A comprehensive modeling framework for hazmat network design, hazmat response team location, and equity of risk

This paper considers a bi-level hazmat transportation network design problem in which hazmat shipments have to be transported over a road network between specified origin-destination points. The bi-level framework involves a regulatory authority and hazmat carriers. The control variables for the regulatory authority are locations of hazmat response teams and which additional links to include for hazmat travel. The regulatory authority (upper level) aims to minimize the maximum transport risk incurred by a transportation zone, which is related to risk equity. Our measure of risk incorporates the average response time to the hazmat incidents. Hazmat carriers (lower level) seek to minimize their travel cost. Using optimality conditions, we reformulate the non-linear bi-level model as a single-level mixed integer linear program, which is computationally tractable for medium size problems using a commercial solver. For large size problems, we propose a greedy heuristic approach, which we empirically demonstrate to find good solutions with reasonable computational effort. We also seek a robust solution to capture stochastic characteristics of the model. Experimental results are based on popular test networks from the Sioux Falls and Albany areas.