Bioattacks, i.e., the intentional release of pathogens or biotoxins against humans to cause serious illness and death, pose a significant threat to public health and safety due to the availability of pathogens worldwide, scale of impact, and short treatment time window. In this paper, we focus on the problem of prepositioning inventory of medical countermeasures (MCM) to defend against such bioattacks. We introduce a two-stage robust optimization model that considers the policymaker's static inventory decision, attacker's move, and policymaker's adjustable shipment decision, so as to minimize inventory and life loss costs, subject to population survivability targets. We consider a heuristic solution approach that limits the adjustable decisions to be affine, which allows us to cast the problem as a tractable linear optimization problem. We prove that, under mild assumptions, the heuristic is in fact optimal. Experimental evidence suggests that the heuristic's performance remains near-optimal for general settings as well. We illustrate how our model can serve as a decision support tool for policy making. In particular, we perform a thorough case study on how to preposition MCM inventory in the United States to guard against anthrax attacks. We calibrate our model using data from multiple sources, including publications of the National Academies of Sciences and the U.S. Census. We find that, for example, if U.S. policymakers want to ensure a 95% survivability target for anthrax attacks that simultaneously affect at most two cities (in the same or different states), the minimum annual inventory budget required is approximately $330 million. We also discuss how our model can be applied in other contexts as well, e.g., to analyze safety-stock placement in supply-chain networks to hedge against disruptions.
Massachusetts Institute of Technology, August 2016