e The sUMiF Function The sumif formula can be used to simplify the node flow constraints.( SUMIF公式可以简 化节点流约束) SUMIF( RangeA,x, Range b) For each quantity in (Range A) that equals x, SUMIF Sums the corresponding entries in ( Range b)(区A中的每 二条件x时 SUMIF函就就会计算区城B中应内容之和 e The net outflow(flow out-flow in) from node x is then(点x的净流出流出羸为就等E) SUMIF(“ From labels”,x,“Flow”) SUMIF(“ To labels”,x,"“Flow”) Copyrigh2007c深圳大学管理学院运筹学6
Copyright 2007 © 深圳大学管理学院 运筹学 26 The SUMIF Function The SUMIF formula can be used to simplify the node flow constraints. (SUMIF公式可以简 化节点流约束) SUMIF(Range A, x, Range B) For each quantity in (Range A) that equals x, SUMIF sums the corresponding entries in (Range B). (区域A中的每一个量满足条件x时， SUMIF函数就会计算区域B中相应内容之和) The net outflow (flow out – flow in) from node x is then (节点x的净流出[流出-流入]就等于) SUMIF(“From labels”, x, “Flow”) – SUMIF(“To labels”, x, “Flow”)
&R Typical Applications of Minimum-Cost Flow Problems Kind of Supply Transshipment Demand Application Nodes Nodes Nodes Operation of a distribution network Sources of goods Intermediate storage Customers facilities Solid waste Sources of solid Processing facilities Landfill locations managent waste Operation of a supply Intermediate Vendors network Processing facilities warehouses Coordinating product Production of a Market for a specific Plants mixes at plants specific product product Cash flow Sources of cash at a Short-term Needs for cash at a management specific time investment options specific time Copyright2007@深圳大学管理学院运筹学27
Copyright 2007 © 深圳大学管理学院 运筹学 27 Typical Applications of Minimum-Cost Flow Problems
e The bmz maximum flow Proble ● The BMz Company is a European manufacturer of luxury automobiles, Its exports to the united states are particularly important. (Bz 是欧洲一家生产豪华汽的制造商,其 产品出口到国无为量要 最大流问题 Copyrigh2007c深圳大学管理学院运筹学8
Copyright 2007 © 深圳大学管理学院 运筹学 28 The BMZ Maximum Flow Problem The BMZ Company is a European manufacturer of luxury automobiles. Its exports to the United States are particularly important. (BMZ公司 是欧洲一家生产豪华汽车的制造商，其 产品出口到美国尤为重要)
e The BMz Maximum Flow Problem .BMZ cars are becoming especially popular in California, so it is particularly important to keep the Los Angeles center well supplied with replacement parts for repairing these cars.(Bmz公司的汽车 尤其在加利福尼亚大受欢迎,因此保持洛 矶中心罗部件的充足供给,以便及时维修这 些汽车就显得特别重要了) Copyrigh2007c深圳大学管理学院运筹学9
Copyright 2007 © 深圳大学管理学院 运筹学 29 The BMZ Maximum Flow Problem BMZ cars are becoming especially popular in California, so it is particularly important to keep the Los Angeles center well supplied with replacement parts for repairing these cars. (BMZ公司的汽车 尤其在加利福尼亚大受欢迎，因此保持洛杉 矶中心零部件的充足供给，以便及时维修这 些汽车就显得特别重要了)
e The bmz maximum flow Proble o BMZ needs to execute a plan quickly for shipping as much as possible from the main factory in Stuttgart, Germany to the distribution center in Los Angeles over the next month。(Bm公司需要迅 物行一项计划,下个月要从于斯图加特 初德国的主要工厂运送尽可能多的配件到洛 矶的配送中心) Copyrigh2007c深圳大学管理学院运筹学30
Copyright 2007 © 深圳大学管理学院 运筹学 30 The BMZ Maximum Flow Problem BMZ needs to execute a plan quickly for shipping as much as possible from the main factory in Stuttgart, Germany to the distribution center in Los Angeles over the next month. (BMZ公司需要迅 速执行一项计划，下个月要从位于斯图加特 和德国的主要工厂运送尽可能多的配件到洛 杉矶的配送中心)