Optimal Control Strategy for Relief Supply Considering Information and Demand Uncertainty after a Major Disaster

Humanitarian logistics is important for minimizing the damage after a disaster. In Japan, based on past disasters, three empirical control strategies related to humanitarian logistics have been proposed: two relief transportation strategies, and an information strategy without ICT. This paper reveals the mathematical properties of these empirical strategies using an analytic model with closed-form solution. Our approach is based on the stochastic optimal control theory that has never been applied for analyzing humanitarian logistics. Specifically, we formulate the inventory distribution problem considering demand uncertainty as a stochastic optimal control problem with the objectives of minimizing inventory holding and handling costs. Additionally, we consider information uncertainty after a disaster using the Bayesian updating process. This process, by updating at different intervals among depots, models information asynchrony caused by not using ICT. Finally, we analyze the optimal control strategy to reveal the mathematical properties of three empirical strategies. Our results clarify that the two empirical transportation strategies are effective. However, we suggest that in the empirical information strategy without ICT the information paradox, wherein the system gets worse by using information, may occur.