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146Vol.14,No.6200512OPERATIONSRESEARCHANDMANAGEMENTSCIENCEDec.2005:2005207204:(10171108):(19592),,,,:;(19742),,,;(19792),,,;(19502),,,:1,1,1,2(1.,100029;2.,):,,,,,:;;;;;:O221.7:A:100723221(2005)0620001207SomeAdvancesoftheResearchesonLocationProblemsYANGFeng2mei,HUAGuo2wei,DENGMeng,LIJian2qiang(SchoolofScience,BeijingUniversityofChemicalTechnology,Beijing100029,Chi2na;DepartmentofManagementSciences,CityUniversityofHongKong,HongKong)Abstract:Medianproblems,coveringproblemsandcenterproblemsarethreeclassiconesinlocationresearch.theirapplicationsareextensive,andtheyhaveprovidedastrongfoundationformanyofthelocationtheoryre2searchessofar.Inthispaper,asurveyoftheiradvancesinrecentyearsispresented,includingmodels,solu2tionapproachesandrelevantproblems,andpossibletrendsanddirectionsoffutureresearchareprovided.Keywords:operationalresearch;locationproblems;survey;medianproblems;coveringproblems;centerproblems0,,,,,,,,,,,1909,Weber[1](Weber),1964,Hakimi[2]p-p-,,,,,Hale[3]200433400,,,,,,,,[46],Weber--,,,[4]50NP-,,,,,,,[4,615],,1p-p-p,,(),(),,,,,,[16],,p-Hakimi[2],:p-[2,17],p-p-()p-(),,,KarivHakimip-NP-[18],np=n!p!(n-p)!=O(np),np,p-,np,p,p-NP-[5,19],p=1p=np-,nj=1nj=2n-1=O(2n)1.11-1-,1-O(n3),O(n2)1-[10]1-,,[20]Goldman[21],,O(n)[5,10]1.2p-(p2)p-[5],,,[10]p-,[5](myopicalgorithm)Lagrangian,,(2200514),O(pn2),,,,,Lagrangianp-,Lagrangian,,Lagrangian,,,,,1-(p-1)-3Lagrangian,p-,1-(p(1)-[22],p-,[23],[24]gamma,,(heuristicconcentration)[25][26][2729][30]p-,[31],,,[32]Lagrangian,p-,,[33,34]p-[35,36](branch2and2price)p-,p-,[37]O(n3p2),[18]O(n2p2),[38]O(n2p)2p-,,(),ABAB:1971Toregas[39],,,,,[40,41]:,,,,,ChurhRevelle[42]Hakimi,(),[43]:,(),,[44],,,,p-,[19][45]NP-,[5][46],,,[47]Lagrange[48,49][50,51][5255][56][57][58,59][60],[61],[62],-Lagrange[5,63][13]36,:3p-p-p,,,,p-,(),[16]p-Hakimi[2,17],p-p-,,Hakimip-,[5][64,65]p-:,p-,p,p-p-[5],,,,p,p-NP-[5,12,19],p-NP-[64],3.11-1-Hakimi,O(En2logn)[2],E,,[66]O(Enlogn),[64]O(Enlogn),O(En),[67]1-O(n3)()1-,GoldmanO(n2)[68],Halfin,O(n)[69]HandlerO(n)[70],,1-2-,1-,,,1-2-,O(n)[71]DearingFrancis1-O(n2)[72],Hakimi[66],KarivHakimiO(nlogn)[64]1-Jordan,1-[73][2]O(n3),[74]O(n)1-[75]1-1-1-3.2p-(p2)p-p-DreznerWesolowskyp-,Drezner2Wesolowsky[76][5,10]p-,p-,,,:,,p,,p,,,;Daskinp-,,[77],[78]p-,[79]p-[5]p-p-,[80]p-,4200514p-p-,[81],[82][64]p-,O(n2logn),[83]p-,O((nlogp)2)[10]p-4p-p-,,,,,,,,,,,,,,,,p-[5],,p-,,p-,[12]p-p-,,,[12][84],,,p-[85]p-[86]p-[87][88],[89,90],[91-93][93],Berman,(,)(,),,[94],p-[95,96]p-[95,97]p-[6,98]()p-[6](),[6,99](),,5,,,,;,,,,,,,;,,;,,[100]::[1]WeberA.Onthelocationofindustries[M].Chicago:UniversityofChicagoPress,1929.[2]HakimiSL.Optimumlocationsofswitchingcentersandtheabsolutecentersandmediansofagraph[J].OperationsResearch,1964,12:4502459.[3]HaleT.TrevorHalesLocationScienceReferences[EB/OL].[4]BrandeauM,ChiuSS.Anoverviewofrepresentativeproblemsinlocationresearch[J].ManagementScience,1989,35:6452674.[5]DaskinMS.Networkanddiscretelocation:modelsalgorithmsandapplications[M].NewYork:WileyInterscience,1995.[6]ErkutE,NeumanS.Analyticalmodelsforlocatingundesirablefacilities[J].EuropeanJournalofOperationalResearch,1989,40:2752291.[7]CurrentJ,MinH,SchillingD.Multiobjectiveanalysisoffacilitylocationdecisions[J].EuropeanJournalofOperationalResearch,1990,49:2952307.56,:[8]PlastriaF.Staticcompetitivefacilitylocation:anoverviewofoptimisationapproaches[J].EuropeanJournalofOperationalResearch,2001,129:4612470.[9]MinH,VaidyanathanJ,SrivastavaR.Combinedlocation2routingproblems:asynthesisandfutureresearchdirections[J].EuropeanJournalofOperationalResearch,1998,108:1215.[10]TanselBC,FrancisRL,LoweTJ.Locationonnetworks:asurveypart1:thep2centerandp2medianproblems[J].ManagementScience,1983,29,(4):4822497.[11]TanselBC,FrancisRL,LoweTJ.Locationonnetworks:asurvey,part2:exploitingtreenetworkstructure[J].ManagementScience,1983,29(4):4982511.[12]OwenSH,DaskinMS.Strategicfacilitylocation:areview[J].EuropeanJournalofOperationalResearch,1998,111:4232447.[13]SchillingDA,VaidyanathanJ,BarkhiLR.Areviewofcoveringproblemsinfacilitylocation[J].LocationScience,1993,1:25255.[14]RevelleCS,EiseltHA.Locationanalysis:asynthesisandsurvey[J].EuropeanJournalofOperationalResearch,2005,165:1219.[15]HaleTS,MobergCR.Locationscienceresearch:areview[J].AnnalsofOperationResearch,2003,123:21235.[16].2[M].:,2003.[17]HakimiSL.Optimumdistributionofswitchingcentersinacommunicationnetworkandsomerelatedgraphtheoreticproblems[J].OperationResearch,1965,13:4622475.[18]KarivO,HakimiSL.Analgorithmicapproachtonetworklocationproblems,part2:thep2medians[J].SIAMJournalAppliedMathematics,1979,37:5392560.[19],.-NP[M].,.:,1987.[20]HuaLG,etal..Applicationsofmathematicalmethodstowheatharvesting[J].ChineseMathematic,1962,2:77291.[21]GoldmanAJ.Optimumcenterlocationinsimplenetworks[J].TransportationScience,1971,5:2122221.[22]HansenP,MladenovicN.Variableneighborhoodsearchforthep2median[J].LocationScience,1997,5:2072226.[23]HribarM,DaskinMS.Adynamicprogrammingheuristicforthep2medianproblem[J].EuropeanJournalofOperational