SCM-2LogisticsNetworkConfiguration供应链管理课件

物流网络设计

LogisticsNetworkConfiguration物流网络设计

LogisticsNetworkConf1

OutlineWhatisit?方法Methodology

–建模Modeling–数据合并DataAggregation–确认可靠性ValidationSolutionTechniques

OutlineWhatisit?2物流网络TheLogisticsNetwork物流网络包括:节点:Vendors（供应商）,ManufacturingCenters,Warehouse/DistributionCenters,andCustomersRawmaterials原材料andfinishedproductsthatflowbetweenthefacilities.物流网络TheLogisticsNetwork物流网络包3SCM-2LogisticsNetworkConfiguration供应链管理课件4决策的分类DecisionClassifications战略层面:涉及到资本投入等有着长期影响的那些决策。如：–决定新工厂、配送中心、仓库的选址、数目、规模等。–新生产设备的购买及工厂内生产方式的选择etc.决策的分类DecisionClassifications战5策略层面:Effectiveallocationofmanufacturing(生产等资源的有效分配)anddistributionresourcesoveraperiodofseveralmonths–工人规模–库存控制的方式–配送渠道的选择–运输、配送及替代方案的选择决策的分类DecisionClassifications策略层面:Effectiveallocationof6操作层面:Includesday-to-dayoperationaldecisions–Theassignment（分派）ofcustomerorderstoindividualmachines–Dispatching,expediting（催单）andprocessingorders–Vehiclescheduling（车辆路线设计）决策的分类DecisionClassifications操作层面:Includesday-to-dayope7网络设计:主要解决的问题决定最优的库房、工厂的地点、数目、规模决定最优的供应方案：–哪家工厂（供应商）生产（供应）哪种产品或部件决定最优的配送路径–哪个库房（配送中心）服务哪个区域的客户网络设计:主要解决的问题决定最优的库房、工厂的地点、数目、8主要目标为平衡服务水准与生产、供应成本库存持有成本订单处理成本运输成本Thatis,wewouldliketofindaminimal-annual-costconfigurationofthedistributionnetworkthatsatisfiesproductdemandsatspecifiedcustomerservicelevels.网络设计:主要解决的问题主要目标为平衡服务水准与网络设计:主要解决的问题9

网络设计的工具:MajorComponents绘图Mapping–Mappingallowsyoutovisualize（可视化）yoursupplychainandsolutions–Mappingthesolutionsallowsyoutobetterunderstanddifferentscenarios（场景、方案）–Colorcoding,sizing,andutilizationindicatorsallowforfurtheranalysis数据–Dataspecifiesthecostsofyoursupplychain–Thebaselinecostdatashouldmatchyouraccountingdata–Theoutputdataallowsyoutoquantifychangestothesupplychain优化工具–相关软件如LINGO、CMOS等。

网络设计的工具:MajorComponents绘图Ma10

MappingAllowsYoutoVisualizeYourSupplyChain

MappingAllowsYoutoVisuali11

DisplayingtheSolutionsAllowsyouToCompareScenarios

DisplayingtheSolutionsAllo12

网络设计所需要的相关数据1.所有产品的清单2.客户、供应来源的地理区域3.每区域客户对每种产品的需求信息。4.运输费率5.库房的相关成本6.订单的模式如订单频率、规模、内容特点、有无季节性等等。7.订单处理成本8.客户服务水平

网络设计所需要的相关数据1.所有产品的清单13信息太多怎么办？CustomersandGeocoding按地理位置进行编码销售数据通常是按照地理区域来统计的。信息太多怎么办？CustomersandGeocodin14为什么要进行数据合并WhyAggregate?

