컯쇷릤돌럖컶랽램ꆪꆪ 뗚죽헂 엤뎵엤쯍볆뮮 뗚죽헂 엤뎵엤쯍볆뮮 믹놾뗄뾼싇랽램 돇쫐쓚뗄벯엤뾨뎵뗄탐뚯ꎬ췹췹탨튪럃컊뛠룶뿍뮧ꆣ샽죧ꎬ퓚짌욷엤쯍믹뗘ꎨdeportꎩ붫짌욷ힰ짏뾨뎵ꎬ쯦뫳럃컊뛠룶뿍뮧ꎬ틀듎엤쯍짌욷ꎬ뛸뫳략믘춬튻룶엤쯍믹뗘ꆣ벯믵뗄쟩뿶쿂튲쫇샠쯆ꎬ듓엤쯍훐탄돶랢ꎬ틀듎럃컊뿍뮧쫕좡믵컯ꎬ뛸뫳략믘춳튻엤쯍믹뗘ꆣ 짏쫶샠탍뗄엤뎵엤쯍컊쳢ꎬ쫇퓚톲믘엤쯍뗄쟩뿶쿂ꎬ럖뇰뛔폚늻춬뎵솾뗄슷뺶뷸탐폅뮯ꆣ웤룸뚨뗄잰쳡쳵볾캪ꎺ뿍뮧뗄캻훃ꆢ뗀슷췸싧뗄쟩뿶ꆢ춨맽슷뛎쯹탨쪱볤ꆢ붻춨맜훆탅쾢뗈ꆣ퓚헢킩믹놾탅쾢뗄믹뒡짏ꎬ볓짏쎿쳬뗄뿍뮧퓋쯍쟫쟳ꆢ쪱볤뗄튪쟳ꆢ횸뚨볝쪻풱뗈탅쾢ꎬ뺭맽퓋쯣믱뗃뎵솾뗄슷쿟볆뮮랽낸ꆣ틔잰ꎬ헢훖릤ퟷ쫇춨맽쫖릤ퟷ튵살볓틔췪돉ꎬ벴쪹쫇폐뺭퇩뗄뗷뛈죋풱튲쫇탨튪쿠떱뗄쪱볤ꆣ쿖퓚ꎬ춨맽볆쯣믺죭볾ꎬ퓚뫜뛌뗄쪱볤쓚뻍뿉틔믱뗃ퟜ퓋쫤럑폃ꆢ늻춬뎵솾뗄샛볆퓋탐샯돌ꆢ샛볆엤쯍쪱볤ꆢힰ퓘킧싊뗈쫽뻝ꎬ듓뛸쪹뗃뚨솿뗄엤쯍볆뮮움볛뗃틔뷸탐ꆣ 톲믘폊뗝풱컊쳢 엤뎵엤쯍맦뮮ꎨVRP: vehicle routing and scheduling problemꎩ컊쳢튻횱쫴폚ORꎨoperations researchꎩ컊쳢뗄퇐뺿쇬폲ꆣ쫗쿈뷩짜엤뎵엤쯍컊쳢뗄풭쪼컊쳢ꆪꆪ폊뗝풱컊쳢ꆣ 폊뗝풱컊쳢뗄쫽톧쒣탍죧쿂쯹쫶ꆣ 짨폐n룶돇쫐ꎬ룸뚨쇋듓돇쫐i떽돇쫐j뗄럑폃cꆣ쒳룶폊뗝풱탨튪듓웤훐튻룶ij돇쫐돶랢ꎬ뛔쎿튻룶돇쫐럃컊튻듎ꎨ쟒횻럃컊튻듎ꎩꎬ좻뫳략믘돶랢뗄돇쫐ꆣ듓뿉쓜뗄슷쿟훐톰헒럑폃ퟮ킡뗄슷쿟ꆣ nnMinZ=cx()∑∑ijiji=1j==1∀i∈N()∑ijj=1nx=1∀j∈N()∑iji=1x≥1∀S⊂N(S≠φ,S≠N)()∑∑iji∈Sj∈N\Sx∈{0,1}∀i,j∈N()ij뛔폚짏쫶컊쳢뗄쫽톧뇭듯쪽캪죧쿂ꎺ 1
