Truck-drone supported humanitarian relief logistics network design: A two-stage distributionally robust optimization approach

In this paper, we investigate a truck-drone supported humanitarian relief logistics network (HRLN) design problem. The objective of this problem is to minimize the total cost while considering the characteristics of truck and drone delivery operations. The uncertainty of the basic relief supply (e.g., tents and food) demand and emergency relief supply (e.g., medicines and vaccines) demand in each disaster area and the uncertainty of highway capacity after the disaster are considered simultaneously. Given the incomplete demand distribution information, we establish a two-stage distributionally robust optimization model, where the two stages correspond to predisaster and postdisaster decision-making. An ambiguity set is adopted on the basis of the type-1 Wasserstein metric. We prove that the abovementioned model has an equivalent computationally tractable form and design a decomposition algorithm with several acceleration strategies. Numerical experiments based on a real-world case (the 2010 Yushu earthquake in Qinghai Province, China) are conducted. The experimental results show that our proposed acceleration strategy (i.e., the level regularization method) can increase algorithm efficiency. Sensitivity analyses for the radius control parameter, the budget, and the penalty cost validate the effectiveness of the model. The results of the out-of-sample analysis show that our model can produce reliable solutions, as there would only be up to 20% additional cost under most out-of-sample scenarios.