节省数据处理成本最详细的数据可能得不到如按每个县、村等。保证模型的可操作性为什么要进行数据合并WhyAggregate?节省数据处15数据合并DataAggregation合并的两种方式:需求的合并:将顾客按位置或服务等级进行合并,在按位置进行合并的情况下,无数个顾客合并为少数的比如几十个顾客区域.按物品进行合并,比如按物品物理化学特性\配送方式等.数据合并DataAggregation合并的两种方式:16按客户的地理位置进行数据合并Customerslocatedincloseproximity接近areaggregatedusingagrid网格networkorclustering（分组）techniques.Allcustomerswithinasinglecellorasingleclusterarereplacedbyasinglecustomerlocatedatthecentroid中心ofthecellorcluster.Werefertoacelloraclusterasacustomerzone顾客区域.按客户的地理位置进行数据合并Customerslocate17可能产生的问题过分合并会导致模型处理的不准确什么影响了数据合并的有效性？合并后区域的数量各区域内客户分布的不同形态可能产生的问题过分合并会导致模型处理的不准确18合理的数据合并的方法合并后至少有150-200个区域。确保每个区域的总需求量大致相同使合并后的中心点在各区域的中心位置Inthiscase,theerroristypicallynomorethan1%合理的数据合并的方法合并后至少有150-200个区域。19例：最优库房数量的选择1个工厂、1种产品客户数据–原始数据有18,000个客户地点–合并后有800个客户地点例：最优库房数量的选择1个工厂、1种产品20ComparingOutput输出结果的比较合并前的原始数据合并后的数据ComparingOutput输出结果的比较合并前的原始数21

Minimizethecostofyourlogisticsnetworkwithoutcompromisingservicelevels

Minimizethecostofyourlog22

增加库房数量会。。。提高对客户响应时间，从而提高服务水平库存增加从而库存成本增加。其它费用如日常管理成本增加总体而言，运输成本会减少，但具体而言–Reduceoutboundtransportationcosts–Increaseinboundtransportationcosts

增加库房数量会。。。提高对客户响应时间，从而提高服务水平23优化的方法数学优化技术:–Exactalgorithms算法:寻找最优解–Heuristics启发式算法:寻找满意解模拟方法优化的方法数学优化技术:24

LogisticsNetworkDesign

LogisticsNetworkDesign25

LogisticsNetworkDesign

LogisticsNetworkDesign26

LogisticsNetworkDesign

LogisticsNetworkDesign27

例一种产品两个工厂p1与p2P1年生产能力为200,000units.p2年生产能力为60,000units.两工厂生产成本相同.两个仓库w1andw2，其库存处理成本相同。三个市场c1,c2andc3，需求分别为50,000,100,000and50,000.

例一种产品28表1单位配送成本表129

WhyOptimizationMatters?

WhyOptimizationMatters?30方案1方案131

方案2

方案232

线性规划法求解

线性规划法求解33

模型

模型34

TheOptimalStrategy

TheOptimalStrategy35HP中国售后备件供应网络的构建Presentedby:

ChenWan,KwanSinMan,LiawChyayi,TanYanTing,YanTaoHP中国售后备件供应网络的构建Presentedby:C36问题描述目前有两个中心备件库房BeijingandShanghaiFromthese2hubs,servicepartsarebeingdeliveredto46citiesacrossthecountry目前服务水准为

3D18通过建立额外的HUB来提高对备件需求的响应时间新的服务水准设定为2D10Toachievethisservicelevel,theyarewillingtosetasideadditionalbudget问题描述目前有两个中心备件库房BeijingandSh37模型与项目说明仅考虑32个最重要的中心城市备件需求量数据为过去12个月用量的平均每天接受订单的截至试点为下午5点，因此，从HUB满足该订单的最长时间为17个小时。Holdingcostincludeslabourcost,insuranceandotherrelatedcostsTransportationcostincludeslabourcost,fuelcost,loading/unloadingcost库房建立成本Setupcost包括库房租金、设备维护费用、材料费等等。模型与项目说明仅考虑32个最重要的中心城市38研究目的MinimizethebudgettoestablishadditionalhubswhilstsatisfyingthecoverageindustrybenchmarkCoverage（覆盖区域）

