A Bi-objective optimization model for contract design of humanitarian relief goods procurement considering extreme disasters

When disaster relief is executed by a monopolistic emergency management agency, this entity is responsible for the procurement and storage of relief goods in the given area. In the case of extreme disasters, relief goods are generally donated to the affected area from all over the world, but the delivery of these donations normally takes time. To ensure effective disaster relief, the emergency management agency should consider extreme disaster scenarios in the procurement of relief goods. Besides, both the supply and demand of relief goods can be differently affected by the disaster depending on its magnitude. And the management agency aims to minimize costs while accounting for potential shortages. In this study, we propose and develop a combined entrusted reserve and option (CEO) contract for humanitarian relief goods procurement. In our model, both the supply and demand of relief goods are described as functions of disasters intensity. Further, a bi-objective optimization problem is formulated with the model to minimize the management agency's expected cost and conditional value-at-risk (CVaR) based shortage risk. Then, we use the epsilon-constraint method to solve the problem and obtain the optimal CEO contract. We also conduct a case study of disasters occurred in Beijing, China from 2000 to 2014. The CEO contract is shown to alleviate losses related to the disasters and reduce costs of the management agency. Insights to further improve the effectiveness of the CEO contract are also discussed in the paper.