The Gateway Location Problem: A Cost Oriented Analysis of a New Risk Mitigation Strategy in Hazmat Transportation

Modern societies rely upon massive supplies of large amounts of commodities, some of which imply the use of hazardous materials (hazmat). A crucial step in the hazmat life cycle is transportation. An accident en route is a “low probability - high consequences” event and much effort has been devoted to the development of risk mitigation strategies. In this paper we are concerned with hazmat transportation by truck on a road network, where several alternative itineraries from origin to destination are worthy of choice. Given a set of origin-destination pairs and the hazmat quantities to be transported for each pair, the road network topology, and the cost and the risk of each arc, the aim is to reduce the total risk related to the hazmat itineraries, hopefully not to a sensitive detriment of cost. In a mixed urban setting, the shortest path is often a risky one. Whenever possible, the network administrator imposes to each driver a specific itinerary with lower risk. If not possible, the network administrator may enforce some restrictions regarding network usage, such as forbidding hazmat transit on some links or imposing tolls. Within this framework, we propose a new method that diverts vehicles from their shortest (and risky) path from origin to destination, by forcing each vehicle to pass through an intermediate check point, so called gateway. We face the problem of selecting the location of a given number of gateways among a larger number of potential locations and assigning a gateway to each vehicle such that the total risk is minimized. Once gateways are located and assigned, the “rational” driver will travel along the shortest path from its origin to its assigned gateway, and then from such a gateway to its destination. While previous studies have experimentally demonstrated the efficacy of our strategy, the issue of the cost of the solutions has never been analyzed in depth. In this work we describe how to efficiently compute the Pareto frontier given by the non dominated solutions with respect to total risk and total cost on realistic instances taken from the literature, and we present computational results showing that the solution yielded by our method represents a very good compromise between the two criteria since it achieves substantial risk mitigation while providing an efficient trade off with cost.