Humanitarian Relief Distribution Problem: An Adjustable Robust Optimization Approach

Management of humanitarian logistics operations is one of the most critical planning problems to be addressed immediately after a disaster. The response phase covers the first 12 hours after the disaster and is prone to uncertainties because of debris and gridlock traffic influencing the dispatching operations of relief logistics teams in the areas affected. Moreover, the teams have limited time and resources, and they must provide equitable distribution of supplies to affected people. This paper proposes an adjustable robust optimization approach for the associated humanitarian logistics problem. The approach creates routes for relief logistics teams and decides the service times of the visited sites to distribute relief supplies by taking the uncertainty in travel times into account. The associated model allows relief logistics teams to adjust their service decisions according to the revealed information during the process. Hence, our solutions are robust for the worst-case realization of travel times, but still more flexible and less conservative than those of static robust optimization. We propose novel reformulation techniques to model these adjustable decisions. The resulting models are computationally challenging optimization problems to be solved by exact methods, and, hence, we propose heuristic algorithms. The state-of-the-art heuristic, which is based on clustering and a dedicated decision-rule algorithm, yields near optimal results for medium-sized instances and is scalable even for large-sized instances. We have also shown the effectiveness of our approach in a case study using a data set obtained from an earthquake that hit the Van province of Turkey in 2011.