The problem of short-term scheduling often involves the satisfaction of variable product demands at specific due dates within the time horizon under consideration. Ierapetritou and Floudas (Ind. Eng. Chem. Res. 1998, 37, 4341-4359, 4360-4374) presented a new continuous time formulation to effectively address the problem of short-term scheduling in batch, continuous, and mixed production facilities where product demands are specified at the end of the time horizon. The primary objective of this paper is to extend the continuous-time formulation so as to deal with intermediate due dates. The mathematical model is developed and the operation mode of the plant (batch or semicontinuous) is further exploited to result in the most efficient solution strategy. Several examples are provided to illustrate the capabilities of the proposed continuous-time formulations, and it is demonstrated that a variety of problems presented in the literature can be addressed efficiently.