Three-Stage Mixed Integer Robust Optimization Model Applied to Humanitarian Emergency Logistics by Considering Secondary Disasters

In recent years, natural disasters occur frequently, and secondary disasters induced by major disasters will also cause huge losses. The diversity of secondary disasters makes humanitarian emergency logistics (HEL) more challenging but often overlooked by researchers. In order to solve the comprehensive HEL problem of major and secondary disasters, a three-stage mixed integer linear optimization (TS-MILO) model is proposed. Among them, the uncertainty of the demand for relief supplies is also extremely difficult to deal with. In order to resist the interference of uncertainty, based on robust optimization, the TS-MILO model is further transformed into a three-stage mixed integer robust optimization (TS-MIRO) model, which are respectively BTS-MIRO (Box set), PTS-MIRO (Polyhedral set), and ETS-MIRO (Ellipsoid set). The experimental results show that the TS-MILO model can provide the lowest cost but cannot solve the uncertainty problem. The improved TS-MIRO model will pay a robust price (increase by at least 10.05%), but maintains supply stability even in the worst-case scenario. Specifically, ETS-MIRO model has strong robustness, and its cost increase only accounts for 44.66% of BTS-MIRO model in the worst case. The service level of the three TS-MIRO models increases with the safety parameters, among which the service level in the ETS-MIRO model increases significantly from 88.53% to 96.44%. The research results can provide a strong support for the decision making of disaster relief management department.