Capacity reliability under uncertainty in transportation networks: an optimization framework and stability assessment methodology

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.