Controlling inventories in omni/multi-channel distribution systems with variable customer order-sizes

• Development of a combined stock heuristic for service differentiation in the presence of direct up-stream demand. • Integrated inventory control in omni/multi-channel system. • Efficient heuristic for determining the inventory control parameters. The fast growth of e-commerce and omni/multi-channel retailing brings new challenges for efficient inventory management. One such challenge concerns service differentiation across channels when upstream central warehouses satisfy both direct customer demand and replenishment orders from downstream retailers. Motivated by industry collaboration, we address this issue by developing a combined stock method for control of one-warehouse-multiple-retailer inventory systems with direct customer demand at the central warehouse. The combined stock method, used for service differentiation at the central warehouse, may be described as a critical level policy. The computationally efficient heuristics we present are designed to deal with real one warehouse multiple retailer inventory systems characterized by highly variable customer order-sizes, ( R , Q ) policies at all stock points, and fill rate constraints. A numerical study, including real data from two different companies, illustrates that the heuristics perform well; offering near optimal solutions close to target fill rates, with significant opportunities to reduce total inventory costs compared to existing methods.