Fair and effective dynamic allocation under stochastic supply and demand

Motivated by humanitarian operations such as food and vaccine distribution, we introduce the fair and effective dynamic allocation under stochastic supply and demand (FEDA-SSD) problem, where real-time resource allocation decisions need to be made under uncertainty. We model the problem as a finite-horizon Markov decision process, in which decisions must be made at pickup and demand points, with supply and demand realizations revealed only upon arrival at each node. With limited vehicle capacity and insufficient total supply, the challenge is to allocate the collected items effectively and equitably. We propose the radial basis function with value function approximation (RBF-VFA) solution framework, employing stage-specific radial basis function interpolants within a backward recursive dynamic programming approach. By training separate models for each decision point and propagating approximations backward, our method enables efficient, near-optimal decision-making. Numerical experiments on empirical and randomly generated instances demonstrate that our RBF-VFA outperforms the best known benchmark for this problem. Our findings provide several managerial insights: we show how conservative early rationing triggers capacity-induced downstream waste, we demonstrate how optimal policies adapt to realized system-wide supply-to-demand ratios, and that the spatial positioning of downstream high-variance demand points alters optimal early allocations.