뎤붭듳톧톧놨(ퟔ좻뿆톧냦)ꆡ2009쓪6퓂뗚6뻭뗚2웚:샭릤ꆤ134ꆤJournalofYangtzeUniversity(NatSciEdit)ꆡJun12009,Vol16No12:Sci&Eng튻샠뻶닟쫽늻좷뚨탍뿢듦컊쳢뗄뚯첬맦뮮쟳뷢ꆡꆡ샮돐룻ꆡ(몫즽쪦랶톧풺쫽톧폫탅쾢벼쫵톧풺,맣뚫뎱훝521041)[햪튪]퓚춬튻룶닟싔듘훐,늻춬뗄닟싔춨뎣폐늻춬뗄뻶닟쫽,뛸뫜뛠뚯첬뿢듦컊쳢뻹뻟폐헢훖쳘뗣,틲뛸뎣맦쯣램뫜쓑뒦샭헢튻샠컊쳢ꆣ훷튪쳖싛쇋샻폃뚯첬맦뮮살뒦샭헢샠뻶닟쫽늻좷뚨탍뗄뛠뷗뛎뿢듦컊쳢,춨맽뛔뿢듦컊쳢뗄뛠뷗뛎톰폅,살톰헒떽튻훖ퟮ폅뗄뷸믵뿢듦쒣쪽ꆣꆡꆡ[맘볼듊]뚯첬맦뮮;ퟮ폅닟싔;뷗뛎톰폅[훐춼럖샠뫅]O224[컄쿗뇪쪶싫]Aꆡꆡ[컄헂뇠뫅]16731409(2009)02N134031ꆡ쒣탍쏨쫶뇊헟쳖싛뗄짺닺뿢듦컊쳢[1]쏨쫶죧쿂:짨폐n룶뷗뛎뗄짺닺볆뮮,뗚i뷗뛎뗄뗄탨쟳캪ai,늢쟒뗚튻룶뷗뛎컞뿢듦,뗚n룶뷗뛎쒩,닺욷컞쪣폠ꆣ훷튪럑폃캪:릺싲돉놾뫍듦뒢돉놾ꆣ쿖퓚훆뚨튻룶n쓪뗄뷸믵뫍뿢듦맦뮮쪹뗃ퟜ돉놾ퟮ킡ꆣ죧뛔폚튻룶6뷗뛎뗄뚯첬뿢듦컊쳢,뿉틔ퟷ튻룶폐쿲춼(죧춼1)살쏨쫶ꆣ0떽6뗄죎틢튻쳵탐ퟟ슷쿟뚼듺뇭튻훖릺싲뫍낲업뿢듦뗄랽쪽ꆣ죧0ꇺ2ꇺ5ꇺ6듺뇭뷸0뷗뛎쒩떽2뷗뛎쒩뗄쯹폐믵컯,늢퓚헢킩뷗뛎훰엺듎싴췪,ퟮ뫳뫋쯣쯹폐돉놾ꆣ좻뫳뷸2뷗뛎쒩떽5뷗뛎쒩뗄쯹폐믵컯,늢훰엺듎싴췪,뫋쯣돉놾ꆣ퓙뷸5뷗뛎쒩떽6뷗뛎쒩뗄쯹폐믵컯,싴췪뫳뫋쯣돉놾ꆣ폖죧0ꇺ3ꇺ6듺뇭쿈뷸0뷗뛎쒩떽3뷗뛎쒩뗄쯹폐믵컯ꆡꆡ춼1ꆡ6뷗뛎뗄뚯첬뿢듦컊쳢,훰엺싴췪,뫋쯣돉놾,퓙뷸3뷗뛎쒩떽6뷗뛎쒩뗄쯹폐믵컯,훰엺싴췪,뫋쯣돉놾ꆣ뿉볻0떽6뗄죎뫎튻쳵탐ퟟ슷쿟뚼듺뇭튻훖뷸믵폫뿢듦랽쪽,ퟮ훕튪헒튻쳵0떽6뗄ퟮ뛌슷쿟ꆣ헢샯폃fi듺뇭0ꇺi뗄ퟮ뛌슷쿟,c(i,j)듺뇭i-1뷗뛎쒩(믲헟i뷗뛎돵웚)떽j뷗뛎쒩,쯹랢짺뗄돉놾,벴i-1떽j뗄뻠샫ꆣ2ꆡ쯣램럖컶폃뚯첬맦뮮[2]뗄랽램살뒦샭헢샠컊쳢ꆣ1)붫컊쳢럖캪n룶뷗뛎:sk캪뗚k뷗뛎돵웚뗄닺욷듦뒢솿;uk캪뗚k뷗뛎뗄뚩믵솿;dk캪뗚k뷗뛎뗄쫐뎡탨쟳솿ꆣ틆ힴ첬랽돌캪:ꆡꆡsk+1=sk+uk-dk벴뗚k뷗뛎뗄뿢듦볓짏뗚k뷗뛎쎻폐싴췪뗄듦믵벴캪뗚k+1뷗뛎돵웚뗄뿢듦솿ꆣn2)퓊탭뻶닟벯뫏Dk=uk;ukꇝ0,dkꇜuk+skꇜ6di,벴뗚k뷗뛎뗄뿢듦솿볓짏뗚k뷗뛎뗄뚩믵i=k솿뇘탫싺ퟣ떱잰뗄쫐뎡탨쟳뛸쟒뿉틔놣횤틔뫳뿉틔싴췪ꆣ3)짨c(i,j)캪뗚i뷗뛎잰닖뿢뿕쪱뷸듓뗚i뷗뛎떽뗚j뷗뛎뗄쫐뎡쯹탨튪뗄쯹폐믵컯,늢퓚헢킩뷗뛎훰늽붫믵컯싴췪ꆣ퓲:ꆡ[쫕룥죕웚]20090320ꆡ[ퟷ헟볲뷩]샮돐룻(1969),쓐,1992쓪듳톧뇏튵,쮶쪿,붲쪦,쿖훷튪듓쫂십쫏맽돌뫍퓋돯톧랽쏦뗄퇐뺿릤ퟷꆣ
