A multi-stage stochastic programming approach for pre-positioning of relief supplies considering returns

A dynamic pre-positioning problem is proposed to efficiently respond to victims’ need for relief supplies under uncertain and dynamic demand in humanitarian relief. The problem is formulated as a multi-stage stochastic programming model that considers pre-positioning with the dynamic procurement and return decisions about relief supplies over a time horizon. To validate the advantages of dynamic pre-positioning, three additional pre-positioning strategies are presented: pre-positioning with one-time procurement and without returns, pre-positioning with one-time procurement and returns, and pre-positioning with dynamic procurement and without returns. Using data from real-world disasters in the United States in the Emergency Events Database, we present a numerical analysis to study the applicability of the proposed models. We develop a sample average approximation approach to solving the proposed model in large-scale cases. Our main contribution is that we integrate dynamic procurement and return strategies into pre-positioning to decrease both costs and shortage risks in uncertain and dynamic contexts. The results illustrate that dynamic pre-positioning outperforms the other three strategies in cost savings. It also indicates that a higher return price is particularly helpful for decreasing unmet demand. The proposed models can help relief agencies evaluate and choose the solutions that will have the greatest overall effectiveness in the context of different relief practices.