컯쇷릤돌럖컶랽램ꆪꆪ 뗚죽헂 엤뎵엤쯍볆뮮 웤훐ꎬ폐ꎺ Zꎺퟜ럑폃 cꎺ듓돇쫐I떽돇쫐j뗄럑폃ꆣ ijxꎺ떱슷쿟춨맽뇟(I,j)쪱캪1ꎬ럱퓲캪0ꆣ ijNꎺ돇쫐뷚뗣뗄벯뫏={1ꎬ2ꎬ3ꎬꆭꆭꎬn} Sꎺ캪N뗄늿럖벯뫏ꎨ늻쫇뿕벯뫏ꎬ튲늻뗈폚Nꎩꆣ 릫쪽ꎨꎩ뇭듯뗄듓돇쫐I떽웤쯼돇쫐뗄슷뺶횻폐1쳵ꎬ뛸릫쪽()뇭듯뗄쫇떽듯돇쫐j뗄슷뺶횻폐1쳵ꆣ뛸릫쪽()쯹뇭듯뗄쫇ꎺ슷뺶탨튪춨맽쎿룶돇쫐1듎ꎬ쟒횸춨맽튻듎ꎬ춼훐늻쓜훐뛏ꆣ릫쪽()훐뗄[\]캪벯뫏복램ꆣ릫쪽()튲뿉틔뇭듯캪ꎺ x≤S−1∀S⊂N(S≠φ,S≠N),2≤S≤n()∑∑iji∈Sj∈S 퓚릫쪽()믲ꎨꎩ훐ꎬ뷻횹죧춼쯹쪾뗄뻖늿믘슷돶쿖ꎬ춬쪱ꎬ|S|뇭쪾벯뫏S뗄풪쯘뗄쫽솿ꎨcardinalityꎩꆣ춼훐ꎬ쿔쪾쇋럃컊4룶돇쫐뗄슷뺶ꎬ퓚헢튻슷뺶훐ꎬ폐ꎺ x=0∑∑iji∈Sj∈S\Nx=2>S−1=1∑∑iji∈Sj∈S 틲듋늻싺ퟣ릫쪽ꎨꎩꎨꎩꆣ 12 34 춼 늿럖믘슷ꎨsubtourꎩ뗄쟩뿶 엤뎵엤쯍볆뮮 쒳룶퓋쫤웳튵뻟폐튻룶엤쯍훐탄ꎬm첨뾨뎵ꆣ듓엤쯍훐탄돶랢ꎬ닉폃뛠첨뾨뎵룸n룶뿍뮧쯍믵ꎨ믲헟듓n룶뿍뮧쓇샯벯믵ꎩꆣ헢쪱ꎬ쎿첨뾨뎵듓엤쯍훐탄돶랢ꎬ럃컊뛠룶뿍뮧횮뫳략믘엤쯍훐탄ꆣ헫뛔헢훖쟩뿶ꎬ쫔춼뷸탐죧쿂뻶닟ꎺ뫏샭뗄뻶뚨쎿첨뾨뎵뗄뿍뮧럖ퟩꎬ늢좷뚨뾨뎵뗄탎쪽슷뺶ꆣ 춼.쿔쪾쇋엤뎵엤쯍컊쳢뗄쫂샽ꎬ헢샯m=5ꎬn=8ꆣ퓚뿉릩쪹폃뗄5첨뎵훐ꎬ쪹폃2첨뎵솾췪돉8룶뿍뮧뗄엤쯍죎컱ꎬ웤탐뎵슷쿟죧춼쯹쪾ꆣ 2
컯쇷릤돌럖컶랽램ꆪꆪ 뗚죽헂 엤뎵엤쯍볆뮮 뾨뎵1 뾨뎵2 훐탄 춼.엤뎵엤쯍컊쳢뗄쫂샽 뛔폚헢훖믹놾뗄엤뎵엤쯍컊쳢ꎬ캪쇋뷸튻늽쫊펦쪵볊컊쳢ꎬ췹췹탨튪ힷ볓죧쿂튪쟳ꎺ ꎨ1ꎩ 뛔폚쎿룶맋뿍듦퓚럾컱쪱볤뗄쿞뚨ꆣ ꎨ2ꎩ 폐뛠룶엤쯍훐탄듦퓚ꆣ ꎨ3ꎩ 슷뛎쯹탨쪱볤붫퓚늻춬쪱뛎랢짺뇤뚯ꆣ 뾼싇헢퇹튻킩컊쳢뗄엤뎵엤쯍컊쳢붫퓚틔쿂볓틔쳖싛ꆣ 뻟폐쿞뚨쪱볤뗄좷뚨탍엤뎵엤쯍볆뮮 컊쳢뗄쫽톧쒣탍 떱듦퓚룷룶뿍뮧뷓쫜럾컱뗄쪱볤튪쟳ꎬ춬쪱엤쯍훐탄ꆢ뿍뮧횮볤뗄춨탐쯹탨쪱볤캪쫂쿈룸뚨뗄좷뚨쫽횵ꎬ뛔폚헢퇹뗄컊쳢돆캪뻟폐쿞뚨쪱볤뗄좷뚨탍엤뎵엤쯍볆뮮ꎨFVRP-TW: forecasted vehicle routing and scheduling problem with time