Stochastic optimization for the carrier selection problem in humanitarian relief

Abstract. The present study delves into the problem of carrier selection to reduce the probability of the occurring carrier shortage by forming carrier rental agreement. In this regard, a new two-stage stochastic model for determining pre-disaster and post-disaster decisions was proposed to deliver relief items to the injured survivors of the disaster. The pre-disaster phase focuses on determining the amount of carrier rental in the framework of contracts with suppliers and also deciding on an appropriate coverage distance with respect to time and cost. The post-disaster phase aims to respond to the requests made by those in disaster-in icted areas swiftly and cost-effectively. The proposed mixed-integer linear programming model considers a scenario-based approach to handle the uncertainty of demand. In addition, a real case study was presented to demonstrate the effciency of the model. Moreover, numerical analyses were conducted to highlight the importance as well as the impacts of the cost and number of carrier rental contracts in the studied problem. Finally, an L-shaped algorithm was used to solve this model in different test instances, and the obtained results conrmed the applicability of the mentioned algorithm.