A Reliability-Based Resource Allocation Model for Transportation Networks Affected by Natural Disasters

Mohaymany, Afshin Shariat; Ehteshamrad, Shideh; Babaei, Mohsen · 1970 · Crossref

DOI: 10.7307/ptt.v24i6.1200

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Summary

This paper addresses the challenge of optimizing resource allocation in transportation networks to maintain performance under supply uncertainty caused by natural disasters, such as earthquakes. The primary motivation is ensuring that emergency trips can be executed successfully after a disaster by maintaining network connectivity and keeping travel times within acceptable thresholds. The authors propose a reliability-based model that simultaneously incorporates two performance measures: connectivity reliability (the probability that an origin-destination pair remains connected) and travel time reliability (the probability that a trip is completed within a pre-specified time interval). These measures serve as constraints in a mathematical programming framework designed to minimize the total investment budget required to upgrade specific network links. The methodology employs a bi-level optimization approach. The upper level determines which links to invest in to minimize costs while satisfying reliability constraints, while the lower level handles traffic assignment. To estimate reliability measures under uncertainty, the authors use Monte Carlo simulation, generating thousands of deterministic network states where links are either normal, degraded (half capacity), or failed. For each state, an all-or-nothing assignment method is used, assuming travelers choose shortest paths based on free-flow times of working links, as they lack precise information about degraded links immediately post-disaster. The optimization problem is solved using a genetic algorithm, which iteratively evaluates investment scenarios against the reliability constraints derived from the simulations. The model is validated using the Sioux Falls network, reduced to 38 links to represent two-way roads. The study sets minimum thresholds of 0.95 for connectivity reliability and 0.85 for travel time reliability. The genetic algorithm, tuned with specific crossover and mutation rates, converged after 39 iterations. The results identified 12 specific links (less than 30% of the total network) that required investment to satisfy all 60 constraints (30 for connectivity and 30 for travel time across all OD pairs). Post-investment analysis showed that connectivity reliability for all OD pairs improved to above 95%, with many reaching 99%. The study found a correlation between the two metrics, noting that the optimal solution often exceeded the minimum connectivity threshold to ensure travel time reliability was met. The significance of this work lies in providing a unified framework for disaster preparedness planning that balances cost efficiency with robust network performance. By integrating connectivity and travel time reliability into a single optimization model, the approach helps decision-makers prioritize infrastructure investments that maximize the likelihood of successful emergency response. The findings demonstrate that targeted investment in a small subset of critical links can significantly enhance network resilience, ensuring that essential services remain accessible even under severe degradation conditions. This model offers a practical tool for urban planners to evaluate and improve transportation systems against natural hazards.

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