windowꎩꆣ퓚헢튻컊쳢훐ꎬ닉폃ퟜ럑폃ퟷ캪쒿뇪몯쫽ꎬ뾼싇뛔폚헢튻쒿뇪몯쫽뗄ퟮ킡뮯컊쳢ꆣ mmmvvvvvMinC(t,X)=cδ(x)+C(t,x)+C(t,x)()0∑f,lll∑t,ll,0l∑p,ll,0ll=1l=1l=1 웤훐ꎬ NlvC(t,x)=c{Tt,n(i),n(i+1)+t}()t,ll,0lt,l∑l,n(i)c,n(i+1)i=0NlvvvaesaC(t,x)=[cmax{0,tt,x)−t}+cmax{0,t−tt,x)}]()p,ll,0l∑d,n(i)l,n(i)l,0ln(i)e,n(i)n(i)l,n(i)l,0li=0 짏쪽럾듓죧쿂쳵볾ꎺ 3
컯쇷릤돌럖컶랽램ꆪꆪ 뗚죽헂 엤뎵엤쯍볆뮮 n≥2()0,lmN=N()∑ll=1vD(n(i)=W(x)()∑llvn(i)∈xlvW(x)≤W()llc,lt≤t()sl,0′t≤t()l,0e 웤훐ꎬ Nl′t=t+{Tt,n(i),n(i+1)+t}()l,0l,0∑l,n(i)(i+1)i=0vvC(t,X)ꎺퟜ럑폃0vvtꎺ뇭쪾뾨뎵l듓훐탄돶랢쪱볤뗄쿲솿ꎬt={tl=1,m}00l,0vXꎺ뇭쪾헫뛔쯹폐뾨뎵뗄엤쯍슷쿟뗄맋뿍럖엤벰럃컊쮳탲뗄쫽쇐vvvꎨ쯹폐뗄n(i)뇘탫놻냼몬퓚X훐ꎩꎬX={xl=1,m}lvxꎺ뇭쪾럖엤룸뾨뎵l뗄엤쯍슷쿟뗄맋뿍뫍럃컊쮳탲뗄쫽쇐ꎬlvx={n(i),d(j)i=1,N,j=1,n}ll0,ln(i)ꎺ쒳뾨뎵뗚I룶럃컊뗄맋뿍뗄뷚뗣뇠뫅ꆣ d(j)ꎺ쒳뾨뎵뗚j룶럃컊뗄엤쯍훐탄뗄뇠뫅ꎨ헢샯=0ꎩꆣ Nꎺ뾨뎵l쯹럃컊뗄맋뿍ퟜ쫽ꆣ lvnꎺ쫽쇐x훐뗄d(j)뗄룶쫽ꆣ0,llmꎺ뿉쓜쪹폃뗄뾨뎵첨쫽뗄짏쿞ꆣ cꎺ뾨뎵l뗄만뚨럑폃f,l1쪹폃뾨뎵l쪱vδ(x)=ll0웤쯼쟩뿶쿂vC(t,x)ꎺ뾨뎵l뗄퓋탐럑폃t,ll,0lvC(t,x)ꎺ뾨뎵l뗄돍랣몯쫽횵p,ll,0lcꎺ뾨뎵l뗄떥캻쪱볤퓋탐럑폃ꆣt,ltꎺ뾨뎵l듓맋뿍n(i)뗄돶랢쪱볤ꆣl,n(i)Tt,n(i),n(i+1)ꎺ쪱뿌t뾨뎵l듓맋뿍n(i)떽