akng anagmn 0() 3-7. Ellam L Sag o managmn n h upply han: a puhang and upply managmn pp. CAS Rah. Elah S. J. Sngh. R Opmal aan uu and poman mpomn o ynhonou amly ln. Opaon Rah 47(4)

23 Faw S. E. Bou L Ju-n-m oung hnqu: un a o adopon and poman n. oduon and Innoy anagmn Jounal 34() 8-4. Fam. 99. Saun o n uppl $500/mnu o dlay. Auomo Nw Dm 36. Ghak Y. ala. 99. Inng n dung lad-m andomn n onnuou w nnoy modl. Engnng Co and oduon Eonom () Guda A. L A o-ad modl o aluang ndo dly poman. S h Dpamn o Indual Engnng Sa Uny o Nw Yok a Bualo. Gunakaan A. C. al C. Gaughy R. E A amwok o upply han poman maumn. Innaonal Jounal o oduon Eonom 87(3) Gunakaan A. C. al C. Toglu E. 00. oman mau and m n a upply han nonmn. Innaonal Jounal o Opaon and oduon anagmn (/) Gadhyn I. S. Ryzhk. I Tal o ngal and podu. Aadm Nw Yok. Gou J. R A modl o nn ona o ju-n-m dly. Euopan Jounal o Opaonal Rah Guöm R. W On h applaon o h Lapla anom o an onom polm. anagmn Sn 3(7) Hada K. C Why do w m dly da? Indual anagmn 38(5) -4. Jauphonga W. Cnnkaya S. L C-H Wahou pa apay and dly m wndow ondaon n dynam lo-zng o a mpl upply han. Innaonal Jounal o oduon Eonom 9() Johnon. E. Da T Impong upply han poman y ung od ulllmn m. Naonal oduy Rw 7(3) 3-6. Lalond B. J. ohln T. L Iu n upply han ong. Innaonal Jounal o Log anagmn 7() -.

24 Lanon R. A Nw dlopmn n upply han managmn o h mllnnum. Indual akng anagmn 9-6. L C-H. Cnnkaya S. Waglman A A dynam lo-zng modl wh dmand m wndow. anagmn Sn 47(0) Lokamy A. Comak K Lnkng SCOR plannng pa o upply han poman. Innaonal Jounal o Opaon and oduon anagmn 4() 9-8. Lokamy A. Spn. S oman maumn n a hoy o onan nonmn. Innaonal Jounal o oduon Rah 36(8) onzka R.. ogan J Today mau ju don mak. uhang 6(6) Nw C. C. Swny T Dly poman and houghpu ny n UK manuaung. Innaonal Jounal o hyal Duon and aal anagmn 4(7) Rull R. Taylo B Opaon anagmn: Foung on Qualy and Compn. n-hall. Sa E. H. Bamon B A mul-oj appoah o mulanou ag and opaonal plannng n upply han dgn. Omga 8(5) Shndman A o h od ulllmn po (pa ). Jounal o Co anagmn 0() Tuno F. Su R Wha knd o num an a ompany xp a mplmnng quk pon manuaung? Quk Rpon anuaung 000 Conn odng R. Su (Ed.) Soy o anuaung Engn Daon I Tywoh J. E. O Nll L Roun o h nomal appoxmaon o ladm dmand n a duon ng Naal Rah Log Van Hok R. I aung h unmaual maung and mpong poman n h upply han Supply Chan anagmn 3(4) Vahon S. Klan R. D. 00. An xploaoy ngaon o h o upply han omplxy on dly poman. IEEE Tanaon on Engnng anagmn 49()

25 Vma R. ullman. E An analy o h uppl aon po. Omga Innaonal Jounal o anagmn Sn 6(6) Walk T. W. Al K. L Undandng upply han managmn. AICSh oman Adanag Januay

26 X ( x) a Ealy On-Tm La x Dly Snao Lgnd: a al dly m gnnng o on-m dly nd o on-m dly la apal dly m Fg. Nomally Dud Dly Wndow. 5

27 η Lgnd: QH η K Q dly lo z H nnoy holdng p un p un m K poduon oppag o wdh o on-m poon o dly wndow aan o dly duon Fg.. Th Rao o Dly Wndow Wdh and Dly Vaan a a Funon o Ealy and La Dly Co. 6

28 Chang Vaan Rdu Vaan Ina Vaan Rdu an Rdu OTW Ina OTW Rdu OTW Ina OTW Chang an Ina an Rdu OTW Ina OTW Rdu OTW Ina OTW No: OTW on-m poon o h dly wndow. Fg. 3. anagmn Opon o Rdung h Expd naly Co. 7