뗚6뻭뗚2웚:샭릤샮돐룻:튻샠뻶닟쫽늻좷뚨탍뿢듦컊쳢뗄뚯첬맦뮮쟳뷢ꆡꆤ135ꆤjj-1jꆡꆡꆡꆡc(i,j)=ci6ds+6hs6dks=is=ik=s+1웤훐,d1,d2,d3,ꆭ,dn캪n뷗뛎뗄쫐뎡탨쟳솿;c1,c2,c3,ꆭ,cn캪n뷗뛎뗄떥캻뚩믵럑폃;뛸n뷗뛎뗄뿢듦럑폃룷캪h1,h2,h3,ꆭ,hn;fi뇭쪾듓룕뾪쪼벴뗚0뷗뛎뾪쪼뷸믵떽뗚i뷗뛎닖뿢뿕쪱쯹폐럑폃(냼몬뚩믵럑폃뫍뿢듦럑폃)ꆣ평듋,뿉틔뗃떽뚯첬맦뮮뗄Bellman뗝췆쪽(틀쮳탲뷢램):fꆡꆡi=minj-1+c(j,i)}1ꇜjꇜ{fiꆡꆡi=1,2,3,ꆭnf0(x)=03ꆡ낸샽럖컶ꆡꆡ샽1[3]ꆡ쒳웻뎵쿺쫛뗣탨튪뛔웻뎵쿺쫛ퟷ튻룶뇭1ꆡ웻뎵쿺쫛맦뮮뇭냫쓪맦뮮,룹뻝쫐뎡낲업쎿룶퓂뗄ퟮ병듦뒢솿,틔퓂럝k탨쟳솿dk/솾떥캻뚩믵럑폃ck떥캻듦뒢럑폃hk웚ퟜ럑폃뗄ퟮ킡뮯,룹뻝틔췹뗄춳볆쇏뛔틔뫳냫15082540쓪뗄쫐뎡탨쟳25577530,뚩믵럑폃,듦뒢럑폃ퟷ쇋죧쿂튻룶맦뮮뇭35085035,쿖퓚룃웻뎵쿺쫛뗣튪샻폃룃맦뮮뇭,ퟷ튻44585020룶냫쓪맦뮮낲업,틔쪹뗃듋ퟜ뾪횧ퟮ킡ꆣ54077540내퓂럝붫컊쳢뮮럖캪6뷗뛎630825,ힴ첬뇤솿Sk캪뗚k뷗뛎뾪쪼쪱닺욷뗄듦뒢솿;뻶닟뇤솿uk캪뗚k뷗뛎뗄뚩믵솿;dk뷗k뛎뗄탨쟳솿ꆣힴ첬틆랽돌캪:ꆡꆡsk+1=sk+uk-dk퓊탭뻶닟벯뫏캪:6ꆡꆡDk(sk)=ukꇃukꇝ0,dkꇜuk+skꇜ6dii=kퟮ폅횵몯쫽fk(sk)뇭쪾퓚뗚k뷗뛎뾪쪼쪱듦뒢캪sk쪱,듓뗚튻뷗뛎떽뗚k뷗뛎(k=1,2,3,4,5,6)뗄ퟮ킡듦뒢럑폃ꆣ폖짨c(j,i)캪닖뿢싴뿕뫳뷸듓뗚j뷗뛎떽뗚i뷗뛎뗄쯹폐믵컯,늢퓚헢킩뷗뛎붫믵컯훰늽싴뿕,퓚헢튻맽돌훐뗄쯹폐돉놾벴캪c(j,i),hk캪뗚k뷗뛎뗄뿢듦돉놾,퓲:ii-1iꆡꆡc(j,i)=cj6ds+6hs6dtꆡꆡ1ꇜjꇜiꆡꆡi=1,2,3,4,5,6s=js=jt=s+1ꆡꆡc(1,1)=50ꇁ825=41250ꆡꆡc(1,2)=(50+55)ꇁ825+40ꇁ55=88825ꆡꆡc(1,3)=(50+55+50)ꇁ825+40ꇁ(55+50)+30ꇁ55=133575ꆡꆡc(1,4)=(50+55+50+45)ꇁ825+40ꇁ(55+50+45)+30ꇁ(50+45)+35ꇁ45=175425ꆡꆡc