맋뿍n(+1)뗄욽뻹쯹탨쪱볤ꆣl,n(i)l,n(i)tꎺ퓚맋뿍n(i)뗄믵컯ힰ킶쪱볤ꆣc,n(i)c(t)ꎺ뛔폚맋뿍n(i)뗄떥캻쪱볤퇓컳뗄돍랣횵ꆣd,n(i)c(t)ꎺ뛔폚맋뿍n(i)뗄떥캻쪱볤퓧떽뗄돍랣횵ꆣe,n(i)vatt,x)ꎺ뾨뎵l폚t듓엤쯍훐탄돶랢뗄뮰ꎬ떽듯뷚뗣n(i)뗄쪱뿌l,n(i)l,0ll,0Nꎺ맋뿍뗄ퟜ쫽ꆣ D(n(I))ꎺ맋뿍n(I)뗄탨쟳ꆣ 4
컯쇷릤돌럖컶랽램ꆪꆪ 뗚죽헂 엤뎵엤쯍볆뮮 ′tꎺ뾨뎵l략믘엤쯍훐탄뗄쪱뿌ꆣl,0tsꎺ뾨뎵돶쟚뿉쓜쪱볤뗄뾪쪼쪱뿌ꆣ teꎺ뾨뎵돶쟚뿉쓜쪱볤뗄훕횹쪱뿌ꆣ vW(x)ꎺ뾨뎵l뗄ힰ퓘솿ꆣllWꎺ뾨뎵l뗄퓘훘솿ꆣc,l 릫쪽ꎨꎩ쮵쏷ퟜ럑폃뗄ퟮ킡뮯ꎬ폒닠뗚1쿮쫇뾨뎵뗄만뚨럑폃ꎬ뗚2쿮쫇뾨뎵뗄퓋탐럑폃ꎬ뗚3쿮뇭쪾뛔폚늻싺ퟣ쪱볤뒰쟩뿶쿂뗄돍랣ꆣ퓚뾨뎵뗄퓋탐훐ꎬ뻟폐폫퓋탐쪱볤컞맘뗄뗄만뚨럑폃ꎬ틔벰쯦퓋탐쪱볤뇤뮯뗄퓋탐럑폃ꆣ 만뚨럑폃냼삨뎵솾럑ꆢ쮰뷰ꆢ놣쿕뗈ꎬ퓋탐럑냼삨폍쇏럑ꆢ탞샭럑ꆢ싖첥럑폃ꆢ죋솦럑ꆢ뗀슷쫕럑뗈ꆣ돍랣몯쫽퓚퓧떽맋뿍뒦쟩뿶쿂캪믺믡쯰쪧럑폃ꎬ췭떽쟩뿶쿂캪컳뗣쯰쪧럑폃ꆣ 튻냣쟩뿶쿂ꎬ뿉틔닉폃죧춼쯹쪾뗄돍랣몯쫽탎쪽ꆣ 럑폃 C d,n(I) 1C e,n(I)1 쪱볤 춼 돍랣몯쫽 컊쳢뗄뷢램 짏쫶FVRP-TW캪NP삧쓑ꎨnon-deterministic polynomial hardꎩ뗄ퟩ뫏폅뮯컊쳢ꎬ쓑틔쟳뗃퇏쏜뷢ꎬ틲듋늻뗃늻닉폃쫔첽랽램ꎨheuristicsꎩ쟳뷢뷼쯆뷢ꆣ 쫔첽랽램뛠훖탎쪽ꎬ퓚FVRP-TW컊쳢짏뺭뎣쪹폃뗄폐ꎺ틅뒫쯣램ꎨGA: genetic algorithmsꎩꆢ쒣쓢췋믰램ꎨSA: simulated annealingꎩꆢTSꎨTS: tabu searchꎩ뗈ꆣ 틅뒫쯣램쫇쒣쓢짺컯뷸뮯맽돌뗄폅뮯쯑쯷랽램ꎬ쫗쿈뻶뚨룷룶쳥ꎨindividualꎩ뗄좾즫쳥ꎨchromosomeꎩꆣ뛸좾즫쳥퓲평뛠룶틅뒫틲ퟓꎨgeneꎩ쯹릹돉ꎬ좾즫쳥뗄쓚늿쳘헷놻돆캪틅뒫틲ퟓ샠탍ꎨgenotypeꎩꆣ 춼.