A stochastic conditional value-at-risk approach to disaster relief planning

Abstract

Following a major disaster, such as Hurricane Katrina or the Indian Ocean Tsunami, organization and efficiency of relief operations is vital to the safety of the affected population and to the speed of recovery. However, disasters cause damage to existing infrastructure further complicating relief efforts. This dissertation aims to account for the variety of potential damages by utilizing a scenario-based stochastic approach to relief planning. Specifically, this research focuses on locating points of distribution, or PODs, from where the population can receive supplies. Further, to ensure adequate levels of service for the population, deprivation costs are included in the model; these deprivation costs represent the costs incurred by the population as a result of the disaster and can range from costs due to lack of access to supplies to the costs incurred from difficulty in obtaining supplies. This research incorporates walking costs, costs due to increased travel distances, into the model, and varies these costs across the scenarios based upon the level of damage to the road network. In order to account for the variability across scenarios, conditional value-at-risk, a commonly used risk measure in financial optimization, is included to look at the costs in the given worst percentage of scenarios. A second approach to the POD placement problem is considered and incorporates ideas from fair division. Fair division encompasses any problem that involves dividing a set of goods "fairly" between a group of agents. The incorporation of fair division helps eliminate disparities in level of service across the population and serves to eliminate biases against select population groups. Results show that the inclusion of deprivation costs influences the solution to the POD placement problem, and we will discuss a variety of ways to formulate scenarios. Further, we will introduce theoretical results that can be implemented in order to reduce computational time when conditional value-at-risk is included in the objective function.