Periodic review inventory control for an omnichannel retailer with partial lost-sales

We investigate the management of stock for a business with integrated online and offline store-fronts selling products facing uncertainty in demand. The integration of channels includes an opportunity for customers to have items sent directly to their home in case of a store stockout. We model a two-echelon divergent, periodic-review inventory model, with partial lost-sales at the store level and an online demand channel. The problem is developed as a Stochastic Dynamic Program minimising inventory costs. For the zero lead-time case, we prove desirable properties and develop ordering decisions based on optimality of a base-stock policy. For positive lead-time, we highlight the effectiveness of adding order caps to reduce system costs. In an extensive numerical study, we improve standard heuristic methods in the literature on costs by up to 19%. Further, we apply methods to real life data for a large mobile phone retailer, Tesco Mobile, with our methods outperforming the internal benchmark method. We show how the company’s target service level can be reached, with a reduction of inventory between 75% and 99% at the store level. By focusing on effective yet interpretable policies, we suggest methods that can be used to aid a decision maker in a practical context.