뇭쪾쇋엤뎵엤쯍볆뮮훐뗄틅뒫틲ퟓ샠탍ꆣ퓚춼훐뿉틔뾴떽ꎬ틅뒫틲ퟓ샠탍쯹랴펳뗄쫇ꎬ듓엤쯍훐탄ꎨ뷚뗣0ꎩ돶랢ꎬ톲믘맋뿍1-5횮뫳략믘춬튻룶엤쯍훐탄ꎬ헢퇹튻훖뾨뎵뗄퓋탐뚯ퟷꆣ 0 521340 춼. 엤뎵엤쯍볆뮮훐틅뒫틲ퟓ샠 닺짺뛠룶뻟폐틅뒫틲ퟓ샠탍뗄룶쳥ꎬ쪵쪩쳔청ꎨselectionꎩ틔벰퓶횳ꎨmultiplicationꎩꆣ헢쪱탨튪볆쯣룷룶룶쳥뗄쫊펦뛈ꎬ쫊펦뛈룟뗄룶쳥붫퓚쿂튻듺 5
컯쇷릤돌럖컶랽램ꆪꆪ 뗚죽헂 엤뎵엤쯍볆뮮 훐볌탸짺듦ꆣퟷ캪쫊펦뛈뿉틔ퟷ죧쿂뾼싇ꎺ샽죧뛔폚닉폃릫쪽()뗄ퟜ럑폃ퟮ킡뮯컊쳢ꎬ뿉틔붫ퟜ럑폃뗄쓦쫽ퟷ캪쫊펦뛈ꆣ뷶톡퓱쫊펦뛈룟뗄룶쳥퓚쿂튻듺훐짺듦뗄뮰ꎬ폐뿉쓜쿝폚뻖늿뷢뛸컞램듯떽헦헽뗄ퟮ폅뷢ꎬ캪듋ꎬ퓚틅뒫쯣램훐쇮늿럖틅뒫틲ퟓ샠탍뷸탐붻닦ꎨcrossoverꎩ믲춻좻뇤틬ꎨmutationꎩꆣ붻닦뗄샠탍뿉틔폐1뗣붻닦ꆢ2뗣붻닦ꆢ튻퇹붻닦ꆢ쮳탲붻닦뗈ꆣ붻닦믲뇤틬뗄뇈싊돆캪붻닦싊믲춻좻뇤틬싊ꎬ탨튪룹뻝늻춬컊쳢볓틔뻶뚨ꆣ SA쫇쒣쓢만쳥뗄췋믰맽돌뗄쯣램ꎬ폃폚쟳뷢ퟩ뫏폅뮯컊쳢ꆣ퓚죈솦톧훐ꎬ퓚컂뛈t쳵볾쿂쿠펦폚쓜솿듳킡ꛄE뗄퓶볓룅싊평틔쿂릫쪽룸돶ꆣ δEp(δE)=exp−()kt 헢샯ꎬk캪늨듄싼뎣쫽ꆣ붫죈솦톧훐뗄쓜솿훃뮻돉캪ퟩ뫏폅뮯컊쳢훐뗄쒿뇪몯쫽ꎬ뻍뿉틔닉폃샠쯆뗄랽램쟳뷢ퟩ뫏폅뮯컊쳢ꆣ 샽죧퓚춼.훐ꎬ짨쒿뇪몯쫽뗄뇤뮯솿캪ꚤEꆣ뾼싇듓떱잰뷢A쿲쇚뷢B쫇럱뷸탐틆뚯쪱ꎬ떱ꚤEꇜ0쪱ꎬB캻훃뗄쒿뇪몯쫽횵킡폚믲헟뗈폚A캻훃뗄쒿뇪몯쫽횵ꎬ쯹틔좷뚨쿲B틆뚯ꆣ A B DC E 춼. 쒣쓢췋믰램쒿뇪몯쫽뗄쪾샽 뛸퓚좷뚨쫇럱듓캻훃C쿲캻훃D틆뚯쪱ꎬ평폚떱잰캻훃뗄ꚤEꆵ0ꎬ탨튪룹뻝틔쿂뗄룅싊횵뻶뚨쫇럱틆뚯ꆣ ∆Ep(∆E)=exp−()T 짏쪽훐T캪볙쿫컂뛈ꆣ 튲뻍쫇쮵ꎬ쯤좻D캴횪뗄쒿뇪몯쫽횵뇈C캻훃뗄쒿뇪몯쫽횵뮹튪닮ꎬ떫죔좻룹뻝릫쪽() 룸돶뗄룅싊뷸탐틆뚯ꎬ헢퇹뿉틔럀횹쿝폚뻖늿ퟮ폅뷢컞램췑돶ꎬ뛸퓬돉늻쓜쫕솲폚좫뻖ퟮ폅뷢뗄쟩뿶돶쿖ꆣ 볙쿫컂뛈뗄붵컂ꎬ뿉틔닉폃죧쿂뗄뛔쫽샤좴믲벸뫎샤좴뗄랽램ꆣ α뛔쫽샤좴T(i)=()log(i+1)벸뫎샤좴T(i+1)=αT(i)() 웤훐ꎬꛁ캪샤좴닎쫽ꎬI캪뗼듺듎쫽ꆣ 6
