Location Models with Routing Considerations for a Single Obnoxious Facility

The problem of optimally locating obnoxious facilities such as hazardous waste repositories, dump sites, or chemical incinerators has been the source of much controversy. Often, the final decision on where to locate the facility has been based on criteria that are difficult to quantify. Previous efforts have focused on where to locate such a facility to minimize the total population which will be exposed to the facility. Similarly, efforts have been made to route the waste as to minimize the exposed population. Attempts at combining the two elements of risk to determine locations have been restricted to selecting from a given set of candidate locations. In this paper a combined model is developed that quantifies the total exposure of the population during transportation as well as long term storage. Some properties of the exposure function are developed that help in the solution of special cases of the problem. We show that the problem admits a nodal optimality result when there are no location risks. The result extends even for biobjective problems involving exposure and cost. When location risks are considered and population is concentrated at nodes, the problem exhibits a finite dominating set. With uniform population distribution on arcs and node populations, it is possible to partition the arcs of the network and search for the global optimum solution.