Data-driven risk-averse newsvendor problems: developing the CVaR criteria and support vector machines

Abstract

Incorporating decision-makers' risk preferences into data-driven newsvendor models and developing machine learning methods to solve the models are the challenging problems addressed in this study. To consider different distributions and decision-makers' different risk preferences for the two losses of the total cost newsvendor model, the symmetrical, the partial symmetrical and the asymmetrical CVaR criteria are introduced. The regularisation, the primal-dual approach and the kernels in support vector machines are used to transform the data-driven risk-averse newsvendor problems under the CVaR criterion into the convex quadratic programming problems with good theoretical properties. Computational experiments are conducted on a real-world dataset. The models under the partial symmetrical and the asymmetrical CVaR criteria obtained good performances, but that under the symmetrical CVaR criterion suffered the underfitting problem. Two factors including the degrees of risk aversion for the two losses in the total cost newsvendor model and the empirical errors of data-driven models affect order decisions. The degrees of risk aversion for the two losses have anti-directional effects on order quantities. The introduction of asymmetrical CVaR criterion paves a new way to reveal the effects of different risk references for different losses on order decisions, and has the potential to improve newsvendor decisions.