A bi-level stochastic optimization model for multi-commodity rebalancing under uncertainty in disaster response

In planning for a large-scale disaster, potential relief centers to accommodate evacuees need to be identified. The quantities of emergency commodities are prepared and stocked at relief centers in advance for possible disasters. In the event of a disaster, due to the different disaster severities and uncertain environment, some relief centers inevitably have surplus commodities, whereas some relief centers are still unmet. To use any surplus commodities effectively, a multi-commodity rebalancing process is necessary to rebalance the commodities among relief centers. However, various uncertainties make the multi-commodity rebalancing process extremely challenging, including uncertain demand and transportation-network availability. By recognizing those practical uncertainties, a bi-level stochastic mixed-integer nonlinear programming model is proposed to formulate this multi-commodity rebalancing problem. The upper-level objective is to minimize the total dissatisfaction level, which is measured by the expected total weighted unsatisfied demand, and the lower-level objective is to minimize the expected total transportation time. Finally, a case study on the Great Sichuan Earthquake in China is implemented; their results show that the proposed model facilitates effective decision-making in the practice of multi-commodity rebalancing.