A machine learning based sample average approximation for supplier selection with option contract in humanitarian relief

The humanitarian relief plays an important role in reducing the impact of disasters and avoiding humanitarian crises. As one of the essential activities, selecting a series of proper suppliers is particularly helpful for a successful and efficient disaster response to provide victims with necessary supplies. To optimize the benefits of the relief agency, victims, and suppliers, this paper proposes a supplier selection problem with consideration of the option contract, in which all-unit quantity and incremental quantity discounts are integrated. The problem is formulated as a multi-objective stochastic programming model with the objectives of minimizing the cost of the relief agency and maximizing the profit of suppliers, which are two conflict objectives, and also reducing the shortage risk for victims. Moreover, a machine learning based sample average approximation (SAA) is designed to solve the proposed model in large-scale cases. Specifically, stratified random sampling is integrated into K-means++ to improve quality of samples. The numerical analysis demonstrates that the proposed strategy can achieve a win–win situation for the relief agency, victims, and suppliers. It also justifies the efficiency of applying the machine learning method to enhance SAA for solving large-scale stochastic programming models.