(599k) Advanced Unit-Specific Event Based Modeling Approach for Short-Term Scheduling of Batch Plants

Scheduling of multipurpose batch plants has received considerable attention during the past two decades. Different modeling approaches have appeared in the literature. Most of the proposed approaches can be classified into two main groups based on time representation: discrete-time models and continuous-time models. Extensive reviews were written by Floudas and Lin [1], Mendez et al. [2], and Shaik et al.[3] who presented comparisons of different models and discussed associated challenges. Continuous-time models in the literature are further classified into slot-based, global-event-based, unit-specific event-based, and precedence-based formulations.

Unit-specific event-based models define events on a unit basis, allowing tasks corresponding to the same event point but in different units to take place at different times. 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 [3]. Shaik and Floudas [4] proposed a novel unified model using three index binary and continuous variables based on unit-specific event based continuous time representation that efficiently allows tasks to span over multiple events. This model is applicable for problems with and without resources such as utilities and with different storage policies, and has been demonstrated to give superior computational performance among all the models considered in their study. Recently, Vooradi and Shaik [5] presented an improved model compared to Shaik and Floudas [4]  by taking advantage of the three-index variables and effectively incorporating the concept of active task leading to fewer constraints and big-M terms. The effectiveness of their model was demonstrated through various examples drawn from literature including Westenberger-Kallrath challenging benchmark problem [6].

Despite the significant advancements in the modeling and solution approaches in the past two decades, it is still a challenging task to solve real industrial scheduling problems because of the issues arising in handling large-scale problems. Hence, there is a global concern and obligation to develop innovative methods to reduce the number of events and/or the problem size of a scheduling model to enable efficient solution. In this study, we investigate innovative methods to further reduce the number of events required to efficiently solve a given scheduling problem using unit-specific event based approaches.

All the conventional approaches for batch process scheduling in the literature are based on the assumption that the consumption task corresponding to a given material/state typically occurs at the next event/slot relative to the production task unless there is enough inventory for the consumption task to start at earlier events.  If we allow production and consumption tasks to correspond to the same event then it is possible to achieve a significant reduction in the number of events. With this motivation, in this work we propose an advanced unit-specific event-based continuous-time modeling approach by exploiting the fact that the unit-specific events correspond to heterogeneous locations along the time axis, thus allowing different tasks to occur at different times and still correspond to the same event point. The basic framework is adapted from Vooradi and Shaik [5] model. The main novelty in this formulation is that the production and consumption tasks corresponding to a given state/material are allowed to occur in a sequential manner at the same event point. We present few benchmark examples from literature [4,5,7-9] involving short-term scheduling of batch plants and compare the computational performance of the proposed model with respect to earlier models. The proposed model significantly reduces the number of event points required leading to fewer constraints, variables and yielding better RMIP values for several problem instances. The proposed model can handle problems with batch splitting and mixing, and different storage polices.

Acknowledgements: The authors gratefully acknowledge financial support received from Department of Science and Technology (DST), India, under SERC scheme, grant no. SR/S3/CE/075/2009.

References:

[1] Floudas, C.A. and Lin, X. (2004). Continuous-time versus discrete-time approaches for scheduling of chemical processes: A review. Comp. Chem. Eng., 28, 2109-2129.

[2] Mendez, C.A., Cerda, J., Grossmann, I.E., Harjunkoski, I. and Fahl, M. (2006). State-of-the-art review of optimization methods for short-term scheduling of batch processes. Comp. Chem. Eng., 30, 913-946.

[3] Shaik, M.A., Janak, S.L. and Floudas, C.A. (2006). Continuous-time models for short-term scheduling of multipurpose batch plants: A comparative study. Ind. Eng. Chem. Res., 45, 6190-6209.

[4] Shaik, M.A. and Floudas, C.A. (2009). Novel unified modeling approach for short-term scheduling. Ind. Eng. Chem. Res., 48, 2947-2964.

[5] Vooradi, R. and Shaik, M.A. (2012). Improved three-index unit-specific event based model for short-term scheduling of batch plants. Comp. Chem. Eng., http://dx.doi.org/10.1016 /j.compchemeng.2012.03.014

[6] Kallrath, J. (2002). Planning and scheduling in the process industry, OR Spectrum, 24, 219.

[7] Ierapetritou, M.G. and Floudas, C.A. (1998). Effective continuous-time formulation for short-term scheduling: 1. Multipurpose batch processes. Ind. Eng. Chem. Res., 37, 4341-4359.

[8] Li, J., Susarla, N., Karimi, I.A., Shaik, M.A. and Floudas, C.A. (2010). An analysis of some unit-specific event-based models for the short-term scheduling of non continuous processes. Ind. Eng. Chem. Res., 49, 633-647.

[9] Susarla, N., Li, J., Karimi, I.A. (2010). A novel approach to scheduling multipurpose batch plants using unit slots. AIChE J., 56, 1859-1879.