Exact robust solutions for the combined facility location and network design problem in hazardous materials transportation

We consider a leader-follower game in the form of a bi-level optimization problem that simultaneously optimizes facility locations and network design in hazardous materials transportation. In the upper level, the leader intends to reduce the facility setup cost and the hazmat exposure risk, by choosing facility locations and road segments to close for hazmat transportation. When making such decisions, the leader anticipates the response of the followers who want to minimize the transportation costs. Considering uncertainty in the hazmat exposure and the hazmat transport demand, we consider a robust optimization approach with multiplicative uncertain parameters and polyhedral uncertainty sets. The resulting problem has a min-max problem in the upper level and a shortest-path problem in the lower level. We devise an exact algorithm that combines a cutting plane algorithm with Benders decomposition