Pre-positioning disaster response facilities at safe locations: An evaluation of deterministic and stochastic modeling approaches

Choosing the locations of disaster response facilities for the storage of emergency supplies is critical to the quality of service provided post-occurrence of a large scale emergency like an earthquake. In this paper, we provide two location models that explicitly take into consideration the impact a disaster can have on the disaster response facilities and the population centers in surrounding areas. The first model is a deterministic model that incorporates distance-dependent damages to disaster response facilities and population centers. The second model is a stochastic programming model that extends the first by directly considering the damage intensity as a random variable. For this second model we also develop a novel solution method based on Benders Decomposition that is generalizable to other 2-stage stochastic programming problems. We provide a detailed case study using large-scale emergencies caused by an earthquake in California to demonstrate the performance of these new models. We find that the locations suggested by the stochastic model in this paper significantly reduce the expected cost of providing supplies when one considers the damage a disaster causes to the disaster response facilities and areas near it. We also demonstrate that the cost advantage of the stochastic model over the deterministic model is especially large when only a few facilities can be placed. Thus, the value of the stochastic model is particularly great in realistic, budget-constrained situations.