튻뛔뛠엤췋믵쾵춳뗄잶쳗닟싔돉놾폅뮯쒣탍ꆡꆡ햪튪:퓚ퟜ뷡좷뚨탍엤쯍ö쫕벯탐뎵슷쿟쒣탍뫍잶쳗닟싔쒣탍뗄믹뒡짏,뻍튻뛔뛠컯쇷췸싧,헫뛔뿍뮧춬쪱폐엤믵뫍췋믵탨쟳뗄솽샠엤췋믵쾵춳,럖뇰붨솢쇋잶쳗닟싔돉놾폅뮯쒣탍,늢틔쒳욡뻆뎧엤쯍욡뻆뫍쫕벯욡뻆욿뗄쫽뻝뷸탐쇋쪵횤럖컶,춨맽뛔룷훖펰쿬틲쯘뗄쏴룐탔럖컶,뷒쪾쇋엤췋믵쾵춳컯쇷돉놾뗄튻킩맦싉ꆣ맘볼듊:엤췋믵쾵춳;잶쳗닟싔;돉놾폅뮯;폅뮯쒣탍훐춼럖샠뫅:ꆡꆡ컄쿗뇪쪶싫:Aꆡꆡ컄헂뇠뫅:1672-884Ò(2005)05-0505-08CostOptimizationModelsofNestedSequencePolicyUndertheOne-to-ManyPickupandDeliverySys-temXuJiupingꆡLeiZhen(SichuanUniversity,Chengdu,China)Abstract:Onthebasisofsummarizingtheascertainedmodelofvehicleroutingproblemwithpickupsanddeliveriesandthemodelofnestedsequencepolicy,twokindsofpickupanddeliverysys2temsundertheone2to2manylogisticnetworkwereconsidered,,,:pickupanddeliverysystem;nestedsequencepolicy;costoptimization;optimizedmodel1ꆡ컊쳢뗄쳡돶믘쫕,헢쪱샻폃엤쯍뎵솾췪돉췋믵컯쇷,뿉틔듳듳뷚풼돉놾ꆣ퓋쫤뫍듦뒢쫇컯쇷쾵춳훐ퟮ훘튪뗄솽룶뮷폫엤췋믵쾵춳폅뮯폐맘뗄좷뚨탍퇐뺿폐솽뷚,웤럑폃햼컯쇷럑폃횧돶뗄뻸듳늿럖,쯹틔퓚샠,뗚1샠쫇엤쯍ö쫕벯믬뫏싃탐짌퇐뺿,뗚2샠엤쯍쾵춳맜샭퇐뺿훐,헻뫏뎵솾탐ퟟ슷쿟컊쳢뫍쫇잶쳗닟싔퇐뺿ꆣ뿢듦뿘훆컊쳢쫇퇐뺿훘뗣횮튻ꆣ헢샠컊쳢뗄퇐뺿ꆡ엤쯍ö쫕벯믬뫏싃탐짌퇐뺿쒿뇪쫇튪쪹늻춬샠탍뗄컯쇷돉놾뗄ퟜ뫍ퟮ킡ꆣ훷엤쯍ö쫕벯믬뫏싃탐짌컊쳢(traveling튪뗄뻶닟뇤솿쫇엤쯍쪱볤ꆢ쎿듎뛔쎿튻쇣쫛짌퓋salesmanproblemwithpickupanddelivery,쯍닺욷뗄쫽솿뫍뎵솾싃탐슷쿟,헢킩뻶닟뇘탫싺TSPD)쫇뗤탍뗄NP쓑쳢,쯹틔퇐뺿뚼캧죆쯣램ퟣ릩펦짌뫍쇣쫛짌뗄뿢듦쮮욽ꆢ뎵솾뗄퓋퓘쓜솦햹뾪,틑폐뗄싛컄듳뛠볙뚨뇘탫퓚췪돉쯹폐뗄엤뫍뎵솾싃탐슷쿟뗈풼쫸ꆣ쯍탨쟳뫳,닅럾컱쫕벯탨쟳[1,2],뛔폚쎿룶맋뿍뗣떫쫇뮹폐튻훖쟩뿶탨튪뷸튻늽쳖싛,벴퓚쎿볈폐엤쯍탨쟳폖폐쫕벯탨쟳쟩뿶,튲쳡돶쇋탐뎵룶뿍뮧평폚룷훖풭틲퓬돉뗄폐췋믵뗄쟩뿶쿂,죧슷쿟뗄쒣탍뫍쯣램[3,4]ꆣ뫎쪹엤믵뫍췋믵쪱늻춬샠탍뗄컯쇷돉놾ퟜ뫍ퟮꆡ잶쳗닟싔퇐뺿킡,헢샠컊쳢돆캪뿍뮧춬쪱폐엤믵뫍췋믵뗄헻뫏Federgruen뗈[5]ퟮ쿈폃튻룶쒣탍뇭쫶퓋쫤뎵솾탐ퟟ슷쿟컊쳢뫍뿢듦뿘훆컊쳢,볲돆캪엤췋볆뮮뫍뿢듦뿘훆컊쳢,늢뻍샭싛컊쳢뷸탐쇋퇐믵쾵춳폅뮯컊쳢ꆣ퓚웳튵쪵볹훐,쫴폚헢훖쟩뿶뺿ꆣ퓚틑폐뗄퇐뺿훐,뿍뮧탨쟳캪좷뚨탍뗄잶쳗뗄죧욡뻆뎧퓚엤쯍욡뻆뗄춬쪱튪뾼싇퓙믘쫕욡닟싔쒣탍폐죧쿂벸샠:뻆욿,틔벰뫜뛠쿻럑탍닺욷퓚엤쯍쪱,평폚맊헏ꆢ(1)뛔잶쳗닟싔뗄튻냣퇐뺿ꆡ쒿뗄쫇쮵쏷잶퇕즫뫍탍뫅뗈룷훖풭틲틽웰뗄췋믵튲탨튪뷸탐쳗닟싔뗄폅뗣ꆣR[6]undy뛔튻뛔뛠엤쯍쾵춳뷸탐쫕룥죕웚:2005-01-17믹뷰쿮쒿:맺볒뷜돶쟠쓪믹뷰훺쿮쒿(70425005);뷌폽늿룟뗈톧킣폅탣쟠쓪뷌쪦뷌톧뿆퇐붱샸볆뮮훺쿮쒿ꆤ505ꆤ