isdefinedasthepercentageofdemandthatcanmeetthenewservicelevel,2D10.研究目的Minimizethebudgettoest39需要求解的问题NumberofhubsLocationofhubsAssignmentofnon-hubstohubsTrade-offbetweenthetotaltransportationcostandthesetupcostsofadditionalhubs需要求解的问题Numberofhubs40问题的建模非线性整数规划NonlinearIntegerProgrammingProblem各集合的定义:DemandCities,C= {Shenzhen深圳,Zhuhai珠海,Shantou汕头,Zhanjiang湛江,Dongguan东莞,Taizhou台洲,Zhongshan中山,Chongqing重庆,Changsha长沙,Zhengzhou郑州,Hefei合肥,Nanchang南昌,Yichang宜昌,Harbin哈尔滨,Changchun长春,Dalian大连,Nanning南宁,Lanzhou兰州,Yinchuan银川,Xiamen厦门,Quanzhou泉州,Qingdao青岛,Yantai烟台,Jinan济南,Fuzhou福州,Xian西安,Shenyang沈阳,Chengdu成都,Guangzhou广州,Wuhan武汉,Beijing北京,Shanghai上海}问题的建模非线性整数规划NonlinearInteger41ProblemFormulationSetsDefinition(cont’)Possiblesupplycities,C2={sameasC+Beijing2北京2,Shanghai2上海2}我们规定Beijing2andShanghai2来满足那些无法被任何一个城市在2D10的时间内覆盖的区域，即我们规定在那样的情况下，这些城市的备件直接由北京或上海供应ProblemFormulationSetsDefini42决策变量

Kijisabinaryintegerandis1whencityiisbeingservicedbycityj,0otherwise.Kjjis1whencityjischosenasahubtoserviceothercities.U(i,j)=[0,Di] Uij,theunitsofproductshippedfromhubcityjtodemandcityiCoverageistheratioofdemandcoveredbythehubsat2D10tothetotaldemandattheold3D18servicelevel决策变量43参数说明D(i)=城市i的月平均备件用量HO(j)=城市j的单位库存持有成本ST(j)=在城市j建立库房的成本transcost(i,j)=costoftransportationperunitfromhubcityjtocityiIftravellingtimebetweencityiandcityjisbeyond17hrs,transcost(i,j)issettoM,whereMisaninfinitelylargeinteger.参数说明44目标函数包括3个部分库存持有成本

=KijxUijxHOjrepresentstheholdingcostofitembeingheldathubjthatistobetransportedtoservicecityi运输成本

=KijxUijxtranscost(i,j)representsthetransportationcostofUijamountofitemsfromhubcityjtoservicecityi库房建立成本

=KjjxSTjrepresentsthesetupcostofahubincityjMinBudget目标函数包括3个部分45约束条件1citytoonly1hubmatchingrequirements 一个城市仅仅能被一个HUB来供货，进一步，一个城市如果被选为HUB的话，那么其自己的需求仅能由自己来满足。SincethesumofKijis1,eachdemandcityisonlymatchedto1hubcity.ThehubcityismatchedtoitselfwhenKij=1fori=j.Onlyhubcitiescanservicedemandcities

AcitycanonlybeservedbyanothercityifitisidentifiedasahubsincejisonlyahubifKjj=1,andthusKijcanthenbe1.Therefore,cityicanonlybeservedbycityjifjisidentifiedasahub.约束条件1citytoonly1hubmatch46约束条件Usageconstrain

Sinceonedemandcityisonlyservedbyonehub,theusageshouldbeequaltothecitydemandsuchthatnoshortageshouldoccur.Coverageconstraint

Thisconstrainensuresthatthenewhubnetworkwouldbeabletocoveratleast85%ofthetotaldemandwiththenew2D10servicelevel

约束条件Usageconstrain47Non-negativityConstraints

NonegativetransportationflowfromhubtodemandcitiesAcitiesiseitherserved(kij=1)ornotserved(kij=0)Budget≥0TherecannotbenegativebudgetCoverage≥0Therecannotbenegativecoverage,worstscenariois0约束条件Non-negativityConstraints约束条48Budget=¥744,503Coverage=93.31%6additionalhubstobesetup,besidesSHandBJZhongshan,Chengdu,Wuhan,Shenyang,JinanandXianHubCitiesServedTotalDemandBeijingBeijing7,835ShanghaiShanghai5,960ZhongshanShenzhen,Zhuhai,Shantou,Zhanjiang,Dongguan,Zhongshan,Guangzhou,Nanning13,468ChengduChongqing,Chengdu4,379WuhanChangsha,Hefei,Nanchang,Yichang,Wuhan6,660ShenyangHarbin,Changchun,Dalian,Shenyang4,472XianLanzhou,Yinchuan,Xian3,416JinanQingdao,Yantai,Jinan,Zhengzhou3,878Total50,068结果Budget=¥744,503HubCitiesSe49Citiesthatcannotbeservedwithin2D10byanyhubs.Thesearecitieswithlowdemand.Itisnotcostefficienttosetupahubspeciallytoservethesecities.HubCitiesthatcannotbecoveredwithin2D10TotalDemandShanghaiTaizhou,Xiamen,Quanzhou，Fuzhou3,591Total3,591结果Citiesthatcannotbeservedw50ComparisonofCoverageagainstBudget

