道路新建与养护的动态最优投资分配模型  

Modelling of dynamic optimal investment allocation between road construction and maintenance

作　　者：王鹏飞[1,2] 王安格 宗恒山 关宏志 刘鹏[5,6] 徐秋实[1] 李松[7] WANG Pengfei;WANG Ange;ZONG Hengshan;GUAN Hongzhi;LIU Peng;XU Qiushi;LI Song(Key Laboratory of Green Construction and Intelligent Maintenance for Civil Engineering of Hebei Province,Yanshan University,Qinhuangdao 066004,China;Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education,Beijing University of Technology,Beijing 100124,China;Faculty of Urban Construction,Beijing University of Technology,Beijing 100124,China;China Aerospace Academy of Systems Science and Engineering,Beijing 100037,China;School of Economics and Management,Beihang University,Beijing 100191,China;Key Lab of Complex System Analysis and Management Decision,Ministry of Education,Beihang University,Beijing 100191,China;School of Traffic and Transportation,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]燕山大学河北省土木工程绿色建造与智能运维重点实验室,河北秦皇岛066004 [2]北京工业大学城市与工程安全减灾教育部重点实验室,北京100124 [3]北京工业大学城市建设学部,北京100124 [4]中国航天系统科学与工程研究院,北京100037 [5]北京航空航天大学经济管理学院,北京100191 [6]北京航空航天大学复杂系统分析与管理决策教育部重点实验室,北京100191 [7]石家庄铁道大学交通运输学院,河北石家庄050043

出　　处：《管理工程学报》2022年第6期244-252,共9页Journal of Industrial Engineering and Engineering Management

基　　金：国家自然科学基金资助项目(71890971、72101011、71971005);河北省自然科学基金资助项目(E2018407051);河北省引进留学人员资助项目(C20190333)。

摘　　要：本研究的主要目的是确定城市道路新建和养护的动态最优投资分配策略。为此,本文以宏观视角构建了含有随机项的连续时间最优控制模型以实现城市所有用户出行成本的最小化。本文利用动态规划原理推导出随机最优控制问题的最优性条件:哈密尔顿-雅克比-贝尔曼方程,得到含有偏导数项的动态最优投资策略,同时对动态最优投资策略与状态变量、各参数之间的关系进行了定性分析。本文采用一种估计最优值函数中参数的方法求解得到动态最优投资策略的解析解,此解析解中只含有各状态变量与参数。最后,本文以实际数据为例,给出了2019-2028年的城市道路新建和养护的动态最优投资策略,并通过蒙特卡洛试验对其与现行投资策略的效率进行定量比较分析。本文通过理论及数值分析得到以下重要结论:(1)动态最优投资策略为一个闭环的反馈控制,即最优策略是路网流量与路网容量两个状态变量的函数。(2)动态最优投资策略在理论上不能保证在一次独立试验中得到的出行成本一定是最小的,因为管理者只能把握随机变量的特征,即期望值与标准差,而并不能准确预知下一年度的实际情况。(3)引入社会贴现率后的最优值函数参数估计方法将会拥有更大的适用范围。(4)在案例分析中,通过10000次的蒙特卡洛试验对动态最优投资策略与现行投资策略进行对比分析可知,动态最优投资策略可降低所有用户1414.1466万元/天的出行成本,同时动态最优投资策略的占优比例为100%。With the rapid development of the national economy and the growth of traffic flow,the contradiction between traffic supply and traffic demand has become increasingly prominent.To alleviate the negative externalities caused by traffic congestion,while promoting both economic and social development,the construction of new roads for increasing the upper bound of the road network capacity is an important measure.Moreover,over their service period,urban roads are damaged to different degrees.To recover their capacity,timely road maintenance measures are required continuously.Therefore,considering limitations imposed by budget,to minimize the total travel cost of all vehicles,the road manager needs to allocate funds scientifically and optimally for both construction and maintenance of roads.A review of the relevant literature shows that:(1)most studies either addressed the method,opportunity,and investment strategy for road maintenance or the optimal total investment amount for regional transportation infrastructure.However,the optimal investment allocation between the construction of new roads and the maintenance of existing roads was not considered;(2)traffic flow is an exact and exogenous value but the uncertainty and interaction mechanisms between road construction and traffic flow were not considered;(3)to address a large-scale road network problem,it is difficult to apply the bi-level programming model based on user equilibrium theory,as commonly used in the literature.To overcome these problems,the present study aims to establish a stochastic optimal control model to identify the dynamic optimal investment allocation between road construction and road maintenance.In the first part,according to the actual situation,the following four important elements are considered:(1)investment budget,(2)costs,(3)road network capacity,and(4)traffic flow.To represent the interaction mechanism between traffic flow and road network capacity more clearly,the growth of the road network capacity is considered to stimulate the growth

关 键 词：交通工程 道路新建与养护 随机最优控制 动态规划原理 哈密尔顿-雅克比-贝尔曼方程 

分 类 号：F570[经济管理—产业经济]