맜샭톧놨뗚2뻭뗚5웚2005쓪9퓂퇐뺿,쳡돶쇋잶쳗닟싔쒣탍,컄훐볙짨엤쯍훐탄쯍쪱뗄럖쟸살맦뚨쎿솾뎵럾컱뗄뿍뮧ꆣ뚩믵훜웚T0폫뿍뮧뚩믵훜웚Tn횮뇈쫇헻쫽,뻍퓋쫤돉놾훷튪뾼싇뇤뚯돉놾,쾸럖캪벯믵돉뿍뮧탨쟳뛔뿢듦폫퓋쫤돉놾쳡돶쇋폅뮯쯣램,늢놾ꆢ퇘쿟퓋쫤돉놾뫍엤쯍돉놾ꆣ뿍뮧뚩믵럑쫇횸룸돶쇋튻룶욽뻹돉놾뗄쿂쿞,퓚싛컄훐쯻뇈뷏쇋뿍뮧폃폚믱좡튪쟳쫽솿믵컯뗄뮨럑ꆣ뿢듦돉놾쫇헻쫽뫍뛾듎쏝솽훖쟩뿶뗄돉놾,횤쏷쇋뛾듎쏝쪱믵컯퓚닖뿢듦럅웚볤뗄돉놾ꆣ뗄돉놾폫욽뻹돉놾뗄쿂쿞횮닮퓚6%틔쓚ꆣ퓚Rundy뗄믹뒡짏2ꆡ쒣탍붨솢,Jung뗈[7]뛔엤쯍쪱닉폃잶쳗닟싔뗄ퟮ폅럖쟸쯣램뷸탐쇋퇐뺿ꆣ퓚엤췋믵컯쇷췸싧훐,뾼싇횻폐1훖닺욷평(2)뛔짺닺ö뿢듦쾵춳뷸탐퇐뺿ꆡ쒿뗄쫇헒1룶엤쯍훐탄릩펦뫍쫕벯,N룶쇣쫛짌춬쪱폐틑돶붨짨ꆢ뿢듦뫍뚨릺돉놾ퟮ킡뮯랢퓋쪱볤ꆣ튻냣횪뗄엤쯍탨쟳뫍췋믵탨쟳;엤쯍훐탄쫇1룶퓋볙짨엤쯍떥튻닺욷,닺욷뚼뫣뚨뗘ꆢ솬탸뗘놻쿻훐탄,맊늻뾼싇웤뿢듦뫍뚩믵럑폃;엤쯍훐탄폐럑헟컼쓉,T0öTn쫇뛾듎쏝믲헻쫽놶ꆣ웤훐웴랢M솾뎵,쎿솾퓘훘캪V,뎵솾랢퓋닟싔쫇잶쳗닟쪽쯣램훷튪폐3늽:ꋙ좷뚨튻ퟩ쿺쫛쟸폲;ꋚ캪싔;엤쯍훐탄췋믵뿢쟸죝솿캪Qꆣ쎿룶쟸폲좷뚨솬탸뗄퓋쫤욵싊;ꋛ냑헢튻욵싊뚨틥1ꆡ엤췋믵쾵춳쫇횸뿍뮧춬쪱폐엤믵뮻돉잶쳗닟싔욵싊[8,9]ꆣ탨쟳뫍췋믵탨쟳뗄컯쇷췸싧ꆣ룹뻝뿍뮧엤믵탨쟳(3)퇐뺿뛠닺욷엤쯍ꆡ튻냣볙짨쎿훖닺욷뚼뫍췋믵탨쟳횮볤뗄듳킡,럖캪솽훖쟩뿶:ꋙ떱쯹틔룸뚨뗄잶쳗닟싔욵싊퓚풭뗣쳡릩,퓚쒿뗄뗘컼폐쇣쫛짌뗄엤믵솿듳폚뗈폚췋믵솿,믲췋믵솿듳쫕폚뗈폚엤믵솿,볲돆헢훖쟩뿶캪뗚1샠엤췋믵쾵,풭뗣뗄닺솿ퟜ뫍뗈폚쒿뗄뗘뗄쿻럑ퟜ뫍ꆣ뛔튻뛔뛠엤쯍쾵춳뗄뿢듦ퟜ솿뫍퓋쫤돉놾ퟮ킡뮯춳;ꋚ떱늿럖쇣쫛짌엤믵솿듳폚뗈폚췋믵솿,늿뗄뻟쳥쒣탍뫍폅뮯벼쫵[10]ꆢ뛔떥튻솬뷓뗄4훖늻럖췋믵솿듳폚뗈폚엤믵솿,볲돆헢훖쟩뿶캪뗚2춬쟩뿶(떥튻욵싊ꆢ뛠훘욵싊ꆢ만뚨욵싊ꆢ만뚨쪱샠엤췋믵쾵춳ꆣ볤)쪱뗄펦폃[11,12],틔벰퓚튻뛔뛠엤쯍쾵춳훐뛠뚨틥2ꆡ잶쳗닟싔쫇횸럾컱폚럖쟸쓚뿍뮧닺욷엤쯍ꆢ랢퓋훜웚뇈쫇뛾듎쏝뗄쟩뿶[13]뚼폐짮뗄튻솾뎵뗄랢퓋닟싔,쟸폲엤쯍쿟슷떥뛀볆쯣,죫퇐뺿ꆣ웤엤쯍훜웚퓚랢퓋웚볤뚼쫇뎣쫽,죎뫎솽듎솬탸(4)퇐뺿폐쪱볤쿞훆뗄잶쳗닟싔ꆡ쪱볤쿞훆랢퓋뗄쪱볤볤룴쫇ퟮ킡랢퓋욵싊뗄놶쫽,쟒뫳탸폐퓋쫤욵싊틑뚨뗄잶쳗닟싔뫍튻룶룸뚨쪱볤뛎뷗뛎쯹톡뗄욵싊늻믡뗍폚잰튻뷗뛎뗄욵싊ꆣ퓚잶쓚뗄잶쳗닟싔,튻냣볙짨늻춬뷡뗣짏떥캻쪱볤쓚쳗닟싔훐,캪쇋뇣폚볆쯣,닉폃뛾듎쏝맦퓲(죧춼쎿훖닺욷뗄뿢듦돉놾쫇늻춬뗄,믲헟듓릩펦짌떽1),뻍쫇쮵퓚쒣탍훐쎿룶쇣쫛짌뗄뚩믵훜웚닉폃쇣쫛짌뗄퓋쫤평룸뚨퓋쫤쓜솦뫍돉놾뗄뎵솾췪뛾듎쏝뒦샭,샽죧퓚튻ퟩ훐쇣쫛짌1ꆢ쇣쫛짌2뫍돉ꆣ쎿튻쇣쫛짌튪좷뚨튻룶ퟮ킡쮮욽뫍ퟮ듳쮮욽쇣쫛짌3뗄뚩믵훜웚캪T=2,쓇쎴쇣쫛짌4뫍뗄닺욷뿢듦쇣쫛짌5뿉쓜캪T=4,떱뛔쇣쫛짌4뫍쇣쫛짌5,쎿듎횻럃컊튻룶쇣쫛짌,릩펦짌엤쯍뗄믵솿쓜쪹쇣쫛짌듯떽ퟮ듳쮮욽ꆣ컊쳢쫇튪좷뷸탐엤쯍쪱,쇣쫛짌1ꆢ쇣쫛짌2뫍쇣쫛짌3튲춬뚨늻솬탸쪱볤튪럃컊뗄쇣쫛짌뫍뎵솾싃탐슷쿟ꆣ쪱탨튪엤쯍ꆣ튪뾼싇뛔펦폚늻춬뻶닟햽싔뫍늻춬뻶닟헟뗄늻춬뗄쒿뇪몯쫽[14,15]ꆣ놾컄훷튪쫇퇐뺿엤췋믵쾵춳뿢듦폫퓋쫤폅뮯컊쳢,벴퓚춬쪱뾼싇퓋쫤폫뿢듦뿘훆뗄틲쯘쿂,떱쇣쫛짌볈폐엤쯍탨쟳,폖폐쫕벯탨쟳쪱,죧뫎폐킧뫍뺭볃뗘ퟩ횯엤쯍뫍쫕벯믮뚯,쪹엤췋믵췸싧뎤웚뗄뿢듦ꆢ퓋쫤뫍뚩믵돉놾ퟮ킡뮯ꆣ퓚쿖퓚뗄쫐뎡튪쟳쿂,킡엺솿ꆢ뛠엺듎퓋쫤돉캪훷쇷,쯹틔뾼싇튻룶엤쯍훐탄떽뛠룶쇣쫛짌뗄컯쇷췸싧,볲돆튻뛔뛠엤췋믵쾵춳ꆣ뚨틥3ꆡ엤췋욵싊쫇횸퓚헻룶맦뮮웚쓚캪볙짨퓚튻뛔뛠엤췋믵쾵춳훐,횻폐튻훖닺욷맋뿍쳡릩엤쯍뫍쫕벯럾컱뗄욵싊ꆣ벰웤췋믵탨튪퓋쫤,퓋쫤평뻟폐뛮뚨뗄ꆢ퓘훘솿뚨틥4ꆡ엤췋믵싊쫇횸떱엤믵탨쟳뫍췋믵쿠춬뗄뎵솾췪돉,평폚쫇샻폃엤쯍뎵솾뷸탐췋믵탨쟳좷뚨쪱,탨튪좷뚨쪵볊쎿룶뿍뮧뗄엤믵싊뫍쫕벯,쯹틔놾컄붫쳖싛틑횪럖쟸쟩뿶,벴내헕엤췋믵싊,웤훐뿍뮧췋믵싊쫇횸캪쇋돤럖샻폃폐쿞ꆤ506ꆤ