MinCost结果ComparisonofCoverageagainst51Discussion2002年HP的实际做法HeuristicsClustercitieswithgeographicalproximitytoformahubDesignatethecitywiththehighestsalesrevenueandhistoricaldemandasthehubBudget=¥803,945with97.39%coverage

HubCitiesServedTotalDemandBeijingBeijing7,835ShanghaiShanghai,Taizhou,Nanning7,359GuangzhouShenzhen,Zhuhai,Shantou,Zhanjiang,Dongguan,Zhongshan,Guangzhou12,686ChengduChongqing,Chengdu4,379WuhanChangsha,Zhengzhou,Hefei,Nanchang,Yichang,Wuhan7,763ShenyangHarbin,Changchun,Dalian,Shenyang4,472XianLanzhou,Yinchuan,Xian3,416FuzhouXiamen,Quanzhou,Fuzhou2,974JinanQingdao,Yantai,Jinan2,775Total53,659

7.39%Discussion2002年HP的实际做法HubCitie52ReAddonemorecostcomponenttotheproblemEvaluatetheriskpoolingeffectAssumptionsAverageleadtimeforvendortodelivertoeachhubis1monthAllvendorshavethesameleadtimeSafetyfactor,kissetat97%ModelExtensionReAddonemorecostcomponent53ReMinBudget

where

isthestandarddev.ofthetotaldemandforeachclustercoverbythehubjDmithehistoricaldemandofcityjinmonthmListheaverageleadtimeforthevendorstodeliverthegoodstotherespectivehubsObjectiveFunctionReMinBudgetObjectiveFunction54ReExtendedNLPmodelwasperformedon10cities–Beijing,Shanghai,Shenzhen,Zhuhai,Shantou,Chongqing,Chengdu,Changsha,Yantai,Jinan.Budget=¥292,80092.73%coverageResultsHubCitiesservedBeijingBeijingShanghaiShanghaiZhuhaiShenzhen,Shantou,Changsha,ZhuhaiChengduChongqing,ChengduHubCitiesthatcannotbecoveredwithin2D10BeijingYantai,JinanReExtendedNLPmodelwasperfo55ReLargenumberofvariablescannotbehandledbyNEOsserver.Hence,unabletotestthemodelusingtheentiredataset.AssumptionofauniformleadtimeforallvendorsmaynotberealisticLimitationsoftheExtendedModelReLargenumberofvariablesca56`ConclusionOurresultsaffirmsthatoptimizationofamodelwillachievebetterresultscomparedtoaheuristicapproach.Usingtheproposedmodel,HPChinawillgenerateasavingsof28.5%againsttheoriginaldistributionnetworkand7.39%savingsagainsttheheuristicmodel.Trade-offbetweentimeandresourcesspenttoobtaintheoptimalsolutionandpotentialcostsavings.`ConclusionOurresultsaffirms57Whatwillbetheresultifmoreechelonsbeadded?Whatwillbetheresultifmor58物流网络设计