컯쇷릤돌럖컶랽램ꆪꆪ 뗚죽헂 엤뎵엤쯍볆뮮 펦폃쫂샽 펦폃짏쫶쒣탍ꎬ틔벰뚯첬붻춨럂헦뗄ퟩ뫏쒣탍ꎬ평마뿚뗈퓚볙쿫뗄뗀슷췸싧짌뷸탐쇋쫔쯣ꆣ헢튻볙쿫뗀슷췸싧캪25룶뷚뗣ꎬ40쳵뇟릹돉뗄랽룱췸싧ꆣ퓚헢튻뗀슷췸싧짏ꎬ10볒퓋쫤웳튵럖뇰펵폐룷ퟔ1룶엤쯍훐탄ꎬퟮ듳퓘훘2뛖ꆢ4뛖ꆢ8뛖뗄벯엤뾨뎵럖뇰룷폐4첨ꎬ릲12첨뷸탐퓋탐ꎬ볙짨뛔폚5~24룶뿍뮧뷸탐믵컯엤쯍ꆣ춬쪱ꎬ엤쯍훐탄뫍뿍뮧뗄캻훃캪쯦믺룸돶ꆣ룷뿍뮧뻟폐룷ퟔ튪쟳뗄쪱볤뒰ꆣ 뛔폚헢퇹튻룶닢쫔컊쳢ꎬ룷퓋쫤웳튵내헕릫쪽ꎨꎩ뚨틥뗄ퟜ럑폃ퟮ킡뮯훆뚨엤쯍볆뮮뗄쟩뿶쿂ꎬ뇈뷏뒫춳엤쯍랽쪽뷚풼35%뗄ퟜ럑폃ꎬ퓋쫤뎵솾퓋탐뻠샫복짙20%ꎬCO2복짙3%ꆣ 헢퇹뗄킧맻쮵쏷ꎬ떼죫쿈뷸엤뎵엤쯍볆뮮벼쫵늻뷶뛔폚퓋쫤웳튵뻟폐붵뗍럑폃뗄킧맻ꎬ뛸쟒뻟폐룄짆붻춨뮷뺳ꎬ붵뗍붻춨펵ퟨ뗄ퟷ폃ꆣ춬쪱ꎬ닢쫔뮹쿔쪾ꎺ죧맻10볒웳튵훐폐2볒쪵탐릲춬엤쯍뗄뮰ꎬ붫뿉쓜붵뗍럑폃20%ꎬ냼삨뿍퓋뎵솾퓚쓚뗄퓋탐쪱볤복짙5%ꆣ 뢽볓쪱볤뒰뗄룅싊탍엤뎵엤쯍볆뮮 쫽톧쒣탍뗄붨솢 짏튻뷚훐쯹쳖싛뗄엤뎵엤쯍볆뮮컊쳢훐ꎬ폐맘뗀슷췸싧룷슷뛎쯹탨춨탐쪱볤뗄풤닢횵뻹캪좷뚨쫽횵ꎬ뛸쪵볊짏쯹탨퓋탐쪱볤튻횱뒦폚뇤뚯횮훐ꆣ캪듋ꎬ놾뷚쳖싛쯹탨퓋탐쪱볤뇤뚯쟩뿶쿂뗄룅싊탍엤뎵엤쯍볆뮮ꎨPVRP-TW: probabilistic vehicle routing and scheduling problem with time windowꎩꆣ샠쯆뗚3뷚ꎬ뾼싇ퟜ럑폃ퟮ킡붨솢쫽톧쒣탍ꆣ mmmvvvvMinC(t,X)=cδ(x)+E[C(t,x)]+E[C(t,x)]()0∑f,lll∑t,ll,0l∑p,ll,0ll=1l=1l=1 웤훐폐ꎺ NlvE[C(t,x)]=c{Tt,n(i),n(i+1)+t}()t,ll,0lt,l∑l,n(i)c,n(i+1)i=0 ∞NlvvE[C(t,x)]=pt,t,x){c(t)+c(t)}dt()p,ll,0l∑l,n(i)l,0ld,n(i)e,n(i)∫i=00 ꎨꎩ쪽럾듓틔쿂풼쫸쳵볾ꎺ 7
