Optimal districting in post-disaster environments

Abstract

Disaster Response Logistics encompasses the logistical activities of the various emergency response functions conducted in post-disaster environments such as search and rescue, volunteer management, and distribution of relief supplies. Conducting these activities in an effective and expeditious manner is critical. In this context, it is often advisable to subdivide impacted areas so that the numerous groups responding to the disaster can focus their attention on specific subareas, while ensuring a comprehensive coverage and minimized completion time. The optimal subdivision of the impacted area —referred in the literature as districting— is the main focus of this dissertation.

This research proposes two mathematical formulations that districts a disaster area among relief groups taking into account the amount of resources brought to the area, as well as capacities of candidate sites and the population needs. The formulations optimize the social costs, i.e. the summation of logistics and deprivation costs, and differ from each other in the way logistics costs are calculated. The first model is based on costs per vehicle-trip and the second model is based on cost per unit of cargo transported.

The formulations are tested with several scenarios that combine a set of relief groups, a set of candidate sites to be set up as Relief Distribution Centers (RDCs) and a set Points of Distribution (PODs). For each model two types of policies for the arrival of supplies are considered. The first, considers the situation where all supplies are available on hand at the start of the operations, while the second, considers the scenario when supplies arrive to the RDCs at a rate per unit of time. An experimental factor ρ, defined as the percentage of supplies available to meet the demand, is used to examine the change in the districting and delivery strategies. The results from the models confirm that districting ensures service coverage of population in impacted areas while minimizing deprivation costs resulting from the relief distribution.