Positioning of omnichannel inventories to protect revenue

Conventional inventory management strategies prove inadequate when confronted with the complexities of omnichannel retailing. Fulfillment from stores and transshipment emerged as alternative methods to supplant the traditional approaches, but unfortunately these methods are often too costly. How to share limited inventory between online and offline channels thus remains a challenging question. We characterize an omnichannel retailer’s inventory sharing policy with limited inventory to be sold during a finite horizon. Inventory reserved for the online channel can later be transferred to the offline inventory pool, but once it is shipped to offline stores, it becomes out of reach for online orders. We use an optimal control framework with limited inventory supply and stochastic demand processes. By recursively solving a series of differential equations, we characterize the optimal inventory positioning policy. We demonstrate that a three-regime time-threshold policy governs the optimal inventory allocation policy; in the central regime, both channels are active and the retailer keeps minimal stock at the stores. During the beginning and end regimes, only one channel is open and has positive inventory. While traditional inventory management techniques tend to favor a high fill rate and availability, our approach focuses on positioning inventory where it generates the most revenue, which depends on the remaining time in the season. Interestingly, this approach sometimes leads to strategic revenue protection decisions wherein it may be more profitable to preclude sales from a lower-margin channel with higher customer reach.