Immediately after a disruption, in order to minimize the negative impact inflicted on the society, its imperative to re-establish the interdicted critical services enabled by the infrastructure networks. In this paper, we study the stochastic network recovery problem that tackles the planning of restoration activities (considering limited resources) on interdicted infrastructure network links so that the pre-disruption critical service flows can be re-established as quickly as possible. As an illustrative case study, we consider a disaster scenario on a road infrastructure network that obstructs the flow of relief-aid commodities and search-and-rescue teams between critical service providing facilities and locations in need of these critical services. As in the case of many realistic applications, we consider the amount of demand for critical services as stochastic. First, we present a Markov decision process (MDP) formulation for the stochastic road network recovery problem (SRNRP), then we propose an approximate dynamic programming (ADP) approach to heuristically solve SRNRP. We develop basis functions to capture the important complex network interactions that can be used to approximate cost-to-go values for the MDP states. We conduct computational experiments on a set of small-scale randomly generated instances and demonstrate that the ADP approach provides near-optimal results regardless of the demand distribution and network topology. In order to develop a practical approach suitable for solving real world sized instances, we propose a framework where we first develop an ADP model and derive a policy on a spatially aggregated network of large scale instance. Next, we show the performance of this policy through computational testing on the large scale disaggregated network. Moreover, we provide managerial insights by assessing the importance of each basis function in the ADP model contributing to the recovery policies. We test this approach on a case study based on the Boston road infrastructure network. We observe that, as the urgency of re-establishing services increases or the resources become more scarce, the information gained from the network characteristics and short-term decisions should be the main driving factors to derive recovery policies. The results of all experiments strongly evidence the significance of utilizing the inherent network interactions and attributes to generate basis function sets for ADP models that yield high-quality recovery policies.

中断之后，为了最大程度地减少对社会的负面影响，必须立即重建由基础架构网络提供的中断的关键服务。在本文中，我们研究了随机网络恢复问题，该问题解决了被中断的基础结构网络链路上的恢复活动（考虑有限的资源）的计划，从而可以尽快重建中断前的关键服务流。作为说明性案例研究，我们考虑了道路基础设施网络上的灾难场景，该场景阻碍了救灾商品和关键服务提供设施与需要这些关键服务的地点之间的搜救团队的流动。与许多实际应用一样，我们认为关键服务的需求量是随机的。首先，我们提出了随机道路网络恢复问题（SRNRP）的马尔可夫决策过程（MDP）公式，然后我们提出了一种近似动态规划（ADP）方法来启发式求解SRNRP。我们开发了基本功能来捕获重要的复杂网络交互，这些交互可用于估计MDP状态的成本成本。我们在一组小规模随机生成的实例上进行了计算实验，并证明了ADP方法提供了近乎最佳的结果，而与需求分布和网络拓扑无关。为了开发一种适用于解决现实世界中大小实例的实用方法，我们提出了一个框架，在该框架中我们首先开发ADP模型并在大型实例的空间聚集网络上推导策略。接下来，我们通过在大规模分类网络上的计算测试来展示该策略的性能。此外，我们通过评估ADP模型中有助于恢复策略的每个基本功能的重要性来提供管理洞察力。我们在基于波士顿道路基础设施网络的案例研究中测试了这种方法。我们观察到，随着重建服务的紧迫性增加或资源变得越来越稀缺，从网络特性和短期决策中获得的信息应该成为制定恢复策略的主要驱动因素。