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1。。。、、。、k-Harmonicmeans。k-Harmonicmeans。21909WeberWeber、()、、、、、。(UncapacitatedFacilityLocationProblem,UFLP)、。[1]UFLP123k-Harmonicmeans，，（，266510）[]k-Harmonicmeans。[]k-Harmonicmeans[]F224.0[]A[]1005-152X200911-0087-03LogisticsCenterLocationModelBasedonk-HarmonicClusteringAnalysisMeansLIQiang,ZHAOMao-xian,YANGLong-fei(SchoolofInformationScience&Engineering,ShandongUniversityofScience&Technology,Qingdao266510,China)Abstract:Thetransportcostinthetraditionallogisticslocationmodelisdiscussed.Thek-Harmonicclusteringanalyticalmeansareappliedinreconstructionofthetransportationcostintraditionallogisticslocationmodel.Thepointtopointdeliveryroutinginthepastissub-stitutedbycontinuouscircledeliveryroutingwhichismoreclosetorealityandalotofnumericalexperimentsprovethesuperiorityofthemeans.Keywords:clustering;logisticscenterlocation;k-Harmonicmeans[]2009-07-22[](Y2008A01)[](1984-)。s.t.k-Harmonicmeansdoi:10.3969/j.issn.1005-152X.2009.11.02887--2009281120620092811206456I={1,2…,n}J={1,2,…,m}fiicijj∈Ji∈I()p。xij0-1j∈Ji∈Ixij=10。yi0-1i∈Iyi=10。23p4iji(5)-(6)xijyi0-1。UFLP[2-6]UFLPUFLPcijcij。[7]k-HarmonicmeansUFLPcij。33.1、、、、、。CiiZniCi。1。“”。ZiiCiii=1,2,…NkStep1k=N,Ci={Zi},i=1,2,…,N。Step2ifk=KThenEnd。Step3CiCjd(Ci,Cj)。Step4CiCjCiCi。Step5Cjk=k-1gotoStep2。。2(k-Harmonicmeans)。k-meansK,K,k,K。,,。,KK,,,,。、。[8]k-Harmonicmeans。{Z}Sj(k)kjNjSj(k)Zj(k)kj{j=1,2,…,K}。k-HarmonicmeansStep1KKZ1(1),Z2(1)…,ZK(1)。Step2kZZ∈Zl(k)。Step3kjSj(k+1)Zj(k+1)。Step4j=1,2,…,KZj(k+1)=Zj(k)Zj(k+1)Zj(k)Step2。[7]cij、k-HarmonicmeanscijcijU-FLP。3.2。。[7]。k-Harmonicmeans。njBj88--ijcij=Bj/nk。Step1Kk-HarmonicmeansKS1(k),S2(k)…Sk(k)k。Step2nj(j=1,2,…,K)Sj(k)Bjcij=Bj/njij。Step3cijUFLP。3.3。(0,100)*(0,100)50I={(51.45,15.23),(17.89,71.41),(90.36,51.12),(21.43,4.24),(74.61,82.68),(32.41,85.51),(31.12,5.74),(37.19,76.95),(63.55,9.78),(80.84,17.50),(70.75,76.52),(3.77,96.22),(63.70,27.83),(26.55,79.87),(79.34,56.69),(10.29,35.55),(6.06,16.45),(76.63,82.40),(33.60,51.90),(51.28,78.22),(89.30,64.01),(65.52,41.08),(65.55,86.06),(61.76,5.64),(60.75,13.43),(47.02,74.22),(30.90,67.99),(64.52,39.19),(18.53,46.48),(37.38,57.65),(85.96,59.85),(70.25,97.00),(81.38,29.57),(6.81,31.10),(96.49,22.85),(7.99,34.69),(88.79,29.74),(47.08,10.68),(94.04,74.58),(21.45,48.49),(41.85,62.62),(70.95,49.67),(58.62,28.55),(21.87,82.00),(67.82,76.82),(53.14,37.99),(88.52,19.47),(30.38,8.49),(99.18,42.23),(15.18,93.90)}。(95,105)50505(p=5)。50UFLPcijLINGO(51.45,15.23),(70.75,76.52),(26.55,79.87),(10.29,35.55),(81.38,29.57)1。111240.88526。2481.76。k-Harmonicmeans5(52.15,16.34),(28.36,77.12),(83.17,40.23),(15.77,33.61),(71.37,81.79)2。5Matlab3。2k-Harmonicmeans335Bi117.0579,132.1640,136.0210,119.5754,107.2033jc1j=11.7c2j=12.02c3j=10.46c4j=14.95c5j=13.40。cijUFLPLINGOCij(31.12,5.74),(20.00,51.28),(21.00,89.30),(85.96,59.85),(6.81,31.10)4。（94）k-Harmonicmeans89--2009281120620092811206（89）41028.26447。4k-Harmonicmeans4k-Harmonicmeans。[][1]AndreasK,AndreasD.Facilitylocationmodelsfordistributionsystemdesign[J].EuropeanJournalOperationalResearch,2005,62:4-29.[2]DonaldE.Adual-basedprocedureforuncapacitatedfacilitylocation[J].OperationResearch,1978,26:992-1009.[3]GuignardM.ALagrangeandualascentalgorithmforsimpleplantlocationproblems[J].EuropeanJournalofOperationalResearch,1988,35:193-200.[4]ShmoysDB,TardosE,AardalK.Approximationalgorithmsforfacilitylocationproblems[A].Proceedingsofthe29thAnnualACMSymposiumonTheoryofComputing[C].1997265-274.[5]ChudakFA,Improvedapproximationalgorithmsforuncapacitatedfacilitylocation[A].Proceedingsofthe6thInternationalIPCOConference[C].In:LectureNotesinComputerScience,1999,3:1412-1420.[6]GoldengorinB,GhoshD,SierksmaG.Branchandpegalgorithmsforthesimpleplantlocationproblem[J].Computers&OperationsResearch,2003,30:967-981.[7],.[EB/OL].,2003,4:115-120.[8]BinZ,MeichunH.K-HarmonicMeans-ADataClusteringAlgorithm[EB/OL].。2、3、4516、876、8。1、2、3、4、5、7。51234561。[][1].[M].2009.[2].[D].20077～9.[3].[D].2006.[4].[J].2008116.[5].CBD[J].19996.[6].[D]..2006. !# $%&’ ()*+ ,)-. /0123 4%5’ 6 78 i9:; v 6 = 66 66 vc? ? ? ? ? ? ? ? 394--