INVENTORY MANAGEMENT IN A (Q,r) INVENTORY MODEL WITH TWO DEMAND CLASSES AND FLEXIBLE DELIVERY

This paper considers a single-product inventory system that serves both online and traditional customers. Demands from both channels follow independent stationary Poisson processes. Traditional customers have their demands fulfilled upon arrival if the retailer has stock on hand; otherwise the demand is lost. However, online customers place their orders in advance, and delivery is flexible in the sense that early shipment is allowed. In particular, an online order placed at time t should be fulfilled by time t+ T , where T is the customer’s demand lead time [1]; late fulfillment incurs a time-dependent backorder cost. A (Q, r) replenishment policy is used and replenishment lead times are assumed to be constant. We develop an approximation for the expected annual cost for the retailer, and compare analytically and simulated results. The optimal parameters of the system are derived by minimizing the expected annual cost. We illustrate the model with numerical examples, and discuss the sensitivity of the results to variables such as demand lead time and the split between online and traditional orders.