Consideration of public donations as a variable in the model.
Using the KKT conditions to convert model to a linear single-level model.
Consideration of the priority index as a criterion of efficiency.
Statistical analysis and detailed experimental results.
Optimal selection of suppliers for covering the demand considering the supply risk.
In recent years, the number and severity of natural disasters occurring in various regions of the world have increased dramatically incurring heavy financial and human losses. Therefore, decision-makers have been concerned with ways of providing relief to reduce the losses. Here, we present a multi-objective bi-level model for disaster location-routing problem that provides the needed supplies through multiple suppliers, considering the supply risk. Moreover, to reduce the risk and increase efficiency, special attention is given to people's help for supplying goods having high priority and low risk. At the first level of the model, the cost and time objectives are considered, and at the second level, the risk and efficiency objectives are considered. To solve the bi-level model, first we solved the follower's perspective model using the augmented epsilon constraint method to convert the second level objectives to a single-objective. Then, using the KKT conditions, the bi-level model is converted to a linear single-level bi-objective model, which is solved by the augmented epsilon constraint method. To validate the model, the suburb of Sari in Iran is selected as a case study and the model is solved by the CPLEX/GAMS. The results show that the lower-risk goods with higher priorities should be supplied by public donations to increase efficiency in provision of relief. The results of sensitivity analysis demonstrate that commodities are not supplied merely by public donations, because if the inventories of Red Cross and Red Crescent decrease, or level of demand rises, exogenous suppliers and/or general public donations can provide goods.