基于不完全理性袭击者的反恐应急设施选址模型及应用

Location of terror response facilities: A perspective of incomplete rational attackers

恐怖袭击正成为当今影响社会安全的主要威胁,提高应急管理效率有利于降低恐怖袭击的后果损失,其中,应急设施点的有效布局和合理配置尤为重要。针对恐怖分子不完全理性的现实情境,提出一类新的反恐应急设施选址模型,将p-median经典选址模型和斯坦克尔伯格博弈选址模型进行整合,用于计算面对不完全理性恐怖分子时政府部门关于应急设施点的最优选址策略,进一步研究政府部门错误地将不完全理性恐怖分子误认为非理性和完全理性两种情形下,经典选址模型和博弈选址模型的鲁棒性。关于模型设计了相应的枚举算法和遗传算法,分别用于中小规模和大规模问题的求解。对上海市进行案例分析,结果发现:恐怖分子越理性,袭击造成的损失越大,随着其理性程度的降低,政府的选址策略从“中心区域重点保护”向“整体区域风险平衡”而转变,面对不同理性程度的恐怖分子时,博弈选址模型和经典选址模型的鲁棒性存在优劣差异,且这种差异受到选址数量的影响。

Since September 11 and a series of terrorist attacks,terrorist attacks have become a major threat in the world.Generally,terrorists aim at causing maximum damages,and they prefer to launch attacks in the places with high population density.Thus,once an attack happens,if police and paramedics cannot arrive in time,the attack losses will be huge.To improve the emergency management and mitigate the attack damage,three kinds of terrorist response facility location models are proposed,in which a terrorist is successively considered as completely rational,irrational,and incompletely rational.Based on the models,we first prove the existence of equilibrium solutions and then propose two algorithms for solving both small and large scale problems.Finally,a case study of Shanghai is provided to verify the validity and correctness of both models and algorithms.In the first part,an introduction and a literature review are presented.We find there is a lack of studies on the design of mathematical models and solution algorithms for the terrorist response facility location problems in which the terrorist is incompletely rational.In the second part,three facility location models are proposed.Firstly,as the completely rational terrorist always make the best response to any of government’s location decisions,a Stackelberg location model is presented to characterize the competition relationship between two decision-makers.Secondly,since the probability for irrational terrorists to attack a city depends on the city’s weight,an improved p-median model is proposed for the irrational terrorist.Finally,a novel hybrid location model is addressed to find out the best location strategy when the attacker ha incomplete rationality.This hybrid model is a combination of the Stackelberg and the improved p-median model,only connected by adjusting parameters that controlling the degree of rationality.Moreover,a further study is also done to compare the robustness of both Stackelberg and the improved p-median model when an incomplete rational terrorist is separately falsely regarded as a completely rational one and an irrational one.In the third part,four theorems are proposed to prove the existence of solutions in all three location models,and the correctness of the improved p-median model.Furthermore,another two properties are proved that in the hybrid location model,although the objective function under equilibrium solution monotonously increases with adjusting the parameter,it monotonously decreases with the facility quantity when its cost is not considered.In the fourth part,an exhaustive algorithm and a genetic algorithm are both designed.The exhaustive algorithm ensures to get an exact solution but limited to the problem size.Thus,it is suited for small instance.However,the genetic algorithm has a powerful search capability,but its solution is approximate.Thus,it is suited for some large instance.In the fifth part,the model is applied in a case study of 19 regions in Shanghai.Numerical outcome reflects that the more rational the attacker is,the more attack losses it causes.With the decreasing of terrorist’rational level,the best location strategy of government varies from“central protection”to“overall risk balance.”When the quantity of facility increases,the marginal utility decreases obviously.There is a difference between the robustness of Stackelberg and improved p-median model,and the robustness is also influenced by facility quantities.Finally,we conclude the whole paper and then suggest some future research problems,such as capacitated terrorist response facility location problem,dynamic terrorist response facility location problem,and terrorist response facility location problem with asymmetric information.