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1811©Vol.18No.11200611JournalofSystemSimulationNov.,2006•3301•121.,110004;2.,110004FLOYDFLOYDTP29A1004-731X(2006)11-3301-04FuzzyProgrammingModelandAlgorithmofLogisticsDistributionVehicleRoutingProblemJIANGZhong-zhong1,WANGDing-wei2(1.SchoolofBusinessAdministration,NortheasternUniversity,Shenyang,110004,China;2.SchoolofInformationScienceandEngineering,NortheasternUniversity,Shenyang,110004,China)Abstract:Thelogisticsdistributionnetworksweredescribedinawayofanincompleteundigraph,whichconsistedoftwokindsofnodes,thedistributioncenternodesandthecustomernodes.Afuzzyprogrammingmodelwasbuilttooptimizelogisticsdistributionvehicleroutingproblem,wherevehicletraveltimeandcustomerservicetimearefuzzy.Themodelwasfirstlyconvertedintoacrispmulti-depotvehicleroutingproblem,andthenitwassolvedbyapredatorsearchalgorithmwithFLOYD.Computationonsimulationexamplesandcomparisonwithgeneticalgorithmshowthemodelandalgorithmareeffective.Keywords:logisticsdistribution;vehicleroutingproblem;fuzzyprogramming;FLOYD;predatorysearchalgorithm[1-2]VehicleRoutingProblem,VRPDantzigRamser1959VRPVRPVRPLaporte[3,4]VRP2005-07-042005-10-1170431003(1979-),,,,,;(1948-),,,,,,TeodorovicLaiVRP[5-6](1)FLOYD[7][8]1()1)2)1811Vol.18No.11200611Nov.,2006•3302•3)4)()()(),,ijijijkkjkjDkKiHjHkKijEijEMinCtxBMaxz∈∈∈∈∈∈∈+∑∑∑∑%(1)()()0,,.:,,ipkpjkpiDjDipEpjEstxxpSkK∈∈∈∈−=∈∈∑∑(2)(),,,ijkjkiHijExzjDkK∈∈≥∈∈∑(3)1,jkkKzjD∈=∈∑(4)(),pjkpjDkKMaxzApS∈∈≤∈∑(5)(),ljljkjDlLwqzQkK∈∈≤∈∑∑(6)0,,jlijiljDqyViSlL∈−≤∈∈∑(7)()(),,,,pkbjjkijijkpkepjDiHjHijEijETsztxTpSkK∈∈∈∈∈++≤∈∈∑∑∑%%(8)01,,,ijkxiHjHkK=∈∈∈(9)01,,ijyiSjD=∈∈(10)01,,jkzjDkK=∈∈(11)1G—G={S,D,E}S={n+1,….n+m}D={1,…n}E={(i,j),i,jH=SD}K—{Kn+1,….Kn+m}KiiKi∩Kj=Φ,(i≠j)L—{1,…T}Bk—kCij—k(i,j)qjl—jlQ—wl—l()Vil—ilTpkb—pkTpke—pkjs~—jijt~—ij2xijk,kijj10yij,ji10zjk,jk10123jkkj45678910110-1Fuzzymulti-depotvehicleroutingproblem,FMDVRP0-1(8)FMDVRP2(sj1,sj2,sj3)(tij1,tij2,tij3)jjs~(i,j)ijt~sj1tij1sj2tij2sj3tij3js~ijt~LiuIwamura[9]FMDVRP(8)fmin(12)()(){()},,.:ijijijkkjkjDkKiHjHkKijEijEstPosCtxBMaxzfα∈∈∈∈∈∈∈+≤≥∑∑∑∑%(13)()(){},,pkbjjkijijkpkejDiHjHijEijEPosTsztxTβ∈∈∈∈∈++≤≥∑∑∑%%(14)FMDVRPPos{·}{·}12(13)fα14(8)βαβ[10]Zadeh[11](13)1412()()[(1)](),,ijijijijkkjkjDkKiHjHkKijEijECttxBMaxzfαα∈∈∈∈∈∈∈−++≤∑∑∑∑(15)1212()()[(1)][(1)],,pkbjjjkijijijkpkejDiHjHijEijETsszttxTββββ∈∈∈∈∈+−++−+≤∑∑∑(16)(15)(16)(13)(14)αβFMDVRP1811Vol.18No.11200611,Nov.,2006•3303•Multi-depotvehicleroutingproblem,MDVRPαβMDVRP-α-βMDVRP-α-β3MDVRP-α-βMDVRP-α-βVRPFLOYDVRPVRPNP[12-13]VRPVRP――FLOYDMDVRP-α-β3.1LinharesAlexandre1998PredatorySearchAlgorithmPSA[14-15]3.23.2.1m-1n3101-2-3-4-0-5-6-7-0-8-9-100112342567389103.2.23.2.3f(x)FLOYD3.2.4A.1)xxmin=xcounter=0level=02)leveln+m-1xs(sn+m)xn_min3)3)f(xn_min)=Restriction(level)x=xn_min4)5)4)f(x)f(xmin)xmin=xlevel=0counter=02)5)5)counter=counter+1counterCOUNTER_MAX()level=level+1counter=06)2)6)level=[(n+m-1)/t]level=n+m-1-[(n+m-1)/t]([])tn+m-12)2)B.(Restriction)()1)n+m-2n+m-22)n+m-23)n+m-1Restriction(0),…,Restriction(n+m-2)431731Q=10Ap=3Bk=400Cij=2.5w1=0.2/w2=0.4/w3=0.3/8:0011:00js~(8,10,12)α=1.0β=0.9121(a,b,c)()abc123()1811Vol.18No.11200611Nov.,2006•3304•1131(2,1,3)8(1,2,3)15(1,1,1)2(3,2,1)9(2,1,1)16(3,2,1)3(4,1,2)10(1,2,1)17(1,1,2)4(1,1,1)11(2,3,2)5(3,3,2)12(1,1,1)18(31,32,28)6(1,2,3)13(4,2,2)19(29,37,30)7(2,1,2)14(2,1,2)20(33,35,32)2(1,2)(4,8,12)(7,18)(11,22,33)(11,19)(15,30,45)(1,3)(8,16,24)(7,19)(12,24,36)(11,20)(13,26,39)(2,3)(5,10,15)(8,10)(8,16,24)(12,14)(4,8,12)(3,4)(10,20,30)(8,18)(3,6,9)(12,19)(5,10,15)(3,8)(11,22,33)(9,11)(12,24,36)(13,20)(8,16,24)(3,18)(2,4,6)(9,18)(13,26,39)(14,15)(8,16,24)(4,5)(9,18,27)(9,19)(17,34,51)(14,17)(6,12,18)(4,7)(8,16,24)(9,20)(11,22,33)(15,16)(7,14,21)(5,6)(6,12,18)(10,13)(6,12,18)(15,20)(14,28,42)(6,7)(7,14,21)(10,18)(7,14,21)(16,17)(17,34,51)(6,19)(9,18,27)(10,20)(10,20,30)(17,19)(10,20,30)(7,9)(8,16,24)(11,12)(10,20,30)3()/9,11,13,10,818-9-11-20-13-10-8-1813,2,118-3-2-1-3-1812,14,15,16,1719-12-14-15-16-17-1926,5,419-6-5-4-5-6-1932495JavaWindowsP4/2.2G256M20COUNTER_MAX=100t=65003356(3)(0.80.0580500)1044(PSA)(GA)()()PSAGAPSAGA12525.02715.00.7510.91222500.02650.00.6811.11132495.02725.00.6910.83142510.02600.00.5110.86152580.02595.00.7610.93162555.02585.00.4810.89272495.02580.00.5210.95182555.02760.00.2510.87192515.02525.00.4200.912102500.02640.00.5000.8812523.02637.50.5570.91590.3225.30.4690.2314PSAGA10PSAGA4.34%2495.02525.0PSAGAPSAGAPSAGAPSAGAGA()PSAFLOYDPSAMDVRP-α-β5FLOYD[1]ElliotR,JosephPB.PhysicaldistributionservicequalityinInternetretailing:servicepricing,transactionattributes,andfirmattributes[J].JournalofOperationsManagement(S0272-6963),2004,21(6):651-672.[2],.B2C[J].,2005,34(4):481-485.[3]LaporteG,LouveauxF,MercureH.Thevehicleroutingproblemwithstochastictraveltimes[J].TransportationScience(S0041-1655),1992,26(3):161-170.[4],.[J].,2003,18(3):244-247.[5]TeodorovicD,KikuchiS.Applicationoffuzzysetstheorytothesavingbasedvehicleroutingalgorithm[J].CivilEngineeringSystems(S0263-0257),1991,8(2):87-93.33121811Vol.18No.11200611Nov.,2006•3312•(1)(2)(3)[1],[D].:,2004.[2]DoucetA,FreitasNd,GordonN.SequentialMonte