We discuss maximizing delivery of aid from an aircraft carrier to people in an area hit by a disaster, such as an earthquake, a hurricane, or a tsunami. We propose a diffusion model for the movement of critical supplies once they are delivered to distribution sites within the disaster area, and we express the model in terms of a parabolic partial differential equation (PDE). The purpose of the model is to estimate better the demand at each distribution site, and thus tune the delivery to best meet the need.
Our model has the potential to increase the speed and effectiveness of humanitarian aid. It demonstrates the value of the weak theory of elliptic boundary value problems to address social problems.
We suggest projects for readers and students to develop and expand the model.
Available at the Journal's supplements site http://www.comap.com/product/periodicals/supplements.html is a version of this article containing also an Appendix, which uses more advanced mathematics to derive the solution to the PDE, gives further details of minimizing the objective function, and offers additional projects and model extensions.
We propose a diffusion model for the movement of supplies in a disaster area, and we use the solution of the corresponding PDE to estimate the optimal delivery rates of much needed supplies to distribution sites in the area of need (AoN). This problem would arise if, for example, a navy aircraft carrier were near the area and had helicopters to airlift material from the ship to landing sites in the AoN.
The humanitarian aid disaster relief (HADR) supply chain has many similarities to the commercial supply chain for commodities, and similar models have been used to optimize speed and efficiency at early and middle stages of this process. A HADR issue not common to commercial supply is the difficulty that the consumers-the victims-have in getting the materials that they badly need, even after it has been delivered to the AoN. Because time, transportation, and human strength are all at their limit in disaster situations, modeling this last step in the chain seems valuable to help estimate actual demand at each site where supplies can be delivered in bulk.
Besides the obvious potential to ease human suffering, we also hope that this article demonstrates the importance of mathematical analysis in addressing challenging social concerns in today's world. While our model has its historical roots in the physical sciences, an increasing number of applications are being presented in the life, economic, and social sciences. By making these applications a part of standard courses, the authors hope that more young STEM professionals can be retained in STEM careers [Diekman et al. 2010; McCallum 2017; Thoman et al. 2014].