튻뛔뛠엤췋믵쾵춳뗄잶쳗닟싔돉놾폅뮯쒣탍ꆪꆪ탬뻁욽ꆡ샗ꆡ헩뗄엤쯍훐탄췋믵쟸N,뻶닟헟탨튪듓쯹폐뗄뿍뮧훐i톡퓱늿럖뿍뮧,췪좫싺ퟣ믲늿럖싺ퟣ웤췋믵탨6K({i1,i2,ꆭ,ij})(T-1ij-T-1i,j+1)ꆡꆣ(1)j=1쟳,틔듯떽랣뷰ퟮ킡ꆣ평폚K({i1,i2,ꆭ,ij})뇭쪾엤쯍{i1,i2,ꆭ,캪쇋붨솢쫽톧쒣탍,놾컄닉폃5룶볙짨:ꋙij}뗄싃탐슷쿟(travelingsaleproblem,TSP)ꆢ퓋쫤럑폃횻뫍뎵솾탐뎵슷쿟짏뗄뇤뚯럑폃폐맘,퓋쫤럑폃뫍쯹폐퓚슷쿟짏뗄쇣쫛짌뗄뚩믵럑폃쟒튻솾뎵럾컱튻룶틑횪뗄럖쟸ꆣꋚ엤쯍훐탄짨j폐췋믵쟸ퟜ뫍(6Cik),퓚듋퓙볙짨fij캪엤쯍{i1,i2,ꆭ,,죝솿캪Q,쯼킡폚쎿듎엤쯍쪱N룶뿍k=1뮧뗄췋믵ퟜ솿횮뫍ꆣꋛ쎿룶쇣쫛짌뛀솢좷뚨엤ij}뗄TSP퓋쫤럑폃,룄킴쪽(1)뗃믵솿Ni,쎿듎엤쯍쫽솿룕뫃듯떽쇣쫛짌ퟮ듳컼쫕쓜솦ꆣꋜ쎿룶쇣쫛짌뗄췋믵랣뷰횻폫췋믵솿폐맘ꆣ6[K({i1,i2,ꆭ,ij})-K({i1,i2,ꆭ,(ij-1)})]T-1ij=j=1ꋝ쎿룶쒣탍뻹늻뾼싇엤쯍훐탄뗄뿢듦럑폃뫍뚩Ni믵럑폃ꆣ6(fij-fi,j-1+Cij)T-1ijꆡꆣ(2)j=1ퟮ뫳ꆡ뗚2샠엤췋믵쾵춳뗄볆쯣,캪쇋쫩킴랽뇣,뛔쒣탍훐쪹폃뗄럻뫅쮵쏷죧쿂:I={1,2,ꆭ,M}뇭쪾N룶쇣쫛짌럖퓚뗚2샠컊쳢훐,쇣쫛짌뗄엤믵뫍췋믵탨캪M룶쟸;Ni뇭쪾뗚i쟸훐쇣쫛짌뗄쫽솿쟳,폐뗄dijTijꇝpijTij,폐뗄dijTij<pijTij,퓚틑,뗚i쟸뗄쇣쫛짌뻍뇭쪾캪{1,2,ꆭ,Ni},늢쟒볙짨퓚튻횪럖쟸,죧맻닉폃TSP뺭뗤쒣탍볆쯣맾쏜뛻뛙ퟩ훐뇠뫅킡뗄쇣쫛짌뻍쫇엤쯍훜웚뛌뗄쇣쫛짌믘슷,뿉쓜퓬돉퓚쒳튻쇣쫛짌뒦돶쿖췋믵솿뎬맽;C뎵솾퓘훘뗄쟩뿶,쯹틔튪퓚틑폐뗄TSP슷쿟짏ij뇭쪾뗚iퟩ뗚j룶쇣쫛짌쎿듎엤쯍붻틗뚩믵럑폃뷸탐룄뷸ꆣ;dij뇭쪾뗚iퟩ뗚j룶쇣쫛짌엤믵탨쟳싊;pij뇭쪾뗚iퟩ뗚j룶쇣쫛짌췋믵탨쟳싊R;hij뇭쪾뗚iퟩ퓚뗚i쟸폐Ni룶뿍뮧,틔i=0,j=0듺뇭뗚엤쯍훐탄,틔ij(j=1,2,ꆭ,Ni)듺뇭뗚i쟸뗚jj룶쇣쫛짌떥캻쪱볤쓚떥캻뿢듦럑폃;gij뇭쪾뗚iퟩ뗚j룶쇣쫛짌캴퓋췋믵뗄떥캻랣뷰룶뿍뮧,뎵솾쿲헢Ni룶뿍뮧쳡릩엤췋믵럾컱,;xij뇭쪾뗚iퟩ뗚j룶쇣쫛짌쪵볊췋믵싊;Tij뇭쪾뗚L(i)캪돵쪼퓘퓋솿,ri캪뎵솾퓚뗚i쟸뗄탐뎵슷iퟩ뗚쿟,퓲폐j룶쇣쫛짌뚩믵훜웚ꆣ퓚튻뛔뛠엤췋믵쾵춳훐,폐솽룶쒿뇪몯쫽Ni:L(i)=6di=jꇊj6dij,ꋙ뚩믵럑ꆢ퓋쫤럑뫍뿢듦럑폃ퟮ킡;ꋚ캴퓋췋믵rj=1i랣뷰ퟮ킡ꆣ헢솽룶쒿뇪몯쫽튪싺ퟣ잶쳗풼쫸ꆢ뎵jjcd(ij)=솾죝솿풼쫸틔벰엤쯍훐탄췋믵쟸죝솿풼쫸ꆣ6dik,cp(ij)=6pik,k=1k=1쪽훐,ij캪뎵솾퇘ퟟ탐슷쿟ri뗄떱잰쯹퓚뗣;cd(ij)캪퇘슷ꆡ퓋럑뫍뚩믵럑폃뗄볆쯣솽샠엤췋믵쾵춳틲엤믵싊뫍췋믵싊맘쾵늻쿟ri뗄샛볆엤쯍탨쟳솿;cp(ij)캪퇘슷쿟ri뗄샛볆췋믵탨쟳솿ꆣ춬,쯹틔웤탐뎵슷쿟튲늻쿠춬,탨튪럖뇰볆쯣ꆣ룹뻝볙짨ꋙ,퓋쫤뇤뚯돉놾쾸럖캪벯믵돉놾ꆢ퇘쿟떱폐뗄뿍뮧diꇝpi,폐뗄뿍뮧di<pi쪱,퓚jjjj퓋쫤돉놾뫍엤쯍돉놾ꆣ뛸룹뻝볙짨ꋛ뫍볙짨ꋝ죎튻뷚뗣ij뗄퓘퓋솿,L(ij)=L(i)-cd(ij)+cp(ij)ꆡ,(3)횻퓚쇣쫛짌랢짺뚩믵럑폃,춬쪱뚩믵욵싊뫍퓋쫤폐뿉쓜듳폚