Modeling and assessing in-kind donations in multistage disaster preparedness and response

In-kind donations play a crucial role in disaster response by adding valuable surge capacity to existing resources. Within the stochastic programming framework, mainstream literature has primarily portrayed donations as information revealed simultaneously with disaster impact information. However, in practical problems, in-kind donation campaigns are typically triggered after the disaster’s impacts and effects have been revealed. In this paper, we propose a novel three-stage location-allocation model in which donation information is revealed in the third stage, conditional on the disaster impacts revealed in the second stage. Our model’s initial stage involves decisions regarding the location and sizing of relief facilities and the prepositioning of supplies, while the second and third stages involve the distribution of prepositioned and donated supplies, respectively. We propose metrics to evaluate the value of donations, as well as their role as third-stage information, via multistage extensions of both the Expected Value of Perfect Information (EVPI) and the Value of Stochastic Solution (VSS). We also develop a Sample Average Approximation (SAA) scheme with sparsity-enforcing and distribution-fitting features to generate additional scenarios that are reliable representations of historical data. Our approaches are implemented using real data on floods and landslides in Rio de Janeiro, Brazil, and produce novel managerial insights, particularly regarding the correlation between donation amounts and relief service levels. Lastly, we explore the efficiency-equity trade-off by integrating a relative mean difference measure to encourage more equitable allocations of relief supplies.