Pre-disaster location and storage model for emergency commodities considering both randomness and uncertainty

Reasonable location of warehouses and adequate storage of emergency commodities before disasters play an important role in providing timely rescue after disasters. For certain disasters, such as typhoons and floods, the affected areas are often relatively fixed in several different places. The likelihood of such disasters can be inferred from historical data, but it is difficult to predict the intensity of a particular disaster in each place. Therefore, both randomness and uncertainty should be considered in the preparation stage of these disasters. In this paper, we propose a two-stage pre-disaster location and storage model to hedge against such disasters. The first stage of the model determines the location of warehouses and the storage level of emergency commodities. The second stage uses stochastic optimization and robust optimization to deal with the randomness of the affected areas and the uncertainty of the disaster intensities, respectively. By linking the damage strength of a disaster to the partial capacity loss of an emergency facility, we also considered the reliability problem of facilities in the framework of robust optimization. A modified column-and-constraint generation method has been implemented to solve the model. The proposed model is applied to a simplified Sioux Falls transportation network to illustrate the effectiveness of combining randomness and robustness in the model.