Summary: A vast amount of literature exists on scheduling to meet due dates, but very little work considers how to set these due dates before scheduling the orders. A method is described for real-time promising of order due dates that is applicable to discrete build-to-order environments facing dynamic order arrivals. When computing a due date, the method considers: (1) dynamic time-phased availability of resources required for each operation of the order, (2) individual order-specific characteristics and (3) existing commitments to orders that arrived previously. Performance of the method surpasses that of due-date assignment methods previously examined in the literature and also those commonly used in practice. The median and standard deviation of absolute flow-time estimation error and of absolute lateness are chosen as the primary performance criteria because they capture both positive and negative error in flow-time estimation of each individual order. Computational results from large-scale simulation studies of realistic systems with 20 resources and up to 100 000 orders also indicate the method is highly scalable.