Multi-product inventory systems with consideration of fulfillment dynamics: with and without demand learning

Abstract

How does the disconnect between back-end inventory control and front-end order fulfillment strategies in e-commerce-stemming from a common organizational structure where an inventory planning team manages the inflow of goods to the warehouse and a separate fulfillment team oversees the outflow of goods to customers-lead to significant financial losses? Additionally, how can a firm control its inventory by accounting for fulfillment dynamics where prior demand information is unknown? In this work, we delve into multi-product inventory systems by accounting for fulfillment dynamics. Order consolidation is implemented by the firm to reduce shipping costs, which take up a significant proportion of the total expenses in e-commerce. We first develop deterministic demand models to derive closed-form results and obtain additional managerial insights with more general features incorporated, e.g., under either a partial fulfillment policy or a whole-order fulfillment policy, and with ordering cost and endogenized reorder cycle lengths. In the subsequent study, we turn to a stochastic inventory model for the problem under a partial fulfillment policy. With known demand information, we formulate the cost function, derive its structural properties-including convexity and submodularity-and characterize the optimal inventory policy. Leveraging these structural properties, we devise asymptotically optimal Parallel Implementation and Optimization (PIO) algorithms that iteratively determine the base-stock levels for each period under unknown prior demand. Furthermore, we conduct numerical experiments to show the performance of our PIO algorithm and demonstrate that neglecting fulfillment dynamics and their associated costs can lead to significant losses. We further make extensions to the case where the commonly assumed lost-sales indicator functions are no longer necessary by developing efficient and effective Cycle-based (Cyc-) PIO and Estimator-based (Est-) PIO algorithms. These extensions address the challenges posed by the lack of information regarding lost-sales indicator function(s), a common issue in existing learning literature. This study contributes to inventory management by highlighting the importance of accounting for fulfillment dynamics in inventory planning for e-commerce companies and provides valuable inventory control algorithms for multiple products under a partial fulfillment policy.