Social optimal disaster relief distribution with mobile beneficiaries

Abstract

In post-disaster scenarios, where there are not enough critical relief supplies to satisfy the needs of individuals, the allocation of supplies available is a complex process. This dissertation proposes mathematical formulations that determine the optimal location of points of distribution (PODs) of relief supplies and the optimal allocation of these supplies to those points. This dissertation enhances the analytical formulations in disaster response logistics by incorporating a frequently overlooked feature of disaster conditions: the movements of the impacted population along the disaster area. These formulations explicitly consider the mobility of beneficiaries searching for aid by incorporating their walking trajectories towards their most preferred PODs. Mixed-integer non-linear discrete-time optimization models, these formulations consider other characteristics, such as the beneficiaries' vulnerability and availability of prepositioned relief supplies. The formulations minimize social costs, which include logistics and suffering costs. The latter comprise deprivation costs, an economic valuation of the lack of access to critical supplies in the aftermath of a disaster, and walking costs, associated with the walking trajectory of the beneficiaries. The proposed formulations differ in the composition of the populations. The first formulation assumes that the populations have the same vulnerability characteristics and deprivation cost function parameters. The second formulation considers a heterogeneous composition of the populations in which there are two groups of individuals in each population. One group comprises less vulnerable individuals who can walk, while the other comprises more vulnerable individuals who cannot walk and require the supplies to be delivered to them directly. This dissertation also provides extensive numerical experiments that serve as proof of concept for the proposed formulations and provide a starting point to understanding disaster response logistics dynamics. Last, this dissertation examines the impact of varying such variables on the formulation's social cost function and other critical outputs by investigating the heterogeneous formulation's properties. This dissertation makes a theoretical contribution to the field of disaster response logistics by providing the first analytical formulations for disaster relief distribution decisions that take into account beneficiaries' behavior in the decision-making process and their preferences and walking movements while being comprehensive and maintaining consistency and theoretical adequacy within the latest theoretical developments.