泄洪设施修建计划的数学模型

A Programming Model for Constructing a Flood Control Installation

某乡政府计划解决防汛水利设施建设问题,即通过开挖小型排洪沟与修建新的泄洪河道来满足防汛需要.针对该乡的泄洪设施修建计划,主要研究以下三个问题:(1)给出同时开挖给定的8条小型排洪沟和新建一条给定的泄洪河道的最优修建方案;(2)已知该乡各村之间新建泄洪河道的长度,给出一个在各村之间互通的另一新泄洪河道的网络修建计划,使之达到可泄洪量100万立方米/小时;(3)当新泄洪河道网络修建完后,安排人员进行维护工作,研究维护人员在各村留宿的概率分布.在费用最省的目标下,建立了问题(1)和问题(2)的数学规划模型,并得到泄洪设施的最优修建方案.应用Markov链及转移概率矩阵等知识,建立了问题(3)的等概率和非等概率的两种数学模型,并得知维护人员在各村留宿的概率分布是稳定的.

One township government plans to solve the problem of constructing a flood control installation by excavating some flood channels and constructing a new drainage watercourse that to satisfy the demand of the flood control.This paper mainly studies the following three problems.（1） Please present an optimal scheme for excavating eight flooding channels and constructing a new river way simultaneity.（2） From the length of the new river way among villages,we need to propose an optimal scheme for building a grid of new river ways,which communicates with each village and can discharge flood up to one millions cubic meters per hour.（3） After the foundation of the new grid of river ways,we send workers to offer maintenance service.The problem is whether the probability distribution of the workers for staying overnight in each village is stable.Under the aim of minimal expense, we build two programming models and present best schemes for the problem（1） and（2）, respectively.For the problem（3）,we propose two probability models by the properties of the Markov chain and the transition probability matrix,which are equiprobability and nonequiprobability respectively.Then,we obtain the result,that is,the probability distribution of the workers for staying overnight in each village is stable.