(1,5)=(50+55+50+45+40)ꇁ825+40ꇁ(55+50+45+40)+30ꇁ(50+45+40)+35ꇁ(45+40)+20ꇁ40=213425ꆡꆡc(1,6)=(50+55+50+45+40+30)ꇁ825+40ꇁ(55+50+45+40+30)+30ꇁ(50+45+40+30)+35ꇁ(45+40+30)+20ꇁ(40+30)+40ꇁ30=243125ꆡꆡc(2,2)=755ꇁ55=42645ꆡꆡc(2,3)=775ꇁ(55+50)+30ꇁ50=82875ꆡꆡc(2,4)=775ꇁ(55+50+45)+30ꇁ(50+45)+35ꇁ45=120675ꆡꆡc(2,5)=775ꇁ(55+50+45+40)+30ꇁ(50+45+40)+35ꇁ(45+40)+20ꇁ40=120675ꆡꆡc(2,6)=775ꇁ(55+50+45+40+30)+30ꇁ(50+45+40+30)+35ꇁ(45+40+30)+20ꇁ(40+30)+40ꇁ30=182075ꆡꆡc(3,3)=850ꇁ50=42500ꆡꆡc(3,4)=850ꇁ(50+45)+35ꇁ45=82325ꆡꆡc(3,5)=850ꇁ(50+45+40)+35ꇁ(45+40)+20ꇁ40=118525ꆡꆡc(3,6)=850ꇁ(50+45+40+30)+35ꇁ(45+40+30)+20ꇁ(40+30)+40ꇁ30=146875ꆡꆡc(4,4)=850ꇁ45=38250ꆡꆡc(4,5)=850ꇁ(45+40)+20ꇁ40=73050ꆡꆡc(4,6)=80ꇁ(45+40+30)+20ꇁ(40+30)+40ꇁ50=101150ꆡꆡc(5,5)=775ꇁ40=31000ꆡꆡc(5,6)=775ꇁ(40+30)+40ꇁ30=55450ꆡꆡc(6,6)=825ꇁ30=24750
ꆤ136ꆤꆡ뎤붭듳톧톧놨(ퟔ좻뿆톧냦)2009쓪6퓂평쳢틢,폐틔쿂Bellman뗝췆맘쾵쪽:f,i)]ꆡꆡi=min1ꇜjꇜ[fj-1+c(j1ꆡꆡi=1,2,3,4,5,6f0=0ꆡꆡf0=0ꆡꆡf1=f0+c(1,1)=41250(1)ꆡꆡf2=min{f0+c(1,2),f1+c(2,2)}=min{0+88825,41250+42625}=83875(2)ퟮ폅뻶닟쯹뺭맽뗄훐볤뷡뗣뇭쪾캪(1ꇺ2):ꆡꆡf3=min{f0+c(1,3),f1+c(2,3),f2+c(3,3)}=min{0+133575,41250+82875,83875+42500}=124125(3)ퟮ폅