Dynamic Inventory Relocation in Disaster Relief^†

This study investigates dynamic inventory relocation to respond proactively to the changing relief demand forecasts over time. In particular, we examine how to relocate mobile inventory optimally to serve nonstationary stochastic demand at several potential disaster sites. We propose a dynamic relocation model using dynamic programming (DP) and develop both analytical and numerical results regarding optimal relocation policies, the minimum cost-to-go function, and the value of inventory mobility over traditional warehouse pre-positioning. Given the computational complexity of the backwards DP algorithm, we develop a base state heuristic (BSH) for general problems by exploiting the real-world disaster pattern of occurrence. For problems with temporally independent demand, we propose a polynomial time exact algorithm based on a spatial–temporal graph. For problems with spatially independent demand, we design a speedup technique to implement BSH in polynomial time. The proposed model and algorithms are further extended to consider the impact of transportation uncertainties. Numerical experiments show that the proposed algorithms return high-quality decisions only in a small fraction of the time required by an exact algorithm and a myopic algorithm. The proposed model and algorithms are applicable to any type of mobile inventory, facility, or server in similar settings.