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A fair division approach to humanitarian logistics inspired by conditional value-at-risk

  • S.I.: Risk Management Approaches in Engineering Applications
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Abstract

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 develops a formulation to choose 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.

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Acknowledgments

We are very grateful to two referees, whose comments enabled us to greatly improve the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Virginia Military Institute, Lexington, VA, 24450, USA

    Amy Givler Chapman

  2. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    John E. Mitchell

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  1. Amy Givler Chapman
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  2. John E. Mitchell
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Correspondence to Amy Givler Chapman.

Additional information

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.

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Chapman, A.G., Mitchell, J.E. A fair division approach to humanitarian logistics inspired by conditional value-at-risk. Ann Oper Res 262, 133–151 (2018). https://doi.org/10.1007/s10479-016-2322-1

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