Integer Solutions Property As long as all its supplies and demands have integer values, any transportation problem with feasible solutions is guaranteed to have an optimal solution with integer values for all its decision variables Therefore, it is not necessary to add constraints to the model that restrict these variables to only have integer values 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 Integer Solutions Property As long as all its supplies and demands have integer values, any transportation problem with feasible solutions is guaranteed to have an optimal solution with integer values for all its decision variables. Therefore, it is not necessary to add constraints to the model that restrict these variables to only have integer values
e数解圆 只要它的供应量和求量部是 。仨何育可行解的输问 题然膏所有变量都是墨数的 优解。国些,没有多要物上 所有变量部是整数的约束条件 Copyrigh2007c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 整数解性质 只要它的供应量和需求量都是 整数，任何有可行解的运输问 题必然有所有变量都是整数的 最优解。因此，没有必要加上 所有变量都是整数的约束条件
e8解(量伤13)器 ●单纯形法 ●网络单纯形法 ●运输单纯形法 ●算法的适应范围越小, 求解效率越高 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 求解(最优化)算法 单纯形法 网络单纯形法 运输单纯形法 算法的适应范围越小， 求解效率越高
2 Distribution System at Proctor and Gamble e Proctor and gamble needed to consolidate and re-design their north American distribution system in the early1990s.( Proctor& Gamble公司需 要巩固并再设针其九十年代早期在北奠建 立起来的配送系统) 50 product categories(50个产品种类) 60 plants(6o家工厂 15 distribution centers(15个配送中心 1000 customer zones(1000个客户区) 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 Distribution System at Proctor and Gamble Proctor and Gamble needed to consolidate and re-design their North American distribution system in the early 1990’s. (Proctor & Gamble公司需 要巩固并再设计其九十年代早期在北美建 立起来的配送系统) ⚫ 50 product categories (50个产品种类) ⚫ 60 plants (60家工厂) ⚫ 15 distribution centers (15个配送中心) ⚫ 1000 customer zones (1000个客户区)
e Distribution System at Proctor and Gamble e Solved many transportation problems(one for each product category)(解决大量运输问题, 每个产品种类都存在一个运输问题) e Goal: find best distribution plan, which plants to keep open,etc.(目标:寻找最优的配送方案, 哪些工厂保持开放) e Closed many plants and distribution centers, and optimized their product sourcing and distribution location.(关闭许多工厂和配送中心, 优化产品来源和配送点) Implemented in 1996. Saved $200 million per year.(1996年实施,北美工厂数减少20%,每年 给公司节约2亿美金) 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 Distribution System at Proctor and Gamble Solved many transportation problems (one for each product category). (解决大量运输问题， 每个产品种类都存在一个运输问题) Goal: find best distribution plan, which plants to keep open, etc. (目标：寻找最优的配送方案， 哪些工厂保持开放) Closed many plants and distribution centers, and optimized their product sourcing and distribution location. (关闭许多工厂和配送中心， 优化产品来源和配送点) Implemented in 1996. Saved $200 million per year. (1996年实施，北美工厂数减少20%，每年 给公司节约2亿美金)