Optimal Event Point Determination for Short-Term Scheduling of Multipurpose Batch Plants

Scheduling of multipurpose batch plants has received considerable attention[1]-[4] during the last three decades. A variety of discrete-time[5]-[6] and continuous-time formulations has appeared in the literature. Discrete-time models discretize the entire scheduling horizon into a number of time intervals of equal or nonuniform length, which corresponds to an approximation of the time horizon and results in a large number of binary variables, that increases the overall size of the model. To overcome the inherent limitations of the discrete-time models, continuous-time models have been developed. All these continuous-time models can be classified into sequence-based[4],[7]-[9], slot-based[10]-[12], and event-based[13]-[25] models based on time representation. Among these models, the unit-specific event-based model developed by Floudas and co-workers[16]-[25] is considered the most general and most rigorous time representation. It is shown that the unit-specific event-based models[16]-[25] performs better than other models[10], [13]-[15] with benchmark examples from the literature. The extensive reviews on comparison of these models can be referred to the papers of Floudas and Lin[1]-[2], Mendez et al.[3], and Pitty and Karimi[4].

Both slot-based and event-based models need an iterative procedure proposed by Ierapetritou and Floudas[16] to decide the optimal number of slots or event points in which they start with a some small number of slots or event points, then increase gradually, until the objective function does not change. This iterative procedure may not lead to the optimal slots or event points and may result in increased computational time.

In this presentation, we use the recently proposed three-index unit-specific event-based model developed by Shaik and Floudas[24] as our basic formulation and develop a procedure to obtain the maximum number of event points in which the sequence-constraints relating different tasks in different units are valid for each intermediate state. Then, we use the approach proposed by Janak and Floudas[25] to decide the minimum number of event points. Based on these maximum and minimum event points, we propose a branch and bound strategy to decide the optimal number of event points. To speed up convergence and reduce computational time, some additional constraints and techniques are also developed. All literature examples with different intermediate storage requirements such as UIS, and FIS are solved to illustrate the capability of our proposed approach.

Keywords: Scheduling, multipurpose plants, batch processes, unit-specific event-based, continuous-time, optimal event point

References

[1] C. A. Floudas, X. Lin, Continuous-time versus discrete-time approaches for scheduling of chemical processes: A review. Comput. Chem. Eng. 2004, 28 (11), 2109-2129.

[2] C. A. Floudas, X. Lin, Mixed integer linear programming in process scheduling: Modeling, algorithm, and applications. Ann. Oper. Res., 2005, 139, 131-162.

[3] C. A. Mendez, J. Cerda, I. E. Grossmann, I. Hajunkoski, and M. Fahl, State-of-the-art review of optimization methods for short-term scheduling of batch processes. Comput. Chem. Eng., 2006, 30 (6-7), 913-946.

[4] S. S. Pitty, I. A. Karimi, Novel MILP models for scheduling permutation flowshops. Chem. Prod. Process Model. 2008, 3 (1), 22.

[5] E. Kondili, C. C. Pantelides, R. W. H. Sargent. A general algorithm for short-term scheduling of batch operations – I. MILP formulation. Comput. Chem. Eng., 1993, 17 (2), 211-227.

[6] K. H. Lee, H.Park Ii, I. B. Lee, A novel nonuniform discrete-time formulation for short-term scheduling of batch and continuous processes. Ind. Eng. Chem. Res. 2001, 40 (22), 4902-4911.

[7] C. A. Mendez, J. Cerda, An efficient MILP continuous-time framework for short-term scheduling of multipurpose batch processes under different operation strategies. Optimiz. Eng., 2003, 4, 7-22.

[8] S. Gupta, I. A. Karimi, An improved MILP formulation for scheduling multiproduct, multistage batch plants. Ind. Eng. Chem. Res. 2003, 42 (11), 2365-2380.

[9] S. Ferrer-Nadal, E. Capon-Garcia, C. A. Mendez, L. Puigjaner, Material transfer operations in batch scheduling. A critical modeling issue. Ind. Eng. Chem. Res. 2008, 47 (20), 7721-7732.

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

[11] I.A. Karimi and C.M. McDonald. "Planning and Scheduling of Parallel Semicontinuous Processes. 2. Short-Term Scheduling." Ind. Eng. Chem. Res. 36 (1997): 2701-2714.

[12] J.M. Pinto and I.E. Grossmann. "A Continuous-Time Mixed-Integer Linear-Programming Model for Short-Term Scheduling of Multistage Batch Plants." Ind. Eng. Chem. Res. 34 (1995): 3037-3051.

[13] 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.

[14] P. M. Castro, A. P. F. D. Barbosa-Povoa, H. A. Matos, A. Q. Novais, Simple continuous-time formulation for short-term scheduling of batch and continuous processes. Ind. Eng. Chem. Res., 2004, 43 (1), 105-118.

[15] 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.

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

[17] M.G. Ierapetritou, 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.

[18] M.G. Ierapetritou, T.S. Hene and C.A. Floudas. "Effective Continuous-Time Formulation for Short-Term Scheduling: 3. Multiple Intermediate Due Dates." Ind. Eng. Chem. Res. 38 (1999): 3446-3461.

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

[20] S.L. Janak, X. Lin, 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.

[21] M. A. Shaik, S. L. Janak, C. A. Floudas, Continuous-time models for short-term scheduling of multipurpose batch plants: a comparative study. Ind. Eng. Chem. Res., 2006, 45 (18), 6190-6209.

[22] M. A. Shaik, C. A. Floudas, Improved unit-specific event-based continuous-time model for short-term scheduling of continuous processes: Rigorous treatment of storage requirements. Ind. Eng. Chem. Res. 2007, 46 (60, 1764-1779.

[23] M. A. Shaik, C. A. Floudas, Unit-specific event-based continuous-time approach for short-term scheduling of batch plants using RTN framework. Comput. Chem. Eng., 2008, 32 (1-2), 260-274.

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

[25] S. L. Janak, C. A. Floudas, Improving unit-specific event-based continuous-time approaches for batch processes: Integrality gap and task splitting, Compt. Chem. Eng., 2008, 32, 913-955.