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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.
A township government plans to solve the problem of flood control and water conservancy facilities construction, that is, through the excavation of small flood discharge ditch and the construction of new flood discharge river to meet the flood control needs.According to the township flood discharge facility construction plan, the main study of the following three questions: (1) The excavation of a given eight small flood discharge ditch and the new construction of a given flood discharge river optimal construction program; (2) known length of the village between the new flood discharge channel, given a village (3) After the new flood discharge channel network is constructed, arrange personnel to carry out maintenance work, and research and maintenance personnel will work in each of the new flood discharge river network construction plan, so that it can achieve flood discharge of 1 million cubic meters / hour; Probability Distribution of Village Dwelling Under the most cost-effective goal, the mathematic programming models of problems (1) and (2) are established and the optimal construction scheme of flood discharging facilities is established.Using knowledge of Markov chain and transfer probability matrix, The two kinds of mathematical models of equal probability and non-equal probability of problem (3) are established and it is found that the probability distribution of maintenance personnel staying in each village is stable.