摘要
新增应急避难点选址问题是应急管理中的一项重要内容。基于就近避难的原则,本文考虑避难者人数的不确定性和道路的通行能力限制,以所有避难者完成撤离时间的最大后悔值最小为目标,研究一般网络图上新增应急避难点的鲁棒选址问题。首先,当避难者人数确定时,本文通过对网络结构及问题性质的分析,把一般网络图分解成多项式个树图,给出了时间复杂度为O(mn^(2))的求解算法。接着,当避难者人数为区间值时,本文分析最大后悔场景的权重结构特征,找出所有可能的最大后悔场景集合,计算相应的后悔值,设计了时间复杂度为O(m^(2)n^(4))的求解算法。最后,基于不同权重区间组距设计了数值算例。通过分析可知,最小最大后悔值不会随着权重区间最大组距的减小而减小,但会随着所有权重区间组距的减小而减小;当组距较小时,平均期望权重具有较好的替代效果。相关结果能够为实际中新增应急避难设施的选址问题提供一定的理论指导。
In the past two decades,various natural disasters,accidents,and events that endanger public health or security have occurred throughout the world,impacting public safety,social order,people′s lives and property.A sound urban emergency management system,of which facility location is vital part,can reduce or even prevent the losses caused by emergencies.An appropriate emergency facility location can expedite evacuation procedures,reduce harm,and prevent the occurrence of secondary disasters.Because of continuous development and the consequent dramatic increase in demand,however,existing facilities may not be able to cope with an emergency under the current conditions.This paper considers edge capacity limits and the uncertainty of supply,and studies the conditional sink location problem in dynamic general networks with accessibility.“Conditional”here refers to the condition that the network already has some emergency facilities.The location problem of adding a new emergency facility(the k-^(th) one)when there are already k-1(k≥2)facilities in a dynamic general network is examined,under the assumption that all weights on the dynamic network will evacuate to the nearest sink point along the shortest path.G=(V,E)is an undirected connected simple graph with n vertices and m edges.The weight of each vertex represents the number of people who need to evacuate.Each vertex has an unknown weight,but the interval to which it belongs is given,and each edge has a positive length and uniform capacity.The assignment of a weight to each vertex creates a scenario.The objective function is based on maximum completion time(when all supplies have reached the sink point).To handle the uncertainty of the vertex weight,robust optimization is adopted and the worst-case scenario is taken as the goal.A new sink point should thus be located such that the maximum regret value of the maximum completion time is minimized.The first part of the paper provides definitions and properties.First,the structural features of the dynamic general
作者
李红梅
邓洁
罗太波
齐捧虎
LI Hongmei;DENG Jie;LUO Taibo;QI Penghu(School of Economics and Management,Northwest University,Xi′an 710127,China;School of Economics and Management,Xidian University,Xi′an 710126,China)
出处
《管理工程学报》
CSSCI
CSCD
北大核心
2022年第4期218-229,共12页
Journal of Industrial Engineering and Engineering Management
基金
国家自然科学基金资助项目(71701162)
教育部人文社科项目(18YJC630114)
教育部基本科研业务费资助项目(XJS190602)。