LogisticsNetworkConfiguration物流网络设计

LogisticsNetworkConf59

OutlineWhatisit?方法Methodology

–建模Modeling–数据合并DataAggregation–确认可靠性ValidationSolutionTechniques

OutlineWhatisit?60物流网络TheLogisticsNetwork物流网络包括:节点:Vendors（供应商）,ManufacturingCenters,Warehouse/DistributionCenters,andCustomersRawmaterials原材料andfinishedproductsthatflowbetweenthefacilities.物流网络TheLogisticsNetwork物流网络包61SCM-2LogisticsNetworkConfiguration供应链管理课件62决策的分类DecisionClassifications战略层面:涉及到资本投入等有着长期影响的那些决策。如：–决定新工厂、配送中心、仓库的选址、数目、规模等。–新生产设备的购买及工厂内生产方式的选择etc.决策的分类DecisionClassifications战63策略层面:Effectiveallocationofmanufacturing(生产等资源的有效分配)anddistributionresourcesoveraperiodofseveralmonths–工人规模–库存控制的方式–配送渠道的选择–运输、配送及替代方案的选择决策的分类DecisionClassifications策略层面:Effectiveallocationof64操作层面:Includesday-to-dayoperationaldecisions–Theassignment（分派）ofcustomerorderstoindividualmachines–Dispatching,expediting（催单）andprocessingorders–Vehiclescheduling（车辆路线设计）决策的分类DecisionClassifications操作层面:Includesday-to-dayope65网络设计:主要解决的问题决定最优的库房、工厂的地点、数目、规模决定最优的供应方案：–哪家工厂（供应商）生产（供应）哪种产品或部件决定最优的配送路径–哪个库房（配送中心）服务哪个区域的客户网络设计:主要解决的问题决定最优的库房、工厂的地点、数目、66主要目标为平衡服务水准与生产、供应成本库存持有成本订单处理成本运输成本Thatis,wewouldliketofindaminimal-annual-costconfigurationofthedistributionnetworkthatsatisfiesproductdemandsatspecifiedcustomerservicelevels.网络设计:主要解决的问题主要目标为平衡服务水准与网络设计:主要解决的问题67

网络设计的工具:MajorComponents绘图Mapping–Mappingallowsyoutovisualize（可视化）yoursupplychainandsolutions–Mappingthesolutionsallowsyoutobetterunderstanddifferentscenarios（场景、方案）–Colorcoding,sizing,andutilizationindicatorsallowforfurtheranalysis数据–Dataspecifiesthecostsofyoursupplychain–Thebaselinecostdatashouldmatchyouraccountingdata–Theoutputdataallowsyoutoquantifychangestothesupplychain优化工具–相关软件如LINGO、CMOS等。

网络设计的工具:MajorComponents绘图Ma68

MappingAllowsYoutoVisualizeYourSupplyChain

MappingAllowsYoutoVisuali69

DisplayingtheSolutionsAllowsyouToCompareScenarios

DisplayingtheSolutionsAllo70

网络设计所需要的相关数据1.所有产品的清单2.客户、供应来源的地理区域3.每区域客户对每种产品的需求信息。4.运输费率5.库房的相关成本6.订单的模式如订单频率、规模、内容特点、有无季节性等等。7.订单处理成本8.客户服务水平

网络设计所需要的相关数据1.所有产品的清单71信息太多怎么办？CustomersandGeocoding按地理位置进行编码销售数据通常是按照地理区域来统计的。信息太多怎么办？CustomersandGeocodin72为什么要进行数据合并WhyAggregate?

节省数据处理成本最详细的数据可能得不到如按每个县、村等。保证模型的可操作性为什么要进行数据合并WhyAggregate?节省数据处73数据合并DataAggregation合并的两种方式:需求的合并:将顾客按位置或服务等级进行合并,在按位置进行合并的情况下,无数个顾客合并为少数的比如几十个顾客区域.按物品进行合并,比如按物品物理化学特性\配送方式等.数据合并DataAggregation合并的两种方式:74按客户的地理位置进行数据合并Customerslocatedincloseproximity接近areaggregatedusingagrid网格networkorclustering（分组）techniques.Allcustomerswithinasinglecellorasingleclusterarereplacedbyasinglecustomerlocatedatthecentroid中心ofthecellorcluster.Werefertoacelloraclusterasacustomerzone顾客区域.按客户的地理位置进行数据合并Customerslocate75可能产生的问题过分合并会导致模型处理的不准确什么影响了数据合并的有效性？合并后区域的数量各区域内客户分布的不同形态可能产生的问题过分合并会导致模型处理的不准确76合理的数据合并的方法合并后至少有150-200个区域。确保每个区域的总需求量大致相同使合并后的中心点在各区域的中心位置Inthiscase,theerroristypicallynomorethan1%合理的数据合并的方法合并后至少有150-200个区域。77例：最优库房数量的选择1个工厂、1种产品客户数据–原始数据有18,000个客户地点–合并后有800个客户地点例：最优库房数量的选择1个工厂、1种产品78ComparingOutput输出结果的比较合并前的原始数据合并后的数据ComparingOutput输出结果的比较合并前的原始数79