컯쇷릤돌럖컶랽램ꆪꆪ 뗚죽헂 엤뎵엤쯍볆뮮 n≥2()0,lmN=N()∑ll=1vD(n(i)=W(x)()∑llvn(i)∈xlvW(x)≤W()llc,lt≤t()sl,0′t≤t()l,0e 웤훐ꎬ폐ꎺ Nl′t=t+{Tt,n(i),n(i+1)+t}()l,0l,0∑l,n(i)c,n(i+1)i=0 짏쫶릫쪽훐ꎬ폐맘볇뫅폫릫쪽()~()쿠춬ꎬ탨튪쳭볓쮵쏷뗄쫇ꎺ vp(t,t,x)ꎺ듓엤쯍훐탄폚쪱뿌t돶랢뗄뾨뎵퓚쪱뿌t떽듯맋뿍n(i)뒦뗄룅싊ꆣl,n(i)l,0ll,0 릫쪽ꎨꎩ-ꎨꎩ쯹뚨틥뗄컊쳢ꎬ쫇룹뻝ퟜ럑폃ퟮ킡뗄풭퓲ꎬ좷뚨뇭쫶쯹폐뾨뎵쿠맘엤쯍슷뺶뗄맋뿍럖엤틔벰럃컊쮳탲뗄Xꎬ뻶뚨뾨뎵듓엤쯍훐탄돶랢뗄쪱뿌t뗄ퟩ뫏폅뮯컊쳢ꆣ 0뛔폚닉폃룅싊뗄랽램쏨쫶쿠뛔폚룷맋뿍뗄동떽ꆢ퓧떽뗄돍랣몯쫽ꎬ붫늻춬폚틔잰뗄랽램ꎬ튲뻍쫇쮵탨튪룄뇤릫쪽ꎨꎩ캪릫쪽ꎨꎩꆣ뛔폚릫쪽ꎨꎩ쯹뇭듯뗄퓋탐쪱볤ꎬ튲뿉틔닉폃룅싊싛뗄랽램살볓틔뒦샭ꎬ떫쫇캪쇋볲뮯쳖싛ꎬ헢샯뷶붫퓧떽ꆢ동떽돍랣몯쫽닉폃룅싊뒦샭ꆣ 춼뇭듯쇋뛔폚동떽ꆢ퓧떽뗄돍랣몯쫽뗄뾼싇랽램ꆣ맋뿍웚췻뗄떽듯쪱볤듸캪ꎺ es∆t=(t−t)n(i)n(i) 퓧떽듯뗄쟩뿶쿂ꎬ평폚탨튪뗈떽풤뚩쪱뿌닅쓜릻쳡릩럾컱ꎬ틲듋탨튪쿻뫄폫쪱볤돉뇈샽뗄럑폃ꎬ뛸퇓컳뗄쟩뿶쿂ꎬ탨튪횧뢶폫퇓컳쪱볤돉뇈샽뗄랣뷰ꆣ붫돍랣몯쫽폫뾨뎵떽듯룅싊ퟩ뫏웰살ꎬ뿉틔믱뗃룅싊쳵볾쿂뗄퓧떽벰퇓컳돍랣횵ꆣ 8
컯쇷릤돌럖컶랽램ꆪꆪ 뗚죽헂 엤뎵엤쯍볆뮮 Cd,n(i) Ce,n(i) 1 1se떽듯쪱뿌[럖] ttn(i)n(i) 떽듯쪱뿌뗄룅싊 떽듯쪱뿌[럖] 퓧떽믲동떽뗄돍랣횵 떽듯쪱뿌[럖] 춼. 룅싊탍엤뎵엤쯍볆뮮훐뗄퓧떽벰동떽돍랣몯쫽 쪹폃쪾샽 [1]마뿚뗈붫짏뷚훐쯹붨솢뗄뾼싇쯹탨쪱볤뇤뚯뗄쫽톧쒣탍ꎬ퓚폫.