A cost-sharing mechanism for multi-country partnerships in disaster preparedness

We study a multi-country disaster preparedness partnership involving the joint prepositioning of emergency relief items. Our focus is the Caribbean region, which faces increasing disaster threats due to weather-related events and has committed to share its resources for regional integration. We collaborate with the inter-governmental Caribbean Disaster and Emergency Management Agency (CDEMA), which is interested in creating a methodology to equitably (fairly) allocate the costs necessary to operationalize this commitment. We present alternative cost allocation methods among the partner countries by considering their risk level and their ability to pay. Specifically, we adapt some techniques such as the Shapley value, the equal profit method, and the alternative cost avoided method, and we also propose a new insurance-based allocation scheme to determine the country contributions. This mechanism, which is formulated as a linear programming model, sets country premiums by considering the expected value and the standard deviation of country demands and their gross national income. We discuss the structural properties of these methods and numerically evaluate their performance in achieving an equitable allocation scheme with respect to three equity indicators based on the Gini coefficient. Our proposed cost-sharing mechanism not only achieves superior solutions compared with other methodologies with respect to the proposed equity metrics, but is also computationally efficient. We numerically illustrate how it can be used to obtain alternative cost allocation plans by giving different weights to disaster risk and economic standing parameters, and we analyze the benefits and fairness of the partnership in a transparent way.