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.

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The problem of short-term scheduling of multiproduct and multipurpose batch plants has received significant attention in the literature compared to the problem of short-term scheduling of continuous processes. In this paper, we present an improved model compared to the work of Ierapetritou and Floudas (Ind. Eng. Chem. Res. 1998, 37, 4360) for short-term scheduling of continuous processes using unit-specific event-based continuous-time representation. The formulation is based on the state-task-network representation resulting in a mixed-integer linear programming model that accurately accounts for various storage requirements such as dedicated, finite, unlimited, and no intermediate storage policies. The formulation allows for unit-dependent variable processing rates, sequence-dependent changeovers, and with/without the option of bypassing of storage. Different variants of an industrial case study from a fast moving consumer goods manufacturing is presented to demonstrate the capability of the proposed model.

During the last two decades, the problem of short-term scheduling of multiproduct and multipurpose batch plants has gained increasing attention in the academic, research, and manufacturing communities, predominantly because of the challenges and the high economic incentives. In the last 10 years, numerous formulations have been proposed in the literature based on continuous representations of time. The continuous-time formulations have proliferated because of their established advantages over discrete-time representations and in the quest to reduce the integrality gap and the resulting computational complexities. The various continuoustime models can be broadly classified into three distinct categories: slot-based, global event-based, and unitspecific event-based formulations. In this paper, we compare and evaluate the performance of six such models, based on our implementations using several benchmark example problems from the literature. Two different objective functions, maximization of profit and minimization of makespan, are considered, and the models are assessed with respect to different metrics such as the problem size (in terms of the number of binary variables, continuous variables, and constraints), computational times (on the same computer), and number of nodes needed to reach zero integrality gap. Two additional computational studies with resource constraints such as utility requirements are also considered.