A Fair Division Approach to Humanitarian Logistics Incorporating Conditional Value-at-Risk∗

Organization and efficiency of relief operations are vital following a major disaster, as well as the guarantee that all of the affected population will adequately have their basic needs met. However, in a post-disaster environment, uncertainty often impacts all aspects of the relief efforts. Placement of relief distribution centers, as well as public knowledge of these locations, is crucial to the speed and efficiency of relief efforts. This research aims to develop a formulation to chose a set of distribution centers to open from a list of available facilities and to assign every member of the population to a distribution center. While developing these assignments, the costs to the affected population are considered in the form of travel costs to reach the assigned distribution center. Incorporation of these travel costs, a form of deprivation costs, minimizes the suffering of the population, and inclusion of ideas from fair division minimizes disparities in these costs to provide each member of the affected population with a fair level of service. Further, the inclusion of a term inspired by conditional value-at-risk, or CVaR, into the formulation helps to further minimize potential disparities. Computational results for two datasets will be discussed to show the impact of including deprivation costs in this humanitarian logistics model. Additionally, theoretical results will show that optimal solutions to the formulation are guaranteed to be Pareto efficient. ∗This research was supported by the National Science Foundations grant entitled Collaborative CDI-Type II: Cyber Enabled Discovery System for Advanced Multidisciplinary Study of Humanitarian Logistics for Disaster Response (NSF-IIS 1124827). This support is both acknowledged and appreciated.