Destruction of the roads and disruption in transportation networks are the aftermath of natural disasters, particularly if they are of great magnitude. As a version of the network capacity reliability problem, this work researches a post-disaster transportation network, where the reliability and operational capacity of links are uncertain. Uncertainty theory is utilized to develop a model of and solve the uncertain maximum capacity path (UMCP) problem to ensure that the maximum amount of relief materials and rescue vehicles arrive at areas impacted by the disaster. We originally present two new problems of \(\alpha\)-maximum capacity path (\(\alpha\)-MCP), which aims to determine paths of highest capacity under a given confidence level \( \alpha\), and most maximum capacity path (MMCP), where the objective is to maximize the confidence level under a given threshold of capacity value. We utilize these auxiliary programming models to explicate the method to, in an uncertain network, achieve the uncertainty distribution of the MCP value. A novel approach is additionally suggested to confront, in the framework of uncertainty programming, the stability analysis problem. We explicitly enunciate the method of computing the links’ tolerances in \({\mathcal{O}}\left( m \right)\) time or \({\mathcal{O}}\left( {\left| {P^{*} } \right|m} \right)\) time (where \(m\) indicates the number of links in the network and \(\left| {{\text{P}}^{*} } \right|\) the number of links on the given MCP \({\text{P}}^{*}\)). After all, the practical performance of the method and optimization model is illustrated by adopting two network samples from a real case study to show how our approach works in realistic contexts.

道路的破坏和交通网络的中断是自然灾害的后果，特别是如果它们是非常严重的。作为网络容量可靠性问题的一个版本，本文研究了一个灾后交通网络，其中链路的可靠性和运行能力是不确定的。利用不确定性理论建立模型并解决不确定的最大容量路径（UMCP）问题，以确保最大数量的救援物资和救援车辆到达受灾地区。我们最初提出\(\alpha\) -最大容量路径( \(\alpha\)-MCP)，其目的是确定在给定置信水平\(\alpha\) 下最大容量的路径，以及最大容量路径(MMCP)，其中目标是在给定容量值阈值下最大化置信水平。我们利用这些辅助规划模型来说明在不确定网络中实现 MCP 值的不确定性分布的方法。另外还提​​出了一种新方法来解决不确定性规划框架中的稳定性分析问题。我们明确阐述了在\({\mathcal{O}}\left( m \right)\)时间或\({\mathcal{O}}\left( {\left| {P ^{*} } \right|m} \right)\)时间（其中\(m\)表示网络中的链接数和\(\left| {{\text{P}}^{*} } \right|\)给定 MCP 上的链接数\({\text{P}}^ {*}\) )。毕竟，通过采用来自真实案例研究的两个网络样本来说明该方法和优化模型的实际性能，以展示我们的方法如何在现实环境中工作。