Abstract: Since the 21st century, terror has become a major threat in the world. To mitigate the effect of terrorist attacks, it is necessary for the State to pre-position enough relief resource before attacks, which raises the location problem of terror response facilities.
This paper considers a new terror response facility location problem which can be treated as a three stage optimization problem. In the first stage, the State determines where to locate terror response facilities and how many resources allocated to those facilities; in the second stage, the Terrorist determines the attack node by knowing the State's decisions in the first stage; in the last stage, the State optimizes a relief resource allocation problem after an attack.
Therefore, the problem is addressed as a tri-level programming model between decision makers of the State and the Terrorist. The upper level model is associated to the facility location and resource pre-position problem of the State, the middle-level model is related to the attack node selection problem of the Terrorist, and the lower-level model refers to the resource allocation problem of the State.
To solve the tri-level model, we first simplified it into a bi-level model by using dual transformation of the lower-level problem, and then linearized the nonlinear product term in the bi-level model by adding variables and constraints, we finally designed a Benders Decomposition algorithm for solving it.
Our model and algorithm is applied in a case study of 16 cities in south Xinjiang province. The results show that: (i)with the increase of relief resource, the State's optimal strategy of locating and sizing has changed greatly. (ii)There is a diminishing marginal utility effect between the amount of relief resource and the attack loss, even its strength is affected by the amount of Terrorist's attack resource. (iii)The Terrorists prefer to attack major cities and those cities without locating facilities.

Key words: counter-terrorism, facility location, sizing, tri-level programming, benders decomposition

摘要： 反恐应急设施的合理布局和资源配置可缩短救援到达时间并提高应急效率。对已有反恐应急设施选址研究拓展,进一步考虑设施容量有限的情形,并将袭击前后关于应急设施的选址、定容和救援物资分配问题进行集成考虑。将该问题构造为三层规划模型,上中下各层规划分别对应袭击前的选址定容问题、袭击时的袭击点选择问题和袭击后的救援物资分配问题。利用下层规划的对偶变换转化为双层规划,并设计Benders分解算法求解。最后,结合南疆交通网络进行仿真分析,验证了模型和算法的有效性。

关键词: 反恐, 设施选址, 定容, 三层规划, Benders分解算法