Applying deep learning to the newsvendor problem

Abstract

The newsvendor problem is one of the most basic and widely applied inventory models. If the probability distribution of the demand is known, the problem can be solved analytically. However, approximating the probability distribution is not easy and is prone to error; therefore, the resulting solution to the newsvendor problem may not be optimal. To address this issue, we propose an algorithm based on deep learning that optimizes the order quantities for all products based on features of the demand data. Our algorithm integrates the forecasting and inventory-optimization steps, rather than solving them separately, as is typically done, and does not require knowledge of the probability distributions of the demand. One can view the optimal order quantities as the labels in the deep neural network. However, unlike most deep learning applications, our model does not know the true labels (order quantities), but rather learns them during the training. Numerical experiments on real-world data suggest that our algorithm outperforms other approaches, including data-driven and machine learning approaches, especially for demands with high volatility. Finally, in order to show how this approach can be used for other inventory optimization problems, we provide an extension for (r, Q) policies.