Solving the hazmat transport network design problem

In this paper, we consider the problem of network design for hazardous material transportation where the government designates a network, and the carriers choose the routes on the network. We model the problem as a bilevel network flow formulation and analyze the bilevel design problem by comparing it to three other decision scenarios. The bilevel model is difficult to solve and may be ill-posed. We propose a heuristic solution method that always finds a stable solution. The heuristic exploits the network flow structure at both levels to overcome the difficulty and instability of the bilevel integer programming model. Testing on real data shows that the linearization of the bilevel model fails to find stable solutions and that the heuristic finds lower risk networks in less time. Further testing on random instances shows that the heuristically designed networks achieve significant risk reduction over single-level models. The risk is very close to the least risk possible. However, this reduction in risk comes with a significant increase in cost. We extend the bilevel model to account for the cost/risk trade-off by including cost in the first-level objective. The biobjective–bilevel model is a rich decision-support tool that allows for the generation of many good solutions to the design problem.