The problem of short-term scheduling of batch plants has received remarkable attention in the past two decades. The scheduling problems are broadly modeled using state-task-network (STN) and resource-task-network (RTN) process representations. In contrast to the STN representation, all the resources such as materials, processing and storage equipment, and utilities are uniformly treated in the RTN representation. Floudas and Lin [1,2] presented extensive reviews comparing various discrete and continuous-time based formulations. The various continuous-time models proposed in the literature can be generally classified into three different 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. Unit-specific event-based models [6-9] define events on a unit basis, allowing tasks corresponding to the same event point but in different units to take place at different times. Most of these formulations are based on either STN or RTN process representations, except the model of Sundaramoorthy and Karimi [3] which is based on generalized recipe diagrams. A detailed comparison of various continuous-time models for short-term scheduling of batch plants is performed in Shaik et al. [9], and concluded that the unit-specific event-based models always require less number of event points and exhibit favorable computational performance compared to both slot-based and global event-based models.

For unit-specific event-based models the RTN process representation has not been explored in the literature. In this work [10], we investigate the RTN representation for short-term scheduling of batch plants using the unit-specific event-based formulation. Based on the improved version of the model of Ierapetritou and Floudas [7] presented in Shaik et al. [9], we propose a new model using the RTN framework. This work builds on the previous works in the research group and improves existing formulations. In particular, it provides better sequencing and tightening constraints resulting in improved LP relaxations.

For the case when dedicated storage is available for an intermediate state, Lin and Floudas [8] considered a separate task for storage and proposed additional constraints for handling storage. In this work [10], we present an alternate approach without the need for considering storage as a separate task for this case. This novel approach eliminates the need for considering additional binary, continuous variables, and constraints for storage tasks.

Additionally, the performance of the proposed model is evaluated against the other continuous-time models from the literature, discussed in the comparative studies of Sundaramoorthy and Karimi [3] and Shaik et al. [9]. Specifically, we compare STN-based continuous-time models [6-8], RTN-based continuous-time models [4,5,10], and generalized recipe diagram based models [3]. The various models are assessed based on our implementations using several benchmark example problems from the literature [3,9]. 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. We will present some interesting comparisons among the alternate formulations.

[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]- P. Castro, A.P.F.D. Barbosa-Povoa and H. Matos. "An Improved RTN Continuous-Time Formulation for the Short-Term Scheduling of Multipurpose Batch Plants." Ind. Eng. Chem. Res. 40 (2001): 2059-2068.

[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]- N.F. Giannelos and M.C. Georgiadis. "A New Continuous-Time Formulation for Short-Term Scheduling of Multipurpose Batch Processes." Ind. Eng. Chem. Res. 41 (2002): 2178-2184.

[7]- 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.

[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]- 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.

[10]- M.A. Shaik and C.A. Floudas. "Unit-Specific Event-Based Continuous-Time Approach for Short-Term Scheduling of Batch Plants using RTN Framework." submitted for publication.