We consider the solution of matching problems with a convex cost function via a network flow algorithm. We review the general mapping between matching problems and flow problems on skew symmetric networks and revisit ...We consider the solution of matching problems with a convex cost function via a network flow algorithm. We review the general mapping between matching problems and flow problems on skew symmetric networks and revisit several results on optimality of network flows. We use these results to derive a balanced capacity scaling algorithm for matching problems with a linear cost function. The latter is later generalized to a balanced capacity scaling algorithm also for a convex cost function. We prove the correctness and discuss the complexity of our solution.展开更多
The authors analyze a finite horizon,single product,period review model in which pricingand inventory decisions are made simultaneously.Demands in different periods are random variablesthat are independent of each oth...The authors analyze a finite horizon,single product,period review model in which pricingand inventory decisions are made simultaneously.Demands in different periods are random variablesthat are independent of each other and their distributions depend on the product price.Pricing andordering decisions are made at the beginning of each period and all shortage are backlogged.Orderingcost is a convex function of the amount ordered.The objective is to find an inventory and pricing policymaximizing expected discounted profit over the finite horizon.The authors characterize the structure ofthe optimal combined pricing and inventory strategy for this model.Moreover,the authors demonstratehow the profit-to-go function,order up to level,reorder point and optimal price change with respectto state and time.展开更多
本文考虑球面S^n上成本函数为c(x,y)=F(d(x,y))的最优运输问题,其中d(x,y)表示S^n上两点x与y之间的球面距离.重点是说明,即使F仅定义于原点的一个邻域内,在适当条件下仍然可以证明最优映射的存在性和唯一性.特别是当F(d)=log(κcos d-1)...本文考虑球面S^n上成本函数为c(x,y)=F(d(x,y))的最优运输问题,其中d(x,y)表示S^n上两点x与y之间的球面距离.重点是说明,即使F仅定义于原点的一个邻域内,在适当条件下仍然可以证明最优映射的存在性和唯一性.特别是当F(d)=log(κcos d-1)(κ>1)和F(d)=log cos d时,相应的最优运输问题分别等价于几何光学中的光线折射问题和凸体几何中的Aleksandrov问题.展开更多
文摘We consider the solution of matching problems with a convex cost function via a network flow algorithm. We review the general mapping between matching problems and flow problems on skew symmetric networks and revisit several results on optimality of network flows. We use these results to derive a balanced capacity scaling algorithm for matching problems with a linear cost function. The latter is later generalized to a balanced capacity scaling algorithm also for a convex cost function. We prove the correctness and discuss the complexity of our solution.
基金Supported by the State Key Program of National Natural Science Foundation of China(No.71131004)National Natural Science Foundation of China(Nos.11071142,71371107)Shandong Province NaturalScience Foundation(Nos.BS2013SF016,ZR2011AL017)
基金supported by the National Natural Science Foundation of China under Grant Nos.70621061,70671100,70501014Beijing Philosophy and Social Science, Research Center for Beijing Transportation Development
文摘The authors analyze a finite horizon,single product,period review model in which pricingand inventory decisions are made simultaneously.Demands in different periods are random variablesthat are independent of each other and their distributions depend on the product price.Pricing andordering decisions are made at the beginning of each period and all shortage are backlogged.Orderingcost is a convex function of the amount ordered.The objective is to find an inventory and pricing policymaximizing expected discounted profit over the finite horizon.The authors characterize the structure ofthe optimal combined pricing and inventory strategy for this model.Moreover,the authors demonstratehow the profit-to-go function,order up to level,reorder point and optimal price change with respectto state and time.
文摘本文考虑球面S^n上成本函数为c(x,y)=F(d(x,y))的最优运输问题,其中d(x,y)表示S^n上两点x与y之间的球面距离.重点是说明,即使F仅定义于原点的一个邻域内,在适当条件下仍然可以证明最优映射的存在性和唯一性.特别是当F(d)=log(κcos d-1)(κ>1)和F(d)=log cos d时,相应的最优运输问题分别等价于几何光学中的光线折射问题和凸体几何中的Aleksandrov问题.
