Extended computational formulations for tolerance-based sensitivity analysis of uncertain transportation networks

Abstract

Catastrophes may lead to disruption of human activities and extended damage to network infrastructures, which makes the transportation networks ’uncertain’. Therefore, crisis managers and transportation network computer-based systems (expert systems) need to use reliable facts and solid computational approaches to solve complex decision-making problems in pathfinding and designing transportation networks. In this context, the present work makes a step towards the stability analysis and reliability assessment of uncertain transportation networks (UTNs) and introduces an uncertainty theory-based mathematical model for post-crisis rescue work and on-time arrival of vehicles in disaster areas. This model incorporates uncertain reliability/risk variables associated with links to assess the maximum reliable transmission paths (MRTP) problem and studies the robustness of MRTPs in a post-crisis transportation network. Particularly, uncertainty theory is utilized to model and solve the problem of uncertain links’ tolerances. Unlike the well-known, straightforward frameworks for the tolerance evaluation of a single element, as studied in OR, a generalization of the tolerance-based stability analysis is articulated while perturbations in a set of links are considered, which characterizes the smallest and largest values between which a group of links may vary simultaneously while retaining the optimality of the MRTPs. Such tolerances are referred as to set tolerances, that are usually challenging to calculate. As far as we are concerned, this study is of the earliest ones investigating the uncertain set tolerance stability analysis problem. It proves that set tolerances are well defined and proposes computational formulations in the framework of uncertainty programming to show how such quantities can be systematically calculated or bounded, which are indeed far superior to successive re-optimizations. Finally, the practicality of the model and methods is demonstrated by adopting samples from our real case study and randomly generated networks.