一类运输问题的非线性规划模型

2002211222,20032022093,33541004(Dept.ofComp.Sci.andAppliedPhy.,GuilinUniv.ofElec.Tech.,Guilin,Guangxi,541004,China)GuangxiSciences2003,10(2):86913AContinuumandNonlinearProgrammingModelofTransportProblem33HeDengxuCaoDunqianMoYongxiangSongXueqiang(80530006)(Dept.ofMath.andComp.Sci.,GuangxiUniv.forNationalities,80Daxuelu,Nanning,Guangxi,530006,China),,LINGO6.0,,,O22112:U116AbstractAsecondtimeprogrammingmodelforpurchaseandtransportationofsteeltubesisdevelopedforalinearprogrammingmodeoftransportcostandpathlength,demandofdestinationsandunknownpriceofgoods,AcomplexproblemareslovedusingthesoftwareLINGO6.0.Themodelcouldbegenelizedandappliedtosolutionofsimilarproblems.Keywordstransportproblem,mathematicalmodel,nonlinearprogramming,shortestpath11A1A2A15,1.7S1,S2,,S7.,,(,),,(km).,1km1.1,500.Sisi,1Pi,11211000km1Table1Yieldandunitpriceofsteeltubesofasteelmillisi(Unit)Pi(Tenthousandyuan)1800160280015531000155420001605200015562000150730001602Table2TransportcostsofrailwayMileage(km)Transportcost(Tenthou2sandyuan)Mileage(km)Transportcost(Tenthou2sandyuan)30020501600373013502360170044351400267018005040145029801900554515003290110006068GuangxiSciences,Vol110No12,May2003©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(kmkm).(A1,A2,,A15,).1,().2,,,,21.2,.,:1SiAjSiAj.,,[1,3]..(),.,,:,.,,,,.31;2,:,;3,:(A1,A2,);4,.,km,.4,1.411,,..,.(),.,1,(Bi),2,1.,,()..:(É)1,1.,2,1,1,7820035102©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(Ê)1().1,3.31Fig13Simplifiedfig113,().,2,13.:111,,3,.,31.,S1B1=160,B1A2=0.3,A1A2=10.4.,.3,Dijkstra[3][4]SiAj,.,,,[4].412()SiAjxij,,71=7i=115j=1Pixij.wijSiAj,72=7i=115j=1(wij)xij.Aj,.3,2,2,AjLj,Rj,Rj+Lj=7i=1xij,j=1,2,,15,R15=0,L1=0.(1)4,,Ajtkm,Lj-t,Aj(73)Lj=eõLj0(Lj-t)dt=12õeL2j.e1,Aj(73)Rj=eõRj0(Rj-t)dt=12õeR2j.73=15j=1((73)Lj+(73)Rj)=15j=112õe(L2j+R2j)..,7=71+72+73=7i=115j=1Pixij+7i=115j=1wijxij+15j=112õe(L2j+R2j).(2)4135171,,7i=115j=1xij=5171.(3)4,(),Rj+Lj+1=AjAj+1,j=1,2,,14,(4)AjAj+1AjAj+1.Sisi,15j=1xijsi,i=1,2,,7.(5).,500,,0.15j=1xij=0,15j=1xij500,i=1,2,,7,(6),():15j=1xij(15j=1xij-500)0,i=1,2,,7.(7)414(1)(7):88GuangxiSciences,Vol110No12,May2003©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=7i=115j=1Pixij+7i=115j=1wijxij+15j=112õe(L2j+R2j).S.T.7i=115j=1xij=5171.15j=1xijsi,i=1,2,,7,Rj+Lj=7i=1xij,j=1,2,,15,R15=0,L1=0.(9)Rj+Lj+1=AjAj+1,j=1,2,,14,15j=1xij(15j=1xij-500)0,i=1,2,,7,xij0,i=1,,7,j=1,,15..51.,.LINGO610,,.,3,71=797725;,3,72=399731.55;,4,73=15j=112e(R2j+L2j)=80916.45.7=71+72+73=1278373.6,,,,,.,21.,,.2,4,214,3,31Table3PlansonconveyingofthesteeltubespurchasedfromsteelmilltothepavingpointinFig.1SteelmillPurchase(Units)Expenses(Tenthousandyuan)(1)Transportroute(infig1)xijQuantitesxij(Units)Unitprice(Tenthousandyuan)Transportcosts(Tenthousandyuan)S1800.0128000S1B6B5B4A5334.538.012711.0S1B6B5A6200.020.54100.00S1B7A7265.53.1823.05S2800.0124000S2B8B3B1A2179.0205.336748.70S2B3A4134.1171.623011.56S2B8B7B6B5B4A5186.9111.020745.90S2B8A8300.071.221360.00S31000.0155000S3B9B8B7B6B5B4A5A4333.9181.660636.24S3B9B8B7B6B5B4A52.1121.0254.10S3B9A9664.048.232004.80S40.00Non0.00.00.00S51015.0157325S5B11B10B9B8B3B2A3508.0225.2114401.60S5B11B10B9B8B7B6B5B4A592.0146.013432.00S5B11A11415.033.013695.00S61556.0233400S6B15B13B10A10351.062.021762.00S6B15B13B12A1286.045.03870.00S6B15B13A13333.026.28724.60S6A14621.011.06831.00S6B15B16A15165.028.04620.00S70.00Non0.00.00.00Total5171.07977255171.01547.9399731.559820035102©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(Units)Rj(Units)Transportcost(Tenthousandyuan)j(Units)Lj(Units)Rj(Units)Transportcost(Tenthousandyuan)10.00.00.09505.0159.014015.32104.075.0822.0510321.030.05197.053226.0282.06530.011270.0145.04696.254468.00.010951.21275.011.0287.35606.09.518366.312513199.0134.02877.856184.515.51714.02514286.0335.09701.057189.576.02084.312515165.00.01361.258125.0175.02312.5(Total)80916.453,D1j,D2j,D3jAj3,(4):(i)Aj1,,D1j,D2j=0,D3j=0.A1,A15,A16,A18,A21;(ii)Aj2,2,D1j,D2j,D3j=0.A2,A3,A4,A5,A6,A7,A8,A10,A12,A13,A14,A19,A20.(iii)Aj3,D1j,D2j,D3j.A9,A11,A17.:min7=7i=121j=1Pixij+7i=115j=1wijxij+21j=112õe(D12j+D22j+D32j).S.T.7i=121j=1xij=5903,21j=1xijsi,i=1,2,,7,21j=1xij(21j=1xij-500)0,i=1,2,,7,D1j+D2j+D3j=7i=1xij,j=1,2,,21,D2j+D1j+1=AjAj+1,j=1,2,,14,D39+D116=42,D311+D117=10,D217+D118=130,D317+D119=190,D219+D120=260,D220+D121=100,D11=D215=D216=D316=D218=0,D318=D319=D320=D221=D321=0,D3j=0,j=1,,8,10,12,,15.xij0,i=1,,7,j=1,,21.56.71=910515,72=412089.55,73=21j=112e(D12j+D22j+D32j)=86087.15,7=71+72+73=1408691.7.7,,,,.,,.,.42Fig4Simplifiedfig.209GuangxiSciences,Vol110No12,May2003©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(Units)Expenses(Tenthou2sandyuan)(1)Transport