End-to-End Deep Learning for Inventory Management with Fixed Ordering Cost and its Theoretical Analysis

Abstract

We herein investigate the single item, multi-period inventory management problem with fixed ordering cost, holding cost, and lost sales cost. Here, both the demand and vendor lead time (VLT) are uncertain; Additionally, the contextual information that may be useful for predicting the distribution of the demand and VLT is available. We assume that the retailer has access to rich history observations and wishes to decide: (1) when to place an order and (2) how much to order. We solve this problem via an end-to-end (E2E) learning approach, where we develop a deep learning framework that directly outputs the optimal order timing and quantity with the given contextual information as the input. Our numerical experiments, which use the real-world data obtained from an online retailer, demonstrate the advantages of our approach over benchmark methods, such as the (r, Q) policy, predict-then-optimize (PTO) framework, and the E2E method with given order timing. Furthermore, we analyze the convergence of our E2E approach and provide upper bounds for the expected daily average cost of our E2E approach under certain conditions. To compare our approach with the optimal policy, we also provide lower bounds for the cost of the optimal policy under certain assumptions.