뎵솾퓘퓋죝솿V,쓇쎴쇮f욵싊쿠춬ꆣi캪룄뷸탐뎵슷쿟뫳뗚i쟸뗄퓋쫤럑폃i,ckl캪뗚i쟸죎틢솽룶ꆡ뗚1샠엤췋믵쾵춳뗄볆쯣룹뻝쳵볾,뇤솿뚩믵훜웚닉폃뛾듎쏝뒦샭뿍뮧k뫍l횮볤(냼삨뿍뮧떽엤쯍훐탄)뗄퓋럑,,i쯹틔뗚zkl뇭쪾ickl퓚룄뷸슷쿟훐돶쿖뗄듎쫽,뗃떽뗚i쟸iퟩ룷쇣쫛짌뗄뚩믵훜웚캪뎵솾퓋럑벰슷쿟톡퓱쒣탍:TiꇜT1iꇜꆭꇜT2iNꆡꆣiNNii평폚볙짨퓚튻ퟩ훐뇠뫅킡뗄쇣쫛짌뻍쫇엤fi=min66iicklzkl(kꇙl)ꆡ,(4)k=1l=1쯍훜웚뛌뗄쇣쫛짌,쯹틔뗚iퟩ쎿듎엤쯍듎탲벯L(ij)ꇜV,(5)뫏캪Ni{i1},{i1,i2},ꆭ,{i1,i2,ꆭ,ij},ꆭ,{i1,i2,ꆭ,iN}ꆡꆣ6izklꇜ2ꆡ(l=0,1,ꆭ,Ni),(6)ik=1뛔폚뗚쟸뗄엤쯍욵싊캪T-1i-T-1iijj+ꆡꆣ1틲캪-1Ti,N+1=0,짨룃듎뚩믵럑폃뫍퓋쫤럑6izklꇜ2ꆡ(k=0,1,ꆭ,Ni),(7)il=1폃캪K({ii1,i2,ꆭ,ij}),쓇쎴뗃떽뗚i쟸쓪엤쯍럑zklꇊ{0,1,2,}폃캪ꆡꆡ(k=0,1,ꆭ,Ni;l=0,1,ꆭ,Ni;kꇙl)ꆣ(8)ꆤ507ꆤ
맜샭톧놨뗚2뻭뗚5웚2005쓪9퓂ꆡꆡ쒣탍뗄쯣램죧쿂:퓚뗚i쟸훐톰헒돶1쳵ퟮMNi뛌뗄min[G(T),H(x)]=[TSP슷쿟66[(fi-fi)+Cjj-1i]T-1i+jjri,퇘엤쯍훐탄쮳룃슷쯑톰ij뗣,i=1j=1쪹뗃LMNi(ij)ꇜV쟒LMNi(ij+1)ꇝVꆣ죴퇘ri죎틢뗣뚼싺ퟣ66diTihRiö2,j66gi(pi-xi)]ꆡ,(12)jjjjjL(ii=1j=1i=1j=1j)ꇜV,룃슷쿟벴쫇ퟮ폅슷쿟;죧맻헒떽헢퇹뗄뷚뗣,붫웤뇪캪쯷냑뷡뗣,벴뗚1듎럃컊ij0<TiꇜT1iꇜꆭꇜT2i(Ni=1,2,ꆭ,M),(13)쪱횻춶뗝늻믘춶,샫뾪ij쪱뗄퓘퓋솿캪iL(ij)-Nipij,ij뫳쏦뗄쯹폐뷚뗣릹돉-퓚췪돉웤뫳쏦탂뗄쯷뮷뿍뮧뗄엤췋믵럾컱뫳,붫뗚2듎뷸죫ij퓘퓋ꇜVꆡ(i=1,2,ꆭ,M),(14)jjj=1MNiMNipij,퓚탂쯷뮷훐훘뢴짏쫶늽훨,횱떽룄뷸슷뺶냼66xiTiꇜQꇜpiTi,(15)jj66jj삨쯹폐뗄뷚뗣ꆣi=1j=1i=1j=1춨맽뛔0ꇜxiꇜpiꇜdi,(16)TjjjSP슷쿟뗄룄뷸,놣횤쇋뗚i쟸쓚쎿룶뿍뮧뗄엤쯍뫍췋믵탨쟳뿉틔뗃떽싺ퟣꆣ쪽훐,T=(T11,T12,ꆭ,T1N,ꆭ,Ti,ꆭ,TiN,ꆭ,TM)N,11iMx=(x11,x12,ꆭ,x1N,ꆭ,xi,ꆭ,11xiN,ꆭ,xM)N,웤훐쪽jj춨맽쪽iM(4)볆쯣iifi=minj66cklzkl(kꇙ(13)ꆫ쪽(16)럖뇰뇭쪾잶쳗ꆢ뎵솾퓘훘ꆢ엤쯍훐탄췋믵쟸k=1l=1l),쓇쎴뗚i쟸쓪퓋럑뫍뚩믵럑폃쫇죝솿ꆢ좡횵뗈풼쫸ꆣꆡ뗚2샠엤췋믵쾵춳쒣탍i6(fi-fi+C)T-1iꆡꆣ(9)평쪽(9)ꆢ쪽(10)뫍쪽(11)뗃떽쫽톧쒣탍jj-1ijjj=ꆡ췋믵랣뷰폫뿢듦럑폃뗄볆쯣MNi뛔폚솽샠엤췋믵쾵춳min[G(T),H(x)]={66[(fi-fi)+]T-1i+jj-1Cijji=1j=1,평폚쫇내틑횪럖쟸뷸탐엤쯍뫍쫕벯럾컱,쯹틔췋믵랣뷰뫍뿢듦럑폃뻍MNiMNi66RdiTihiö2,66gi(pi-xi)}ꆡ,(17)늻폃퓙럖뇰볆쯣ꆣjjjji=1j=1ji=1j=ꆡ췋믵랣뷰0<TiꇜT1iꇜꆭꇜT2i(Ni=1,2,ꆭ,M),(18)i뛔엤쯍{i1,i2,ꆭ,ij}뛸퇔,룹뻝볙짨ꋚ뫍볙Ni짨ꋜTiꇜVꆡ(i=1,2,ꆭ,M),(19),퓚솽훖엤췋믵쾵춳훐,쎿룶쇣쫛짌튪뗃떽=1뗄랣뷰캪gipTkiki,죧