Data-driven ordering policies for target oriented newsvendor with censored demand

In today’s fiercely competitive business environment, meeting and surpassing earnings expectations is paramount for public companies. This study focuses on how companies selling newsvendor-type products determine the order quantity to maximize the probability of achieving a target profit (known as profitability). Decision-makers often face challenges in real-life situations where the true demand distributions are unknown, and they have to rely on historical demand data. In some cases, they may only have access to sales data, which is referred to as censored demand. We propose data-driven ordering policies that aim to maximize profitability based solely on historical demand data and sales data respectively. Specifically, we first develop a data-driven nonparametric model using historical demand data, and then present a mixed-integer programming to solve the model. In the case of censored demand, we further propose an enhanced data-driven nonparametric model that leverages the Kaplan–Meier estimator to correct sales data. We prove that the proposed data-driven ordering policies are asymptotically optimal and consistent, regardless of whether the demand is censored or not. To avoid overestimation of true profitability due to sampling error, we propose nonparametric bootstrap methods to estimate the lower confidence bound of profitability, providing a conservative estimate. We also demonstrate the consistency of the lower confidence bound of profitability obtained through the bootstrap-based numerical methods. Finally, we conduct numerical experiments using synthetic data to showcase the effectiveness of the proposed methods.