훐춬퇹뗄뗀슷췸싧짌뷸탐쇋닢쫔ꆣ헢튻볙쿫뗀슷췸싧캪25룶뷚뗣ꎬ40쳵뇟릹돉뗄랽룱췸싧ꆣ퓚헢튻뗀슷췸싧짏ꎬ10볒퓋쫤웳튵럖뇰펵폐룷ퟔ1룶엤쯍훐탄ꎬퟮ듳퓘훘2뛖ꆢ4뛖ꆢ8뛖뗄벯엤뾨뎵럖뇰룷폐4첨ꎬ릲12첨뷸탐퓋탐ꎬ볙짨뛔폚14~22룶뿍뮧뷸탐믵컯엤쯍ꆣ춬쪱ꎬ엤쯍훐탄뫍뿍뮧뗄캻훃캪쯦믺룸돶ꆣ 붫엤뎵엤쯍볆뮮쒣탍폫뚯첬붻춨럂헦쒣탍쿠뷡뫏ꎬ뷸탐쇋10듎ꎨ10죕ꎩ볆쯣ꆣ캪쇋랴펳쎿쳬뗄붻춨뇤뮯ꎬ붫뇭쫶럇펵벷붻춨ힴ첬뗄닺짺붻춨솿ퟷ캪믹놾쫽횵ꎬ퓚ꇀ10%랶캧쓚쯦믺뇤뚯ꆣ듋췢ꎬ퓚뗚11죕뗄쟩뿶훐짨솢붻춨ힴ첬랢짺벱뇤ꆣ샻폃짏쫶짨훃ꎬ붫룅싊탍엤뎵엤쯍쒣탍폫좷뚨탍엤뎵엤쯍쒣탍퓚ퟜ럑폃벰뮷뺳랽쏦뷸탐뇈뷏ꆣ 웤닢쫔뷡맻ꎬ퓚붻춨늻첫펵벷뗄쟩뿶쿂ꎨ욽뻹쯙뛈=38km/hꎩꎬ닉폃룅싊탍엤뎵엤쯍볆뮮쒣탍쿠뇈좷뚨탍엤뎵엤쯍볆뮮쒣탍ꎬ퓋쫤웳튵뗄ퟜ럑폃복짙풼11%ꆣ뛸퓚펵벷뗄ힴ첬쿂ꎨ욽뻹쯙뛈=30km/hꎩꎬퟜ럑폃복짙풼14%ꆣ 룅싊쒣탍복짙럑폃뗄풭틲퓚폚ꎺ동떽돍랣뇈뷏퓧떽돍랣튪훘ꎬ퓚룅싊쒣탍훐ꎬ뻟폐뺡뿉쓜뇜쏢동떽ꎬ뛸쓾풸퓧떽뗄쟣쿲ꆣ벴쪹퓚붻춨펵벷뗄ힴ뿶쿂ꎬ캪쇋룏짏맋뿍횸뚨뗄쪱볤랶캧ꎬ늻듳믡랢짺동떽뗄쟩뿶ꆣ캪듋ꎬ풽쫇붻춨펵벷뗄쟩뿶쿂ꎬ룅싊탍엤뎵엤쯍볆뮮쒣탍풽쓜릻좡뗃붵뗍럑폃뗄킧맻ꆣ [1]th Taniguchi, E. T. Yamada and Y. Kakimoto, Probabilistic vehicle routing and scheduling with variable travel times. 9 IFAC Symposium Control in Transportation Systems 2000, pp. 45-50, 2000. 9
컯쇷릤돌럖컶랽램ꆪꆪ 뗚죽헂 엤뎵엤쯍볆뮮 듋췢ꎬ듓뮷뺳펰쿬랽쏦뗄뾼싇살뾴ꎬ뛔폚CO2업럅솿뗄뇈뷏ꎬ퓚붻춨늻첫펵벷뗄쟩뿶쿂ꎨ욽뻹쯙뛈=38km/hꎩꎬ룅싊탍엤뎵엤쯍볆뮮쒣탍뇈뷏좷뚨탍엤뎵엤쯍볆뮮쒣탍ꎬ붵뗍쇋%뗄업럅솿ꆣ퓚붻춨펵벷ힴ첬ꎨ욽뻹쯙뛈=30km/hꎩꎬ붵뗍쇋%뗄업럅솿ꆣ 틲듋뿉틔쮵ꎬ펦폃뾼싇쯹탨쪱볤뇤뮯뗄룅싊탍엤뎵엤쯍볆뮮쒣탍ꎬ늻뷶뛔폚웳튵뻟폐붵뗍돉놾뗄폅뗣ꎬ뛸쟒뛔폚짧믡살쮵튲붵뗍쇋뮷뺳펰쿬ꆣ 10