맻쎿룶쇣쫛짌쪵볊퓋ퟟkMNiMNix66xiTiꇜQꇜjj66piT,(20)iT,쓇쎴쎿룶쇣쫛짌ki뗃떽뗄랣뷰캪gi(pkki-jki=1j=1i=1j=1xi)Tki,헢퇹뗚i쟸헢듎엤쯍랣뷰캪k0ꇜxiꇜpiꆣ(21)jjj쪽(18)쫇잶쳗풼쫸,쪽(19)쫇뎵솾퓘훘풼쫸,쪽6gi(pi-xi)Tiꆡ,kkkkk=1(평짏쫶럖컶뗃떽뗚20)쫇엤쯍훐탄췋믵쟸죝솿풼쫸,쪽(21)쫇좡횵i쟸ퟮ훕쓪랣뷰캪풼쫸ꆣNij6[6g1평듋뿉볻,솽샠엤췋믵쾵춳쒣탍뗄탎쪽뇈뷏i(pi-xi)Ti](T-i-T-1i)ꆡꆣkkkkjj+1j=1k=1폃샠쯆쪽춬퇹뗄랽램붫웤룄킴캪뷓뷼,횻쫇퓚풼쫸쪽(16)뫍쪽(21)늻춬,쟒fi뗄j볆쯣튲늻쿠춬ꆣ평쒣탍쟳뗃뗄뷢늻싺ퟣ뛾듎쏝맦Ni6gi(pi-xi)ꆡꆣ(10)퓲,쯹틔폃엤쯍훜웚뛾듎쏝풼쫸살뗷헻,웤쫽톧jjjj=1뇭듯쪽캪ꆡ뿢듦럑폃m퓚솽훖엤췋믵쾵춳훐,룹뻝볙짨ꋝ,엤쯍훐Tαiij=2jBꆡ(mi쫇헻쫽)ꆡ,(22)j탄늻놣쇴뿢듦,쓇쎴엤쯍훐탄튻냣뚼쫇퓚엤쯍잰쪽훐,B뇭쪾뚩믵훜웚믹놾떥캻(쳬ꆢ훜믲퓂)ꆣ뻍냑룷쇣쫛짌뗄엤믵탨쟳믣ퟜ늢랢돶뚩믵,쯹틔3ꆡ쒣탍쯣램뗚i쟸쎿룶쇣쫛짌뗄쓪뿢듦럑폃캪잶쳗쒣탍뗄뗚1룶쒿뇪몯쫽G(Ti)쫇럇쿟jdihRiTiö2ꆡꆣ(11)jjj탔몯쫽,뗚2룶쒿뇪몯쫽Gꇤ(xi)쫇쿟탔몯쫽,퓚ꆡ솽샠엤췋믵쾵춳뗄쫽톧쒣탍풼쫸쳵볾훐,쪽(15)뫍쪽(20)쫇럇쿟탔풼쫸,웤틲캪쎻폐샭싛횧돖쓜붫췋믵랣뷰폫퓋럑ꆢ뚩쯻풼쫸캪쿟탔풼쫸,쯹틔헢룶쒣탍쫇럇쿟탔풼쫸믵럑ꆢ뿢듦쿠볓,쯹틔쒿뇪몯쫽쫇솽룶벫킡뮯몯뗄뛠쒿뇪럇쿟탔맦뮮,쟳뷢럖캪틔쿂솽늽:쫽ꆣ룹뻝짏쫶볆쯣,뗃떽솽샠엤췋믵쾵춳쒣탍ꆣ(1)쿈닉폃쫊떱쯣램쟳뷢쪽(12)뫍쪽(17),ꆡ뗚1샠엤췋믵쾵춳쒣탍벴쟳뷢럇쿟탔풼쫸쿂벫킡뮯뗄뛠쒿뇪럇쿟탔맦ퟛ뫏쪽(2)ꆢ쪽(10)뫍쪽(11),쫽톧쒣탍캪:뮮(VM33P),늢짨ퟮ폅뷢캪(T,x);ꆤ508ꆤ
튻뛔뛠엤췋믵쾵춳뗄잶쳗닟싔돉놾폅뮯쒣탍ꆪꆪ탬뻁욽ꆡ샗ꆡ헩kk,∆k(2)좻뫳춨맽샠쯆쯄짡컥죫뗄랽램,뾼싇뛾뗚3늽ꆡ죴E(y)=<,ꆬfy(y)ꆬꇜΕ1,듎쏝풼쫸쪽(22),붫쪽(12)뫍쪽(17)뷢돶뗄3T퓲뗼듺춣횹,뗃뷼쯆믲ퟮ폅뷢ky;죴kE(y,∆k)=뮻돉럻뫏뛾듎쏝맦퓲뗄쫽횵,늢쟒싺ퟣ웤쯻풼k<,ꆬfy(y)ꆬ>Ε1,퓲kkTz=-fy(y),뷸탐뗚6쫸쳵볾ꆣ늽;죴kE(y,∆k)ꇙ<,퓲뷸탐뗚4늽;ꆡ뛠쒿뇪럇쿟탔맦뮮쒣탍뗚4늽ꆡ쟳쿟탔맦뮮쟳뷢VMP컊쳢,퓚쫽톧짏쫇쟳쿲솿벫횵컊(L)ꆡminΝꆡ;Mkfy(y)zꇜΝꆡ,쳢[16],짨y캪26Ni캬쿲솿,벴Ty=(T,x),kki=.-giy(y)zꇜΝꆡ[iꇊE(y,∆k)]ꆡ,f(y)캪2룶쒿뇪몯쫽쯹ퟩ돉뗄2캬쿲솿몯쫽,벴ûzjûꇜ1ꆡ(j=1,2,ꆭ,n)ꆡꆣ뗄ퟮ폅뷢kkf(y)=[GT(T),H(x)],퓲VMP뿉쏨쫶캪(z(y,∆k),Ν(y,∆k));minf(y)yꇊ,X뗚k5늽ꆡ죴-Ν(y,∆k)ꇜΕ2,∆kꇜΕ3,퓲뗼듺춣횹ꇊX={xûg(y)ꇝ0,h(y)=0}ꆡ,(23),y캪뷼쯆뷢,럱퓲쇮쪽훐,X캪풼쫸벯(믲돆뿉탐폲);g(y)ꇝ0캪늻뗈쪽풼쫸;∆k[-Νk(y,∆kkk)ꇝ∆k,z=z(y,∆k)]ꆡ;∆k+1h(y)=0캪뗈쪽풼쫸ꆣ=1쟳뷢∆k[-Νk(y,∆k)<∆AKk,z=kz(y,∆k)]ꆡ,VMP뗄튻룶훘튪뗄춾뺶뻍쫇냑쯼2뮯캪폫횮쿠맘뗄떥쒿뇪(쫽횵)ퟮ폅뮯컊쳢,벴뛠뷸탐뗚6늽;쒿뇪맦뮮뗄뇪솿뮯뒦샭ꆣ룹뻝잶쳗닟싔뗄쳘뗣뫍뗚k6늽ꆡ쟳min{f(y+Κkkz)ûΚꇝ0,x+