In this paper, we study a stochastic single-item, single-stage inventory system, in which orders from several production facilities are placed at one warehouse. An (R, Q) policy is applied to control the inventory at the warehouse, and orders arrive according to a Poisson process and include a due date such that some information about future demand is available. This advance demand information (ADI) can be used to adapt a time-based shipment consolidation policy applied to replenish stock at the production facilities. We develop a model to incorporate flexible deliveries, indicating that orders can be shipped before their due date if sufficient reserved transportation capacity is available. We derive analytical, approximate expressions for the expected inventory and shipment costs and therefore enable the evaluation of different inventory and shipment policies including outbound transportation capacities. We additionally show how to compute the optimal policy parameters and conduct a detailed numerical study. Our computational experiments indicate that our approximation works extremely well, with an average total cost deviation of 0.20%, and finds optimal policy parameters in more than 90% of our instances. In line with existing research, we can show that ADI leads to large cost reductions. However, the main cause of the cost reduction is the flexible delivery option. To be able to completely utilize this option, even larger safety stocks are obtained compared to systems without ADI, but savings due to a more efficient transportation policy far exceed the cost increase due to higher safety stocks.