(372e) A Novel Unified Modeling Approach For Short-Term Scheduling

In the past two decades, the research area of batch and continuous process scheduling has received grand attention from both academia and industry [1,2]. In the past 10 years, numerous formulations have been proposed in the literature based on continuous-time representation, due to their established advantages over discrete-time representations. On the basis of the time representation used, the different continuous-time models proposed in the literature can be broadly classified into three distinct categories: slot-based, global event-based, and unit-specific event-based formulations. In the slot-based models [3], the time horizon is represented in terms of ordered blocks of unknown, variable lengths, or time slots. Global event-based models [4,5] use a set of events that are common across all units, and the event points are defined for either the beginning or end (or both) of each task in each unit. On the other hand, unit-specific event-based models [6-11] define events on a unit basis, allowing tasks corresponding to the same event point but in different units to take place at different times. For sequential processes, other alternative approaches based on precedence relationships have also been used.

A detailed comparison of various continuous-time models for short-term scheduling of batch and continuous plants was performed recently by Shaik et al. [10] and Shaik and Floudas [11]. They concluded that, due to heterogeneous locations of event points used, the unit-specific event-based models always require less event points and exhibit favorable computational performance compared to both slot-based and global event-based models. For continuous plants, Shaik and Floudas [11] presented an improved model, compared to Ierapetritou and Floudas [7], that outperforms the other models considered in their study. For batch plants that do not have resource considerations such as utility constraints, it was found [10] that the modified model of Ierapetritou and Floudas [6] as presented in Shaik et al. [10], outperforms the other models both in terms of least problem size and fast computational performance. For batch plants with resource constraints, the enhanced model of Janak et al. [9] was found [9,10] to perform well. For handling dedicated finite storage we need to apply the model of Lin and Floudas [8] by considering storage as a separate task; and for flexible storage cases as well we need additional storage related constraints as discussed in Janak et al. [9]. The model of Ierapetritou and Floudas [6] does not allow a task to continue over several events, while the model of Janak et al. [9] is an enhanced version that allows tasks to take place over multiple event points in order to accurately account for the resource considerations such as utility requirements.

With this motivation, in this study [12], we propose a unified modeling approach using unit-specific event-based continuous-time representation, which (i) can handle problems with resource constraints by allowing tasks to take place over multiple events, (ii) efficiently reduces to the case of no resources, and (iii) is applicable for batch as well as for continuous processes with mixed storage policies.

Additionally, the performance of the proposed model [12] is evaluated against the other continuous-time models from the literature for batch and continuous plants. The various models are assessed based on our implementations using several benchmark example problems from the literature [3,9,10,11]. Two different objective functions, maximization of profit and minimization of makespan, are considered. Two different storage policies, unlimited and finite dedicated storage, are also considered along with problems with resource constraints such as utility requirements.

[1]- C.A. Floudas and X. Lin. "Continuous-Time versus Discrete-Time Approaches for Scheduling of Chemical Processes: A Review." Comp. Chem. Eng. 28 (2004): 2109-2129.

[2]- C.A. Floudas and X. Lin. "Mixed Integer Linear Programming in Process Scheduling: Modeling, Algorithms, and Applications." Ann. Oper. Res. 139 (2005):131-162.

[3]- A. Sundaramoorthy and I.A. Karimi. "A Simpler Better Slot-Based Continuous-Time Formulation for Short-Term Scheduling in Multipurpose Batch Plants." Chem. Eng. Sci. 60 (2005): 2679-2702.

[4]- C.T. Maravelias and I.E. Grossmann. "New General Continuous-Time State-Task Network Formulation for Short-Term Scheduling of Multipurpose Batch Plants." Ind. Eng. Chem. Res. 42 (2003): 3056-3074.

[5]- P.M. Castro, A.P. Barbosa-Povoa, H.A. Matos and A.Q. Novais. "Simple Continuous-Time Formulation for Short-Term Scheduling of Batch and Continuous Processes." Ind. Eng. Chem. Res. 43 (2004): 105-118.

[6]- M.G. Ierapetritou and C.A. Floudas. "Effective Continuous-Time Formulation for Short-Term Scheduling: 1. Multipurpose Batch Processes." Ind. Eng. Chem. Res. 37 (1998): 4341-4359.

[7]- M.G. Ierapetritou and C.A. Floudas. "Effective Continuous-Time Formulation for Short-Term Scheduling: 2. Continuous and Semi-continuous Processes." Ind. Eng. Chem. Res. 37 (1998): 4360-4374.

[8]- X. Lin and C.A. Floudas. "Design, Synthesis and Scheduling of Multipurpose Batch Plants via an Effective Continuous-Time Formulation." Comp. Chem. Eng. 25 (2001): 665-674.

[9]- S.L. Janak, X. Lin and C.A. Floudas. "Enhanced Continuous-Time Unit-Specific Event-Based Formulation for Short-Term Scheduling of Multipurpose Batch Processes: Resource Constraints and Mixed Storage Policies." Ind. Eng. Chem. Res. 42 (2004): 2516-2533.

[10]- M.A. Shaik, S.L. Janak and C.A. Floudas. "Continuous-Time Models for Short-Term Scheduling of Multipurpose Batch Plants: A Comparative Study." Ind. Eng. Chem. Res. 45 (2006): 6190-6209.

[11]- M. A. Shaik and C.A. Floudas. "An Improved Unit-Specific-Event based Continuous-Time Model for Short-Term Scheduling of Continuous Processes: Rigorous Treatment of Storage Requirements." Ind. Eng. Chem. Res. 46 (2007): 1764-1779.

[12]- M.A. Shaik and C.A. Floudas. "Novel Unified Modeling Framework for Short-Term Scheduling using Unit-Specific Event-Based Continuous-Time Representation." submitted for publication.