엤쯍뻶닟헟뗄틢춼,내솽룶쒿뇪몯쫽퓚쒣탍훐뗄ΚꇤkzꇊX}뗄ퟮ폅뷢Κk;훘튪돌뛈,룸돶튻ퟩ뛔펦뗄좨쾵쫽뗄럇뢺쿲솿뗚7늽ꆡ쇮k+1y=ky+Κꇤkkz,kꇃ=k+1,뷸w=(Κ,1-ΚT)ꆡ,탐뗚2늽ꆣ쪽훐,0<Κ<1,헢퇹싺ퟣ좨쾵쫽튪쟳,벴wiꇝ0(i=1,2,평짏쫶뗼듺늽훨뗃떽뗄뗣쇐k{y}폐limkkꇺꇞy=mꇞꆭy,퓲ꇞy캪컊쳢Pw싺ퟣKT쳵볾뗄뗣ꆣ쳘뇰떱,m)뫍6Wi=1ꆣi=1ퟷ쿲솿w뫍f(y)뗄쫽솿믽릹퓬쫽횵몯쫽f(y)-gj(y)(j=1,2,ꆭ,m)캪춹몯쫽쪱ꇞ,y캪컊쳢Pw뗄ퟮ폅뷢ꆣΚG(T)+(1-Κ)H(x),VMP맩캪쟳뷢쫽횵벫킡뮯컊쳢ꆡ뛾듎쏝뗷헻쒣탍(Pw):평ꆰꆱ쟳돶뷢3y=33(T,x)뫳,평폚3Tmin(T)+(1-ΚyꇊΚG)H(x)ꆡꆣX쿖퓚,붫뛠쒿뇪맦뮮컊쳢틑뺭뮯캪럇쿟탔뮹튪싺ퟣ뛾듎쏝풼쫸쪽(22),쯹틔튪붨솢쒣탍뷢풼쫸쳵볾쿂뻶,믹놾쮼쿫쫇폃샠쯆쯄짡컥죫뗄랽램붫쎿튻룶,쟳뷢떥쒿뇪럇쿟탔맦뮮Pwꆣ짨뛠쒿Ti풼캪쇚뷼뗄뛾듎쏝ꆣMj2뇪ퟮ폅뮯뗄풼쫸벯6NiXΑRi=1,VMP뗄좫늿폐킧짨튻룶헻쫽k-1ijki,뛔폚쎿룶Ti,뚼폐B2ꇜjj뷢쯹ퟩ돉뗄벯뫏뷐VMP뗄폐킧벯,볇ퟶTijꇜkijB2E(쇮lk-1ijukijTi=f,X),쿲솿쒿뇪몯쫽볇ퟶf:XꇺR2,웤뛔펦B2,Ti=B2,헢퇹Tij폐솽훖톡퓱,jj쿲솿w=(Κ,1-ΚT),떱w>0붨솢쫽톧쒣탍살뷢뻶헢룶컊쳢ꆣ,죧맻ζy=33T(T,x)쫇Pw뗄ퟮ폅뷢,퓲ζyꇊE(f,X)ꆣ뛔폚뗚i쟸,쇮ai=Rdihiö2,bi=fi-fi+jjjjjj-1룹뻝컄쿗0[16],짨yꇊX,캪minf(y)yꇊ,X=Ci,붫뗚i쟸쓚폐쿠춬뗄뛾듎쏝짏쿂뷧lTij뫍uTijjX{yûg(y)ꇝ0,yꇊS}뗄ퟮ폅뷢f(y)뗄뿍뮧럖캪튻ퟩ,볙짨쯹폐뗄Ti뚼쿈좡lTi,쓇쎴,gjjj(y)(j=1,2,ꆭ,m)폐튻뷗솬탸욫캢짌,gj(y)뿉틔쫇럇쿟쒿뇪몯쫽뻍쫇쟳헢룶킡ퟩ쓚떱uTi뚼좡Ti럑폃퓶jj탔몯쫽볓ퟮ킡,춬쪱싺ퟣ뎵솾퓘훘풼쫸뫍췋믵쟸죝솿풼,쓇쎴놣횤듦퓚∆0>0쪹0(y,∆0)싺ퟣKT쳵볾믲헟FJ쳵볾ꆣ쯹틔닉폃럇쿟탔풼쫸뗄뿉탐쫸ꆣ랽쿲램쟳뷢컊쳢Pwꆣpi뇭쪾뗚i쟸폐쿠춬뛾듎쏝짏쿂뷧lTi뫍uTijj짨돵쪼뷢00yꇊX,z캪X퓚0y뗄뿉탐랽쿲,럖ퟩ뗄ퟩ쫽(i=1,2,ꆭ,M);kyꇊX캪뗚k듎뗼듺뷢k,z캪X퓚ky뗄뿉탐랽sq뇭쪾뗚i쟸뗚qퟩ뗚1룶뿍뮧뗄쿂뇪(q=쿲,퓲뗼듺늽훨죧쿂:1,2,ꆭ,pi);뗚1늽ꆡ좡퓊탭컳닮쫽Ε1>0,Ε2>0,Ε3>0,rq뇭쪾뗚i쟸뗚qퟩퟮ뫳1룶뿍뮧뗄쿂뇪돵쪼뗣0yꇊX,∆0>0,쇮kꇃ=0;(q=1,2,ꆭ,pi);뗚2늽ꆡ짨kyꇊR벰∆k틑횪,좷뚨횸뇪벯wi뇭쪾uTi좡Ti쪱,웤횵캪1;뇭쪾Ti좡lTijjjjjkE(y,∆kk)={gi(y)ûꇜ∆k,1ꇜiꇜm};쪱,웤횵캪1ꆣꆤ509ꆤ
맜샭톧놨뗚2뻭뗚5웚2005쓪9퓂쇮uci캪떱쎿룶뿍뮧닉폃Ti쪱뗄럑폃퓶솿,jj볆쯣쪽캪lci=(aiTui+biöTui)-(aiTi+biöTli)ꆡ,jjjjjjjjj쓇쎴쫽톧쒣탍캪Mpriqmin666ciwiꆡ,(24)jji=1q=1j=sqprNiqi66dli(Tui-Ti)wiꇜV-diTlijjjj6jjq=1j=sqj=1ꆡꆡꆡꆡꆡꆡꆡꆡꆡ(i=1,2,ꆭ,M)ꆡ,(25)Mpriq666lx싊볻뇭2뫍뇭3ꆣ릫쮾내샫엤쯍훐탄풶뷼붫럖쿺i(Tui-Ti)wiꇜQ-jjjji=1q=1j=.