Minimizethecostofyourlogisticsnetworkwithoutcompromisingservicelevels

Minimizethecostofyourlog80

增加库房数量会。。。提高对客户响应时间，从而提高服务水平库存增加从而库存成本增加。其它费用如日常管理成本增加总体而言，运输成本会减少，但具体而言–Reduceoutboundtransportationcosts–Increaseinboundtransportationcosts

增加库房数量会。。。提高对客户响应时间，从而提高服务水平81优化的方法数学优化技术:–Exactalgorithms算法:寻找最优解–Heuristics启发式算法:寻找满意解模拟方法优化的方法数学优化技术:82

LogisticsNetworkDesign

LogisticsNetworkDesign83

LogisticsNetworkDesign

LogisticsNetworkDesign84

LogisticsNetworkDesign

LogisticsNetworkDesign85

例一种产品两个工厂p1与p2P1年生产能力为200,000units.p2年生产能力为60,000units.两工厂生产成本相同.两个仓库w1andw2，其库存处理成本相同。三个市场c1,c2andc3，需求分别为50,000,100,000and50,000.

例一种产品86表1单位配送成本表187

WhyOptimizationMatters?

WhyOptimizationMatters?88方案1方案189

方案2

方案290

线性规划法求解

线性规划法求解91

模型

模型92

TheOptimalStrategy

TheOptimalStrategy93HP中国售后备件供应网络的构建Presentedby:

ChenWan,KwanSinMan,LiawChyayi,TanYanTing,YanTaoHP中国售后备件供应网络的构建Presentedby:C94问题描述目前有两个中心备件库房BeijingandShanghaiFromthese2hubs,servicepartsarebeingdeliveredto46citiesacrossthecountry目前服务水准为

3D18通过建立额外的HUB来提高对备件需求的响应时间新的服务水准设定为2D10Toachievethisservicelevel,theyarewillingtosetasideadditionalbudget问题描述目前有两个中心备件库房BeijingandSh95模型与项目说明仅考虑32个最重要的中心城市备件需求量数据为过去12个月用量的平均每天接受订单的截至试点为下午5点，因此，从HUB满足该订单的最长时间为17个小时。Holdingcostincludeslabourcost,insuranceandotherrelatedcostsTransportationcostincludeslabourcost,fuelcost,loading/unloadingcost库房建立成本Setupcost包括库房租金、设备维护费用、材料费等等。模型与项目说明仅考虑32个最重要的中心城市96研究目的MinimizethebudgettoestablishadditionalhubswhilstsatisfyingthecoverageindustrybenchmarkCoverage（覆盖区域）

isdefinedasthepercentageofdemandthatcanmeetthenewservicelevel,2D10.研究目的Minimizethebudgettoest97需要求解的问题NumberofhubsLocationofhubsAssignmentofnon-hubstohubsTrade-offbetweenthetotaltransportationcostandthesetupcostsofadditionalhubs需要求解的问题Numberofhubs98问题的建模非线性整数规划NonlinearIntegerProgrammingProblem各集合的定义:DemandCities,C= {Shenzhen深圳,Zhuhai珠海,Shantou汕头,Zhanjiang湛江,Dongguan东莞,Taizhou台洲,Zhongshan中山,Chongqing重庆,Changsha长沙,Zhengzhou郑州,Hefei合肥,Nanchang南昌,Yichang宜昌,Harbin哈尔滨,Changchun长春,Dalian大连,Nanning南宁,Lanzhou兰州,Yinchuan银川,Xiamen厦门,Quanzhou泉州,Qingdao青岛,Yantai烟台,Jinan济南,Fuzhou福州,Xian西安,Shenyang沈阳,Chengdu成都,Guangzhou广州,Wuhan武汉,Beijing北京,Shanghai上海}问题的建模非线性整数规划NonlinearInteger99ProblemFormulationSetsDefinition(cont’)Possiblesupplycities,C2={sameasC+Beijing2北京2,Shanghai2上海2}我们规定Beijing2andShanghai2来满足那些无法被任何一个城市在2D10的时间内覆盖的区域，即我们规定在那样的情况下，这些城市的备件直接由北京或上海供应ProblemFormulationSetsDefini100决策变量

