Coordinating International Humanitarian Inventory by Stochastic Dual Dynamic Programming

ABSTRACT International humanitarian organizations face challenges in inventory management due to unpredictable disasters, evolving emergencies, participant coordination, long planning horizons, and broad geographical coverage. This paper develops an international humanitarian inventory coordination framework, using multi‐stage stochastic programming to make long‐term (monthly or quarterly) procurement, inventory, and transportation decisions. As a counterpart of monetary expense in the objective, a target‐based disutility , that is monotonically non‐increasing and convex, is proposed to measure the suffering caused by insufficient consumption. The model is solved by the generalized Stochastic Dual Dynamic Programming (SDDP), which allows convex recourse functions. The SDDP takes historical demands as input and generates an optimal policy for making future decisions without knowing exact demand information. Unlike deterministic equivalent formulations based on scenario trees, this policy is implementable for out‐of‐sample data. Extensive numerical experiments are conducted with publicly available data from the United Nations Humanitarian Response Depot, the United Nations Office for the Coordination of Humanitarian Affairs (OCHA), and the EM‐DAT international disaster database. The method can generate a policy in under two hours using 216 months (18 years) of data from the 34 most disaster‐vulnerable countries or territories where the OCHA works. The SDDP policy offers up to 21% cost savings over myopic or deterministic policies. Results demonstrate that good out‐of‐sample coordination results can be achieved with a moderate sample size, a reasonable number of iterations, and within the current OCHA organization structure.