뻶닟쯹뺭맽뗄훐볤뷡뗣뇭쪾캪(1ꇺ3):ꆡꆡf4=min{f0+c(1,4),f1+c(2,4),f2+c(3,4),f3+c(4,4)}=min{0+175425,41250+120675,83875+82325,124125+38250}=161925(4)ퟮ폅뻶닟쯹뺭맽뗄훐볤뷡뗣뇭쪾캪(1ꇺ4):ꆡꆡf5=min{f0+c(1,5),f1+c(2,5),f2+c(3,5),f3+c(4,5),f4+c(5,5)}=min{0+213425,41250+155075,83875+118525,124125+73050,161925+31000}=192925(5)ퟮ폅뻶닟쯹뺭맽뗄훐볤뷡뗣뇭쪾캪(4ꇺ5):ꆡꆡf6=min{f0+c(1,6),f1+c(2,6),f2+c(3,6),f3+c(4,6),f4+c(5,6),f5+c(6,6)}=min{0+175425,41250+120675,83875+82323,124125+38250}=161925(6)ퟮ폅뻶닟쯹뺭맽뗄훐볤뷡뗣뇭쪾캪(4ꇺ6)ꆣ평쪽(6)횪,0떽6뗄ퟮ폅솬뷓훐튪뺭맽훐볤뷚뗣4,벴폐0ꇺ4ꇺ6ꆣ평쪽(4)횪,0떽4뗄ퟮ폅솬뷓훐튪뺭맽훐볤뷚뗣1,벴폐0ꇺ1ꇺ4ꇺ6ꆣꆡꆡ맊헻뛎뗄ퟮ폅뻶닟슷뺶캪0ꇺ1ꇺ4ꇺ6ꆣ뇭2ꆡퟮ폅뚩믵뿢듦탲쇐뇭ퟮ폅랽낸벴캪:쿈내헕쫐뎡탨쟳솿싲뗚튻룶퓂뗄믵컯,붫쯼퓂럝k뿢듦솿싴췪,좻뫳퓙내헕쫐뎡탨쟳솿싲2떽4퓂럝뗄믵컯,붫쯼쏇내헕10퓂럝럖엺싴췪295,좻뫳퓙내헕쫐뎡탨쟳솿싴5떽6퓂럝뗄믵컯,내헕퓂럝럖엺싴췪ꆣ34540맊ퟮ폅뚩믵탲쇐캪:뗚튻룶퓂돵웚뗄뚩믵솿캪50,뗚뛾룶530퓂돵웚뗄뚩믵솿캪15060,뗚5룶퓂뗄뚩믵솿캪70ꆣ쎿룶퓂뗄뿢듦탲쇐죧뇭2쯹쪾ꆣ4ꆡ뷡ꆡꆡ폯뚯첬맦뮮ퟷ캪뷢뻶ퟮ폅뮯컊쳢뗄튻훖랽램,춨맽쎿룶ퟓ맽돌뗄ퟮ폅뮯럖컶,쿈헒떽ퟓ맽돌뗄ퟮ폅뷢,좻뫳퓙헒떽헻쳥뗄ퟮ폅뷢,헻룶뚯첬맦뮮헒ퟮ폅뷢뗄맽돌,뻍쫇튻룶폅훐톡폅뗄맽돌,뻍쿱즳훐쳔뷰,늻뛏쳔청쇓뗈ퟓ뻶닟,듓뛸뗃떽헻쳥뗄ퟮ폅뷡맻,헢킩캪뒦샭뚯첬뿢듦헢튻샠뛎뷗뛎뻶닟컊쳢쳡릩쇋랽뇣,틲캪퓚늻뛏뗄폅톡ퟓ뻶닟뗄맽돌훐뇘좻캪쿂튻뷗뛎뗄폅톡뷚쪡듳솿뗄볆쯣솿ꆣ뛔폚뒦샭헢튻샠뻶닟쫽늻좷뚨탍뚯첬뿢듦컊쳢,뚯첬맦뮮쿔쪾돶뷏듳뗄폅풽탔ꆣ[닎뾼컄쿗][1]싞죙맰1탂뇠퓋돯톧쳢뷢[M]1커몺:뮪훐뿆벼듳톧돶냦짧,20021[2]뫺퓋좨1퓋돯톧믹뒡폫펦폃[M]1놱뺩:룟뗈뷌폽돶냦짧,20041[3]맋믹랢,뫺퓋좨1퓋돯톧[M]1놱뺩:쟥뮪듳톧돶냦짧,19901[뇠벭]ꆡ뫩퓆량
