Unit-specific event-based continuous time models have gained significant attention in the past decade for their advantages of requiring less number of event points, smaller problem size, and hence, a better computational performance. In the literature, different models had been proposed for short-term scheduling problems involving with and without resource constraints using unit-specific event-based formulations. For scheduling problems involving no resource constraints, generally the unit-specific event-based models do not allow tasks to continue over multiple events unlike in models that account for resource constraints explicitly. In this work, we emphasize the necessity for allowing tasks to take place over multiple event points even for simpler scheduling problems involving no resource constraints. We propose a novel short-term scheduling model using three-index binary and continuous variables that efficiently merges both the problems involving resources and no resource constraints into a unified, generic common framework. The proposed approach is based on state-task-network (STN) representation and is suitable for both batch and continuous plants, although we focus only on batch plants in this paper. Detailed computational case studies are presented to demonstrate the efficacy of the proposed model.