(610b) An Improved Continuous-Time Model for Short-Term Scheduling of Continuous Processes: Rigorous Treatment of Storage Requirements

The scheduling problem of multiproduct and multipurpose continuous plants has received less attention in the literature despite their practical importance in the chemical process industries that produce a variety of products using both batch and continuous production modes. One of the key differences between scheduling of batch processes versus scheduling continuous plants is in handling the processing times. In batch plants, the processing times are typically fixed and known a priori, and the production amount depends on the capacity of the batch unit. In continuous plants, the processing times are a function of unit-dependent processing rates, final product demand, and storage limitations. Additionally, in continuous plants, the production amount is available continuously while it is being produced, unlike in batch plants, where the amount is available only after the end time of the batch that is processing. Due to these differences, the problem of scheduling of continuous plants has drawn separate attention.

Recently, Floudas and Lin [1-2] presented extensive reviews comparing various discrete and continuous-time based formulations. 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 [3-5], the time horizon is represented in terms of ordered blocks of unknown, variable lengths or time slots. Global-event based models [6-7] 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 [8-9] define events on a unit basis, allowing tasks corresponding to the same event point but in different units to take place at different times. On the other hand, Mendez and Cerda [10] proposed a production campaign based formulation without the use of time events for short-term scheduling of continuous processes leading to compact models. A detailed comparison of various continuous-time models for short-term scheduling of batch plants is performed in Shaik et al. [11] 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. It is demonstrated in this work that this conclusion holds true for scheduling problems involving continuous processes as well.

For an industrial case study from fast moving consumer goods manufacturing, that is solved extensively in the literature, comprising continuous making-storage-packing tasks most of these models [6-10] could handle different storage scenarios such as unlimited, finite, flexible, dedicated and no intermediate storage policies. For this problem Ierapetritou and Floudas [9] proposed an approximation of the storage task timings for handling different storage requirements. Mendez and Cerda [10] and Giannelos and Georgiadis [8] reported suboptimal solutions for the case of finite intermediate storage with no maximum demand limits. Castro et al. [6-7] could not find the global optimal solution for the no intermediate storage case even at higher event points and large computational times and classified the problem as intractable despite using a decomposition strategy [7] for improving the computational performance.

With this motivation in this study, we present an improved model for short-term scheduling of continuous processes using unit-specific-event based continuous-time representation [12]. The formulation proposed by Ierapetritou and Floudas [4] is extended so as to precisely handle the different storage requirements. The proposed formulation is based on the state-task-network representation resulting in a mixed-integer linear programming (MILP) model that accurately accounts for various storage requirements such as dedicated, flexible, 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 fast moving consumer goods are presented to reveal the capability of the proposed model. It is also demonstrated that the unit-specific-event based formulations require less number of event points to obtain the global optimal solution compared to slot-based/global-event based models.

[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]- 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.

[4]- J.M. Pinto and I.E. Grossmann. "Optimal Cyclic Scheduling of Multistage Continuous Multiproduct Plants." Comp. Chem. Eng. 18 (1994): 797-816.

[5]- S.A. Munawar, M. Bhushan, R.D. Gudi and A.M. Belliappa. "Cyclic Scheduling of Continuous Multi-product Plants in a Hybrid Flowshop Facility." Ind. Eng. Chem. Res. 42 (2003): 5861-5882.

[6]- 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.

[7]- P.M. Castro, A.P. Barbosa-Povoa and A.Q. Novais. "A Divide and Conquer Strategy for the Scheduling of Process Plants Subject to Changeovers Using Continuous-Time Formulations." Ind. Eng. Chem. Res. 43 (2004): 7939-7950.

[8]- N. F. Giannelos and M.C. Georgiadis. "A Novel Event-Driven Formulation for Short-Term Scheduling of Multipurpose Continuous Processes." Ind. Eng. Chem. Res. 41 (2002): 2431-2439.

[9]- 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.

[10]- C.A. Mendez and J. Cerda. "An Efficient MILP Continuous-Time Formulation for Short-Term Scheduling of Multiproduct Continuous Facilities." Comp. Chem. Eng. 26 (2002): 687-695.

[11]- M. A. Shaik, S. L. Janak and C.A. Floudas. "Continuous-Time Models for Short-Term Scheduling of Multipurpose Batch Plants: A Comparative Study." submitted for publication.

[12]- 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." submitted for publication.