Facility location under demand uncertainty: Response to a large-scale bio-terror attack

In the event of a catastrophic bio-terror attack, major urban centers need to efficiently distribute large amounts of medicine to the population. In this paper, we consider a facility location problem to determine the points in a large city where medicine should be handed out to the population. We consider locating capacitated facilities in order to maximize coverage, taking into account a distance-dependent coverage function and demand uncertainty. We formulate a special case of the maximal covering location problem (MCLP) with a loss function, to account for the distance-sensitive demand, and chance-constraints to address the demand uncertainty. This model decides the locations to open, and the supplies and demand assigned to each location. We solve this problem with a locate-allocate heuristic. We illustrate the use of the model by solving a case study of locating facilities to address a large-scale emergency of a hypothetical anthrax attack in Los Angeles County.