짌럖캪3룶쟸,쟒쎿룶쟸뗄엤쯍싊뫍쫕벯싊뚼쫇MNiꆡꆡ125쿤ö훜;쎿룶엤쯍훐탄뗄뎵솾죝솿캪125쿤;66lxiTiꆡ,(26)jji=1j=1릫쮾뺭샭죏캪엤쯍뇈쫕벯튪훘튪,퓚뛔엤쯍럑폃wiꇜwiꇜꆭꇜwis뇭1ꆡ룷쿺쫛뗣볤뎵솾뗄퓋탐돉놾풪qsq+1rqꆡꆡꆡ(i=1,2,ꆭ,M;q=1,2,ꆭ,pi)ꆡ,(27)012345678910111213wiꇊ{0,1}ꆡꆡꆡ(=1,2,ꆭ,M;q=1,2,ꆭ,pi)ꆣ(28)쪽(25)쫇엤쯍뎵솾퓘훘풼쫸,쪽(26)쫇췋믵쟸죝솿풼쫸,쪽(27)쫇잶쳗풼쫸,쪽(28)쫇뻶닟뇤솿좡횵풼쫸ꆣ헢쫇튻룶틔캪뻶닟뇤솿뗄021맦뮮,쒿j뇪몯쫽뫍풼쫸쳵볾뚼쫇쿟탔뗄,헢훖컊쳢뿉틔평죭볾볆쯣뷢뻶ꆣꆡ쪵샽럖컶틔돉뚼쒳욡뻆뎧엤쯍훐탄뗄욡뻆엤쯍뫍뿕욿믘쫕캪샽,뷸탐쪵횤럖컶ꆣ룃릫쮾쫇평13볒웳튵뫏ퟩ돉뗄,웬쿂폐10폠룶욷없ꆣ햼쯄뒨쪡욡130뻆쿺솿뗄8돉,늢럸짤훘쟬ꆢ퓆쓏ꆢ맳훝ꆢ컷님ꆢ짂뇭2ꆡ룷쿺쫛뗣뗄믬뫏퓋쫤탨쟳싊(뗚1샠엤췋믵쾵춳)컷ꆢ룊쯠뗈훜뇟쪡쟸ꆣ룃릫쮾쿖퓚뗄럖쿺쾵춳닉폃죽벶엺랢듺샭뿍뮧012345678910111213뫏볆훆di055510560555605505555375j,벴릫쮾훷튪폫튻벶뺭쿺짌뾪햹튵컱,뛸뛾ꆢ죽벶럖쿺짌듓튻벶뺭쿺짌좡믵늢뢶뿮ꆣ웤뷡릹죧춼pi055510560555605505555375j2ꆣhRi020202020202020202020202020260j쯦ퟅ쫐뎡뗄랢햹,뇘탫톰헒룼폐킧뗄쟾뗀쒣gi08888888888888104j쪽ꆣCi016161616161616161616161616208뺭맽쪵볹첽쯷뫍쫐뎡뗷퇐,춼3쯹쪾쒣쪽쿖j놻욡뻆웳튵죏캪쫇폐킧뗄럖쿺쒣쪽ꆣ헢훖쒣쪽뗄떥캻:di뫍pi캪쿤ö훜;gi캪풪ö쿤;hRi캪풪ö훜;Ci캪풪ö듎ꆣjjjjj쳘뗣쫇뇭3ꆡ룷쿺쫛뗣뗄믬뫏퓋쫤탨쟳싊(뗚2샠엤췋믵쾵춳):욡뻆웳튵퓚뛔뺭쿺짌뷸탐컯쇷엤쯍ꆢ탅쾢릲쿭뫍맜샭뗄춬쪱,뛔럖쿺짌튲뷸탐컯쇷엤뿍뮧012345678910111213ퟜ뫍쯍ꆢ탅쾢릲쿭뫍맜샭di055510560555605505555375,틔듋잿뮯럖쿺짌뛔쇣쫛짌j뗄뿘훆,뺭쿺짌뛔럖쿺짌컯쇷엤쯍횰쓜복죵ꆣpi030151525156520551045153035375j캪쇋쪵쪩룃쒣쪽,욡뻆뎧탨뗷헻엤쯍뫍쫕벯hRi020202020202020202020202020260j뻶닟,틔듯떽돉놾ퟮ뗍ꆣ틔쿂쫇룃욡뻆릫쮾퓚돉gi뚼뗄튻룶엤쯍훐탄럾컱13룶폐믬뫏퓋쫤탨쟳쿺08888888888888104j쫛뗣Ci016161616161616161616161616208j,룷쿺쫛뗣볤뎵솾뗄퓋탐돉놾볻뇭1,웤훐쫽ퟖ0듺뇭엤쯍훐탄,룷쿺쫛뗣뗄믬뫏퓋쫤탨쟳떥캻춬뇭2ꆣꆤ510ꆤ
튻뛔뛠엤췋믵쾵춳뗄잶쳗닟싔돉놾폅뮯쒣탍ꆪꆪ탬뻁욽ꆡ샗ꆡ헩뗄훘튪탔쾵쫽좡횵뗄뗷닩훐,톡퓱쇋Κ=015ꆣ쇮T24=1훜;뎵솾죝솿V=125쿤ö뎵,뚩믵훜웚B=1훜,늢뗚3쟸엤쯍훜웚T31=T32=0125훜,T33=짨1룶퓂캪4훜ꆣT34=1훜ꆣꆡ뗚1샠엤췋믵쾵춳쟳뷢뗚1쟸럑폃:퓋럑폫뚩믵럑캪31319풪,뿢룃릫쮾붫13룶뿍뮧럖캪3룶쟸,웤럖늼죧듦럑캪38715풪,랣뷰캪0풪,뗚1쟸ퟜ럑폃쿂:70114풪ꆣ뗚1쟸ꆡ{1,2,11,12,13},맊N1=5;뗚2쟸럑폃:퓋럑폫뚩믵럑캪26917풪,뿢뗚2쟸ꆡ{3,8,9,10},맊N2=4;듦럑캪425풪,랣뷰캪0풪,뗚2쟸ퟜ럑폃69417뗚3쟸ꆡ{4,5,6,7},맊N3=4;풪ꆣ엤쯍훐탄췋믵쟸죝솿Q=200쿤;뗚3쟸럑폃:퓋럑폫뚩믵럑캪30819풪,뿢룹뻝엤쯍뻶닟헟뗄틢춼,엤쯍럑폃훘튪탔쾵듦럑캪38715풪,랣뷰캪0풪,뗚3쟸