Kijisabinaryintegerandis1whencityiisbeingservicedbycityj,0otherwise.Kjjis1whencityjischosenasahubtoserviceothercities.U(i,j)=[0,Di] Uij,theunitsofproductshippedfromhubcityjtodemandcityiCoverageistheratioofdemandcoveredbythehubsat2D10tothetotaldemandattheold3D18servicelevel决策变量101参数说明D(i)=城市i的月平均备件用量HO(j)=城市j的单位库存持有成本ST(j)=在城市j建立库房的成本transcost(i,j)=costoftransportationperunitfromhubcityjtocityiIftravellingtimebetweencityiandcityjisbeyond17hrs,transcost(i,j)issettoM,whereMisaninfinitelylargeinteger.参数说明102目标函数包括3个部分库存持有成本

=KijxUijxHOjrepresentstheholdingcostofitembeingheldathubjthatistobetransportedtoservicecityi运输成本

=KijxUijxtranscost(i,j)representsthetransportationcostofUijamountofitemsfromhubcityjtoservicecityi库房建立成本

=KjjxSTjrepresentsthesetupcostofahubincityjMinBudget目标函数包括3个部分103约束条件1citytoonly1hubmatchingrequirements 一个城市仅仅能被一个HUB来供货，进一步，一个城市如果被选为HUB的话，那么其自己的需求仅能由自己来满足。SincethesumofKijis1,eachdemandcityisonlymatchedto1hubcity.ThehubcityismatchedtoitselfwhenKij=1fori=j.Onlyhubcitiescanservicedemandcities

AcitycanonlybeservedbyanothercityifitisidentifiedasahubsincejisonlyahubifKjj=1,andthusKijcanthenbe1.Therefore,cityicanonlybeservedbycityjifjisidentifiedasahub.约束条件1citytoonly1hubmatch104约束条件Usageconstrain

Sinceonedemandcityisonlyservedbyonehub,theusageshouldbeequaltothecitydemandsuchthatnoshortageshouldoccur.Coverageconstraint

Thisconstrainensuresthatthenewhubnetworkwouldbeabletocoveratleast85%ofthetotaldemandwiththenew2D10servicelevel

约束条件Usageconstrain105Non-negativityConstraints

NonegativetransportationflowfromhubtodemandcitiesAcitiesiseitherserved(kij=1)ornotserved(kij=0)Budget≥0TherecannotbenegativebudgetCoverage≥0Therecannotbenegativecoverage,worstscenariois0约束条件Non-negativityConstraints约束条106Budget=¥744,503Coverage=93.31%6additionalhubstobesetup,besidesSHandBJZhongshan,Chengdu,Wuhan,Shenyang,JinanandXianHubCitiesServedTotalDemandBeijingBeijing7,835ShanghaiShanghai5,960ZhongshanShenzhen,Zhuhai,Shantou,Zhanjiang,Dongguan,Zhongshan,Guangzhou,Nanning13,468ChengduChongqing,Chengdu4,379WuhanChangsha,Hefei,Nanchang,Yichang,Wuhan6,660ShenyangHarbin,Changchun,Dalian,Shenyang4,472XianLanzhou,Yinchuan,Xian3,416JinanQingdao,Yantai,Jinan,Zhengzhou3,878Total50,068结果Budget=¥744,503HubCitiesSe107Citiesthatcannotbeservedwithin2D10byanyhubs.Thesearecitieswithlowdemand.Itisnotcostefficienttosetupahubspeciallytoservethesecities.HubCitiesthatcannotbecoveredwithin2D10TotalDemandShanghaiTaizhou,Xiamen,Quanzhou，Fuzhou3,591Total3,591结果Citiesthatcannotbeservedw108ComparisonofCoverageagainstBudget

MinCost结果ComparisonofCoverageagainst109Discussion2002年HP的实际做法HeuristicsClustercitieswithgeographicalproximitytoformahubDesignatethecitywiththehigh