In this paper, we consider a make-to-stock production system with known exogenous replenishments and multiple customer classes. The objective is to maximize profit over the planning horizon by deciding whether to accept or reject a given order, in anticipation of more profitable future orders. What distinguishes this setup from classical airline revenue management problems is the explicit consideration of past and future replenishments and the integration of inventory holding and backlogging costs. If stock is on-hand, orders can be fulfilled immediately, backlogged or rejected. In shortage situations, orders can be either rejected or backlogged to be fulfilled from future arriving supply. The described decision problem occurs in many practical settings, notably in make-to-stock production systems, in which production planning is performed on a mid-term level, based on aggregated demand forecasts. In the short term, acceptance decisions about incoming orders are then made according to stock on-hand and scheduled production quantities. We model this problem as a stochastic dynamic program and characterize its optimal policy. It turns out that the optimal fulfillment policy has a relatively simple structure and is easy to implement. We evaluate this policy numerically and find that it systematically outperforms common current fulfillment policies, such as first-come-first-served and deterministic optimization
