Emergency relief network design under ambiguous demands: A distributionally robust optimization approach

This paper focuses on an emergency rescue network design problem in response to disasters under uncertainty. Considering the limited distribution information of the uncertain demands extracted from the historical data, we use the mean absolute deviation (MAD) that can derive tractable reformulations and better capture outliers and small deviations, to construct a MAD-based ambiguity set. A distributionally robust optimization model is proposed with the objective of minimizing the preparedness cost and the expected penalty cost of demand shortage under the worst-case distribution over the ambiguity set. We analyze the constructed model and provide some features such as the theoretical bounds of the objective value. For large-scale cases, we reformulate the knotty model using the linear decision rule to obtain tight and tractable problems. Computational experiments verify that the out-of-sample performance of the proposed model is better than that of the stochastic optimization model, especially for extreme cases. The MAD-based ambiguity set combined with the approximation technique can reduce the solution time and obtain high-quality solutions. Moreover, the results show that the amount of data has a significant effect on model performance. These results provide references for decision-makers in the practice of emergency response network design.