Pre‐positioning planning for emergency response with service quality constraints

Pre‐positioning of emergency supplies is a means for increasing preparedness for natural disasters. Key decisions in pre‐positioning are the locations and capacities of emergency distribution centers, as well as allocations of inventories of multiple relief commodities to those distribution locations. The location and allocation decisions are complicated by uncertainty about if, or where, a natural disaster will occur. An earlier paper (2010) describes a stochastic mixed integer programming formulation to minimize expected costs (including penalties for unmet demand) in such a situation. This paper extends that model with additional service quality constraints. The added constraints ensure that the probability of meeting all demand is at least α, and that the demand is met with supplies whose average shipment distance is no greater than a specific limit. A case study using hurricane threats is used to illustrate the model and how the additional constraints modify the pre‐positioning strategy.