A novel stochastic-robust optimization model for emergency supplies prepositioning under uncertain scenario probabilities

• The deprivation cost is incorporated into the prepositioning of emergency supplies. • Intervals are employed to symbolize the uncertainty in the scenario probabilities, and a stochastic-robust optimization model is formulated based on the utilization of worst-case scenarios probabilities. • A Benders decomposition algorithm is proposed by considering the optimal solution structure of the worst-case scenario probabilities. • The validity and robustness of the proposed modeling approach are illustrated through a case study. A thorough examination is conducted to evaluate the impact of several key parameters. The strategic placement of emergency supplies has been demonstrated to have a substantial impact on the efficacy of emergency response. However, the prepositioning of emergency supplies is accompanied by a multitude of uncertainties, primarily due to the impracticality of predicting the location and intensity of a disaster. Despite the demonstrated efficacy of scenario-based stochastic optimization in addressing these uncertainties, determining scenario probabilities remains a challenging. In this paper, intervals are employed to symbolize the uncertainty in the scenario probabilities, and a stochastic-robust optimization model is formulated based on the utilization of worst-case scenario probabilities. The model under consideration integrates facility location, storage level decision, and post-disaster distribution of emergency supplies. Moreover, the deprivation cost is incorporated into the allocation of emergency supplies. A Benders decomposition algorithm is proposed by considering the optimal solution structure of the worst-case scenario probabilities. The validity and robustness of the proposed modeling approach are illustrated through a case study. A comparison of the optimal solutions for the baseline model and the proposed model reveals that the latter, despite an increase in cost of 9.36 %, successfully mitigates the cost escalation due to probabilistic uncertainty in the worst probability case by 22.12 %. A comprehensive analysis is conducted to assess the impact of the uncertainty surrounding scenario probabilities and the deprivation cost of emergency supplies.