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Medium-Term and Short-Term Scheduling of a Large-Scale Industrial Continuous Plant

Munawar A. Shaik1, Christodoulos A. Floudas1, Josef Kallrath2, and Hans-Joachim Pitz2. (1) Department of Chemical Engineering, Princeton University, Engineering Quadrangle, Princeton, NJ 08544, (2) BASF Chemical Co., D-67056, Ludwigshafen, Germany

The scheduling problem of multiproduct and multipurpose continuous plants has drawn special attention but received less consideration compared to that of batch plants in the literature although continuous units are universal in the chemical process industries. The distinguishing feature between scheduling of batch plants and scheduling of continuous plants is in handling the processing times which are typically fixed in batch plants, while in continuous plants they are allowed to be different depending on the processing rate and the storage limitations. Another unique feature in scheduling continuous plants is that the amount produced is immediately available for consumption in the downstream units in contrast to batch plants where the production amount is available only after the end time of the batch.

Depending on the length of the time horizon considered planning and scheduling problems are classified in a different way as long-term planning, medium-range scheduling and short-term scheduling problems. In long-term planning, extended time horizons of the order of several months are considered involving strategic decisions for efficient timing and capacity utilization of several facilities. For the production targets (or demands) set by the planning problem, the operational issues are addressed in medium-range and short-term scheduling problems that involve decisions related to optimal sequencing resulting in efficient utilization of the processing and storage units. In medium-range scheduling relatively longer time horizons of several weeks are considered while short-term scheduling deals with shorter time horizons of the order of several hours to days. The long-term planning and medium-term scheduling problems have drawn less attention compared to short-term scheduling problems in the literature. They are more difficult to solve and hence invariably involve some kind of decomposition schemes in practice [1-2].

Another important consideration in scheduling problems is the choice of time representation. Recently, Floudas and Lin [3-4] presented extensive reviews comparing various discrete and continuous-time based formulations. During the last two decades, numerous models based on different continuous-time representations have been extensively used due to their established advantages over the discrete-time representations. 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, the time horizon is represented in terms of ordered blocks of unknown, variable lengths or time slots. Global-event based models 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 define events on a unit basis, allowing tasks corresponding to the same event point but in different units to take place at different times. The unit-specific-event based models usually require less number of event points and exhibit favorable computational performance [5] compared to both slot-based and global-event based models.

In this work, we present medium-term and short-term scheduling for large-scale continuous process plants [6]. For medium-range scheduling we use the rolling horizon decomposition scheme of Lin et al. [2] and solve two sub-problems. At the upper-level, we use a variation of the model proposed in [2] to find the optimal number of products and length of the time horizon to be considered for solving the short-term scheduling problem at the lower level. At the lower level, we proposed an improved model for short-term scheduling of continuous processes using unit-specific-event based continuous-time representation. For short-term scheduling of continuous plants, Ierapetritou and Floudas [7] had proposed an approximation of the storage task timings for handling different storage requirements. In this work we extend the formulation proposed in [7] in order 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. The proposed formulations are demonstrated on an industrial large-scale polymer compounding plant comprising several processing and storage units operating in a continuous-mode for producing hundreds of different articles over a one month time horizon. The multipurpose plant comprises of feed transfer, feed silo storage, polymer extrusion tasks, product silo storage, and final product filling. The plant additionally has several other practical restrictions such as limitation on the usage of number parallel filling units, restriction on product lifting on weekends, time-dependent limitation on raw material availability, and restrictions on changeover timings, which are handled efficiently using the proposed formulation.

[1]- A.D. Dimitriadis, N. Shah and C.C. Pantelides. "RTN-based Rolling Horizon Algorithms for Medium Term Scheduling of Multipurpose Plants". Comp. Chem. Eng. 21 (1997): S1061-S1066.

[2]- X. Lin, C.A. Floudas, S. Modi and N.M. Juhasz. "Continuous-Time Optimization Approach for Medium-Range Production Scheduling of a Multiproduct Batch Plant." Ind. Eng. Chem. Res. 41 (2002): 3884-3906.

[3]- 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.

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

[5]- 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.

[6]- M. A. Shaik, C.A. Floudas, J. Kallrath and H.-J. Pitz. "Production Scheduling of a Large-Scale Industrial Continuous Plant: Medium-Term and Short-Term Scheduling." in preparation.

[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.