ퟜ럑폃쫽좡Κ=016ꆣ69614풪ꆣ붫쫽뻝듸죫쪽(12),웤뛔펦뗄좨쾵쫽뗄럇뢺ퟜ럑폃캪209215풪ꆣ쿲솿캪w=T(015,014),뗃떽쒣탍:ꆡ뗚2샠엤췋믵쾵춳쟳뷢3Ni퓚뗚2샠쒣탍,평폚튪룄뷸TSP탐뎵슷뺶,min[(T)+(x)]={[66[(fi-ji=1j=1쯹틔튪볆쯣fiꆣ붫쫽뻝듸죫쪽(17),웤뛔펦뗄좨j3Ni-1쾵쫽뗄럇뢺쿲솿캪w=T(016,014)뗃떽쒣탍:fi)+Ci]Ti+j-1jj66diTihRiö2],+jjji=1j=13Ni3Nimin[(T)+(x)]={[66[(fi-j0i=1j=(pij-xij)},i=1j=13Ni10ꇜT11ꇜT12ꇜT13ꇜT14ꇜT15;fi)+C]T-i+ihRiö2],+j-1ijj66diTjjji=1j=10ꇜT21ꇜT22ꇜT23ꇜT24;3Ni0ꇜT31ꇜT32ꇜT33ꇜT34;(pi-xi)},jjji=1j=155T11+5T12+55T13+5T14+5T15ꇜ125;0ꇜT11ꇜT12ꇜT13ꇜT14ꇜT15;50T21+60T22+5T23+10T24ꇜ125;0ꇜT21ꇜT22ꇜT23ꇜT24;+60T32+5T33+5T34ꇜ125;0ꇜT31ꇜT32ꇜT33ꇜT34;(T11,ꆭ,T15,T21,ꆭ,T24,T31,ꆭ,T34)ꆣ55T11+5T12+55T13+5T14+5T15ꇜ125;ꆡꆡ(x11,ꆭ,x15,x21,ꆭ,x24,x31,ꆭT,x34)ꇜ200;50T21+60T22+5T23+10T24ꇜ125;+60T32+5T33+5T34ꇜ125;200ꇜ66piTi;jji=1j(T11,ꆭ,T15,T21,ꆭ,T24,T31,ꆭ,T34)ꆣ0ꇜxiꇜpi=diꆣꆡꆡT(xjjj11,ꆭ,x15,x21,ꆭ,x24,x31,ꆭ,x34)ꇜ200;닉폃LINGO죭볾뷸탐쟳뷢,캪쇋뇣폚닉폃3Ni죭볾쟳뷢,튪뛔쪽200ꇜ(12)훐뗄뇤솿T66piTi;jji뫍xi뷸탐뒦jji=1j샭,폃탂뇤솿xi(i=1,2,ꆭ,26)듺쳦,쯼쏇뗄뛔0ꇜxiꇜpiꆣjj펦맘쾵뫍퓋럑볆쯣싔ꆣ닉폃LINGO죭볾뷸탐쟳뷢,캪쇋뇣폚닉폃평뷡맻뾴돶,ퟮ폅뷢쫇1509117풪,떱죭볾쟳뷢,튪뛔쪽(17)훐뗄뇤솿Ti뫍xi뷸탐뒦jjQ=200쿤쪱,xi=pi,쯹폐뗄췋믵뚼믘쫕쇋ꆣ떫jj샭,폃탂뇤솿xi(i=1,2,ꆭ,26)듺쳦,웤뛔펦맘쫇Ti뚼늻럻뫏뛾듎쏝맦퓲,튪폃쪽(24)뗷헻ꆣj쾵뫍볆쯣뷡맻싔ꆣ퓚뗚1쟸폐솽훖쟩뿶-2,2<T11=T12=평볆쯣뷡맻뾴돶,ퟮ폅뷢쫇1576191풪,떱T13<-12뫍02<T14=T15<12;Q=200쿤쪱,쯹폐뗄췋믵뚼믘쫕쇋ꆣ떫쫇Tij뚼퓚뗚2쟸폐솽훖쟩뿶-2,2<T21=T22<-12늻럻뫏뛾듎쏝맦퓲,튪폃쪽(24)뗷헻ꆣ뫍02<T23=T24<12;퓚뗚1쟸폐튻훖쟩뿶-1:2<T11,T12,T13,퓚뗚3쟸폐솽훖쟩뿶-2,2<T31=T32<-12T14,T15<02;뫍02<T33=T34<12;퓚뗚2쟸폐솽훖쟩뿶-2:2<T21=T22<-12뗷헻볆쯣맽돌싔,뗷헻뷡맻죧쿂:뫍-12<T23=T24<02;뗚1쟸엤쯍훜웚T11=T12=T13=0125훜,퓚뗚3쟸폐솽훖쟩뿶-2:2<T31<-12뫍T-114=T15=1훜;2<T32=T33=T34<02ꆣ뗚2쟸엤쯍훜웚T21=T22=0125훜,T23=뗷헻볆쯣맽돌싔,뗷헻뷡맻죧쿂:ꆤ511ꆤ
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