A Cost‐Sharing Mechanism for Multi‐Country Partnerships in Disaster Preparedness

Abstract

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.

Equity in Health and Humanitarian Logistics: A Beneficiary Perspective

“…Except for Rodríguez-Pereira et al (2021), who consider cost allocation among Caribbean countries and incorporate inter-country solidarity, we found no other paper explicitly discussing beneficiaries' distributional preferences.…”

Collaboration–competition dilemma in flattening the COVID‐19 curve

“…Our findings illustrate the temporal dimension of combining competition and cooperation (Hoffman et al., 2018 ). Our discussion of sequential coopetition, involving the taking and giving of scarce resources, indicates some similarities with risk pooling through joint stockpiles for disaster relief when demand is diverse because disasters strike at different times in different places (Balcik et al., 2019 ; Rodriguez‐Pereira et al., 2021 ; Toyasaki et al., 2017 ). However, unlike physical stockpiles that require comprehensive risk‐ and cost‐sharing mechanisms, our findings imply alternative risk‐pooling options, such as taking and giving depending on how disasters evolve, which can function as a virtual and flexible mitigation strategy.…”

“…Building on this study, Rodriguez‐Pereira et al. ( 2021 ) analyzed solidarity in the region in terms of cost allocation considering disaster risk and economic standing parameters.…”

“…Historical data indicate that sufficient diversity exists to achieve risk-pooling benefits and that resource sharing might help countries cope with the immediate consequences of disasters. Building on this study, Rodriguez-Pereira et al (2021) analyzed solidarity in the region in terms of cost allocation considering disaster risk and economic standing parameters.…”

Cooperative Security Against Interdependent Risks

“…This is, arguably, an innocent fairness criterion which, along with the marginal contribution interpretation discussed before, we shall return to later on in this work. The Shapley value is widely adopted as a cost-sharing or a profit-sharing, as the case may be, allocation method in diverse contexts, including several mentioned in §2, such as inventory pooling (Kemahlıoglu-Ziya and Bartholdi III 2011), capacity allocation and scheduling (Aydinliyim and Vairaktarakis 2010), group purchasing (Chen and Yin 2010), disaster preparedness (Rodríguez-Pereira et al 2021), emission responsibility allocation in supply chains (Gopalakrishnan et al 2021b), and so forth.…”