Including deprivation costs in facility location models for humanitarian relief logistics

Humanitarian assistance is meant to save lives and alleviate human suffering during and in the aftermath of man-made and natural disasters. To prevent and strengthen preparedness for the occurrence of such situations, having available relief supplies in the short-term becomes crucial. The lack of access to life-sustaining items implies a loss in people's welfare, treated as an externality called deprivation costs which must be incorporated into decision-making processes. Since typical humanitarian applications are extensions of commercial logistic models, they usually do not account for externalities, leading to high social costs and likely to unfeasible or suboptimal solutions. This paper develops a facility location model for prepositioning supplies in preparation for disasters; the key feature of this formulation being the fact that it explicitly considers deprivation costs in the objective function. The model attempts to minimize the global social costs, as the sum of both private costs (i.e. costs of transportation, inventory costs and fixed costs of facilities) and deprivation costs, determining the amount per type of product to be prepositioned for serving the areas affected by a disaster during the initial response. The model focuses on those assistance interventions that should be carried out immediately, i.e. within the first 24 h of a humanitarian crisis. We applied the model, using real information, to the Colombian Caribbean region, which was affected by floods in 2010 and 2011. Results demonstrate that deprivation costs represent more than 50% of the total social cost.