A discrete-continuous approximation model for optimal facility location in disaster response logistics

Abstract

Disaster preparedness efforts regarding the location and prepositioning of relief supplies are becoming much more crucial than ever before. After major disasters and catastrophic events, local distribution is challenging as resources are mostly or entirely destroyed in the affected region, posing unique challenges to distributing relief supplies. As a result, local supplies may not be available for the population in need. This research considers the decisions made by disaster relief organizations on the location of points of distribution (PODs) in a continuous geographical region and the size of the region (district) served by the POD. Given a fixed distribution center where relief supplies are stored, the problem considers identifying the districts' shapes and the location of the PODs inside the district, such that it minimizes the total social costs. The social costs are the summation of the private or logistics costs and the externalities of the distribution of relief in the form of deprivation costs. These deprivation costs are incurred by the population in need because of the time spent without the relief supplies.

This research develops a discrete-continuous facility location model that has two main components. The first component is a mixed-integer programming (MIP) formulation to select the best districting configuration for the PODs and the distribution strategy for relief supplies prepositioned at the PODs, subject to time and capacity constraints. The second component is a set of continuous-approximation models that compute the total deprivation costs for different shapes integrated into the MIP formulation. The analytical and numerical results provide unique insights that can be used by disaster responders in their preparedness efforts for the distribution of relief. Mainly regarding the location and number of PODs required in areas impacted by disasters. These findings also provide alternative distribution strategies in the affected regions.