End-to-End Deep Learning for Automatic Inventory Management with Fixed Ordering Cost

Problem Definition: We design an automatic decision-making system for an e-commerce platform to help manage the inventory of millions of stock keep units sold on the platform. The platform has accumulated a significant amount of contextual information, which may be useful for predicting both the demand and vendor lead time. Our proposed decision-making system makes the following decisions automatically based on contextual information and historical data: (1) order timing and (2) order quantity. Methodology: We solve this problem using an end-to-end (E2E) learning approach, where we develop a deep learning framework that directly outputs the optimal order timing and quantity with given contextual information as the input. Results: Our numerical experiments, which use real-world data obtained from an online retailer, demonstrate the superiority of our approach to benchmark methods: (r, Q) policy, predict-then-optimize (PTO) framework, and E2E method with given order timing. Furthermore, we analyze the convergence of our E2E approach and provide the upper bounds for its expected daily average cost under certain conditions. To compare our approach with the optimal policy, we also provide the lower bounds for the cost of the optimal policy under certain assumptions. Managerial implications: Our study elucidates the empirical success of the E2E method in inventory management. The analysis and results of the numerical experiments also suggest that considering the order timing and order quantity jointly in an E2E method can lower the lost sales cost than the E2E method with a pre-specified order timing