Robust optimization model for relief supplies distribution considering fairness

The emergency management agency (EMA) needs to distribute limited relief supplies efficiently. However, it is difficult to develop a reliable system for relief supplies distribution owing to the uncertainties in emergencies. This paper investigates a robust multiperiod relief supplies distribution problem that considers the uncertainties of transportation time, the amount of donation amount, and the secondary disasters. First, a satisfaction model is constructed by considering the relief supplies and the transportation time. The negative effect of the delay in transportation time is considered in the satisfaction model. Second, based on the satisfaction model, a comprehensive fairness strategy is constructed that considers both vertical fairness and horizontal fairness. Finally, a relief supplies distribution model is built for the EMA that considers the actions of the non-governmental organization (NGO) and donors. Both the utility and the fairness are considered in the objective of the proposed model. In numerical experiments, the Wenchuan earthquake is conducted to illustrate the applicability of the model and provide implications for decision-makers. The results show the benefits of considering both vertical fairness and horizontal fairness. Then the suitable threshold is given by the analysis of the time delay. Finally, managerial insights and recommendations for the EMA and the NGO derived from the numerical experiments are presented. The findings in this paper help improve the reliability of the relief supplies distribution system.