A Bilevel Network Flow Model for Planning HazMat Shipments

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be low as much as possible, forcing the regional authority to assure also risk equity. We provide a bilevel programming formulation for this hazmat transportation design problem that takes into account both total risk minimization and risk equity. The model is experimented on real scenarios of an Italian regional network.