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A Trilevel r-Interdiction Selective Multi-Depot Vehicle Routing Problem With Depot Protection
Computers & Operations Research ( IF 4.6 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.cor.2020.104996
Mir Ehsan Hesam Sadati 1 , Deniz Aksen 2 , Necati Aras 3
Affiliation  

Abstract The determination of critical facilities in supply chain networks has been attracting the interest of the Operations Research community. Critical facilities refer to structures including bridges, railways, train/metro stations, medical facilities, roads, warehouses, and power stations among others, which are vital to the functioning of the network. In this study we address a trilevel optimization problem for the protection of depots of utmost importance in a routing network against an intelligent adversary. We formulate the problem as a defender-attacker-defender game and refer to it as the trilevel r-interdiction selective multi-depot vehicle routing problem (3LRI-SMDVRP). The defender is the decision maker in the upper level problem (ULP) who picks u depots to protect among m existing ones. In the middle level problem (MLP), the attacker destroys r depots among the (m–u) unprotected ones to bring about the biggest disruption. Finally, in the lower level problem (LLP), the decision maker is again the defender who optimizes the vehicle routes and thereby selects which customers to visit and serve in the wake of the attack. All three levels have an identical objective function which is comprised of three components. (i) Operating or acquisition cost of the vehicles. (ii) Traveling cost incurred by the vehicles. (iii) Outsourcing cost due to unvisited customers. The defender aspires to minimize this objective function while the attacker tries to maximize it. As a solution approach to this trilevel discrete optimization problem, we resort to a smart exhaustive enumeration in the ULP and MLP. For the LLP we design a metaheuristic algorithm that hybridizes Variable Neighborhood Descent and Tabu Search techniques adapted to the Selective MDVRP (SMDVRP). The performance of this algorithm is demonstrated on 33 MDVRP benchmark instances existing in the literature and 41 SMDVRP instances generated from them. Numerical experiments on a large number of 3LRI-SMDVRP instances attest that our comprehensive method is effective in dealing with the defender-attacker-defender game on multi-depot routing networks.

中文翻译:

具有仓库保护的三级r-拦截选择性多仓库车辆路径问题

摘要 供应链网络中关键设施的确定一直引起运筹学界的兴趣。关键设施是指对网络运行至关重要的桥梁、铁路、火车站/地铁站、医疗设施、道路、仓库和发电站等结构。在这项研究中,我们解决了一个三级优化问题,以保护路由网络中最重要的仓库免受智能对手的攻击。我们将该问题表述为防御者-攻击者-防御者博弈,并将其称为三级 r 拦截选择性多站点车辆路径问题 (3LRI-SMDVRP)。防御者是上层问题(ULP)中的决策者,他从现有的 m 个仓库中选择 u 个仓库进行保护。在中层问题(MLP)中,攻击者摧毁(m-u)个未受保护的仓库中的r个仓库,以带来最大的破坏。最后,在较低级别的问题(LLP)中,决策者又是防御者,他优化车辆路线,从而选择在攻击后访问和服务的客户。所有三个级别都具有相同的目标函数,该目标函数由三个部分组成。(i) 车辆的运营或购置成本。(ii) 车辆产生的交通费用。(iii) 由于未拜访客户而产生的外包成本。防御者希望最小化这个目标函数,而攻击者则试图最大化它。作为此三级离散优化问题的解决方法,我们在 ULP 和 MLP 中采用智能穷举枚举。对于 LLP,我们设计了一种元启发式算法,该算法混合了适用于选择性 MDVRP (SMDVRP) 的可变邻域下降和禁忌搜索技术。该算法的性能在文献中现有的 33 个 MDVRP 基准实例和由它们生成的 41 个 SMDVRP 实例上得到了证明。大量3LRI-SMDVRP实例的数值实验证明,我们的综合方法在处理多站路由网络上的防御者-攻击者-防御者博弈方面是有效的。
更新日期:2020-11-01
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