Humanitarian logistics encompasses a wide spectrum of conditions or constraints for supply chains, yet its focus on mitigating human suffering efficiently is what has motivated organizations and governments to make rapid decisions in real time. In this article, through the approach to an emergency such as COVID-19, we propose a two-stage model capable of considering human suffering, the cost of humanitarian logistics, and the benefit obtained by the interaction of suppliers that generally behave as oligopolies through a mathematical programming model and one of the cooperative games. Our main finding was the adaptability of a previously validated model for humanitarian logistics to the ongoing COVID-19 pandemic, where the externalities had greater relevance in social costs than private costs.