Interpretable Contextual Newsvendor Models: A Tree-Based Method to Solving Data-Driven Newsvendor Problems

Abstract

In this thesis, we consider contextual newsvendor problems where one seeks to determine ordering quantities of perishable products based on the observations of past demands and some features (such as seasonality, weather forecasts, economic indicators, etc.) related to the demand. We propose solving the problems via a single-step optimal decision-tree approach. Unlike the traditional two-step approach that first predicts a demand distribution based on given features and then optimizes the order quantity, our approach seeks to determine a tree-based ordering policy that directly maps given features to optimal order quantities. We show how the optimal policies can be found by solving mixed-integer programming (MIP) problems. The tree structure overcomes the black-box nature of most machine learning algorithms while reaching better performance than simple solutions such as linear regression. In addition to risk-neutral newsvendor problems, we further extend the method to address risk-averse newsvendor problems formulated based on Conditional Value-at-Risk (CVaR). Numerical experiments on synthetic and real-world data suggest that our approach outperforms existing approaches with the same objective function, such as the ERM-based convex optimization model which is referred to as Ban and Rudin's big data newsvendor model, and quantile regression decision trees.