A bilevel flow model for hazmat transportation network design

Abstract

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be stable, and we provide an approach for testing its stability and for evaluating the range of the its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and heuristic algorithm are experimented on real scenarios of an Italian regional network.

Methodological Advances and New Formulations for Bilevel Network Design Problems

“…Further, a stable MILP was introduced by Amaldi et al (2011). To also distribute the risk fairly, Bianco et al (2009) introduced a bilevel model that not only minimizes the total risk in the network, but also the maximum risk over all arcs. This idea was also used in a game-theoretic approach for the fair distribution of risk by Bianco et al (2015).…”

“…Alp, 1995;Bianco et al, 2009;Kara and Verter, 2004), the risk calculation is associated with arcs. With P ij being the accumulated effected population in the area of arc (i, j), Erkut and Verter (1998) define the risk of an arc by k∈K σ km ij P ij φ k x km ij .…”

“…Even though some researchers already pointed out that risk equilibration needs to be considered (e.g. , so far only a few publications in this direction exist (Bianco et al, 2009(Bianco et al, , 2015. These ideas distribute the risk fair among arcs, but neglect that different transportation modes need to be considered.…”

Generalized route planning model for hazardous material transportation with VaR and equity considerations

“…Carriers usually focus on the routing problem of singlecommodity single O-D pair trips individually-to select a route between a given O-D pair for a given hazmat type-which is called local route planning [7]. However, the main concern of a government authority is to control the total risk over the population and the equity distribution of this risk over population zones, which can only achieved by simultaneously considering all of the local route planning problems, i.e.…”

The Research of Hazardous Chemicals Transportation Risk Assessment Based on Classification

“…(1991)提出用可能的暴露人 数来度量危险化学品运输风险； Abkowitz et al [5] (1992) 提出了反映感知风险的度量模型；Erkut and Verter [6] (1995)在总结前人研究的基础上提出了用"期望损失" 来表示风险，认为风险等于事件概率与事件所带来后 果的乘积；Sivakumar et al [7] (1995)针对该类问题提出 了条件风险(事故发生后的风险值)；Erkut and Ingolfsson [8] (2000)针对危险化学品运输事故的低概率高 危害的特征，提出了 3 个基于大灾害规避的风险度量 模型，分别用运输路径上的最大暴露人口、最小期望 损失方差和最小期望效用来度量运输风险；Fabiano et al [9] (2002)考虑了与路径独立和与路径相关的两种信 息，综合了内在因素(隧道、弯曲半径、斜率、路的特 征等)和与运输条件相联系的外在因素(运输车辆等)， 提出了一般危险化学品运输风险分析的框架；Erkut and Ingolfsson [10] (2005)又针对传统模型提出了三个改 进的风险模型，通过改进事故率使得模型更加准确。 在路径选择中，Wijeratne et al [11] (1993)在随机网 络下对有害物品运输的路径选择进行了研究，给出了 随机条件下路径的比较原则，并设计了求解的算法； Patell [12] (1994)对有泄漏危险的化学品的最优运输路 径进行了研究；Kara et al [13] (2004)先后使用了类似的 危险品运输双层规划模型并使用库恩-塔克条件提 出该模型的一个简单解法；邵辉等 [14] (2010)将多目标 优化问题与危险化学品运输紧密联系起来，建立基于 多目标优化的危险化学品运输路径模式；Chang et al [15] (2005)在时变随机条件下对有害物品运输的路径 选择问题进行了研究，建立了运输时间、人口覆盖率 和事故率的概率分布函数，然后给出了一种求解的算 法；Bianco et al [16] (2009)采用双层规划研究了道路路 化学品运输网络的构建问题，将双层规划模型转化为 单层混合整数规划问题，用商业软件进行求解；Rojee et al [17] (2010)运用蚁群算法提出了一种后启发式算法 基于分级的危险化学品运输风险评价研究 来解决多目标路径优化的问题；储庆中等 [18] [19] (1991)等对危险 品运输风险评价和选线进行了综合分析，概述了20世 纪80年代的主要研究方法；John [20] (1995)将风险、运 输平衡及费用情况建立危险化学品公路运输的多目 标风险评估方法；吴宗之 [21] (2007)等基于危险品道路 运输过程风险分析，系统地研究了路径优化选线问 题，提出了危险品道路运输路径优化的一般程序，构 建了优化选线评价指标体系和决策框架；Verter and Kara [22] …”