Mathematical problems for designing a short-distance relief goods distribution network in urban areas

In the humanitarian relief efforts after an earthquake strikes, local capabilities are critical in the first hours to assess the situation and deliver relief supplies to the victims. Usually, the relief goods required by victims are unlikely to be found in the impacted areas, and resources from other places need time to be mobilized to the affected areas. Often in earthquakes in cities in developing countries, relief goods do not arrive on time causing victims to suffer even more. In this paper, we present the mathematical formulations and solutions techniques for designing a short-distance distribution network of relief goods, which can be managed by local governments. In the preparation phase, as a part of the immediate response plan based on scenarios, the facilities location and the preliminary distribution paths must be determined. Hence, a p-median problem and a multi-depot heterogeneous fleet vehicle routing problem (MDHFVRP) must be solved. These problems are usually small and there is time to find a solution. However, in the response phase, a dynamical VRP must be solved.