(298b) A General Framework for Chemical Process Scheduling

In the context of process scheduling, existing methods can be broadly classified into sequential and network-based. The former are used to address scheduling problems in processes where batches are processed in a predefined sequence of operations; mixing and splitting of batches are not allowed thereby preserving the identity of each batch. The latter are used for processes where batches are allowed to be mixed, split and recycled (network processes), which implies that the identity of a batch is not preserved and material balances (rather than batch tracking) are important.

The approaches for sequential processes rely on the notion of "batch", and the decisions such as the number and size of batches are often fixed (given) (Mendez et al., 2006; Pinto and Grossmann, 1995; Hui and Gupta, 2000; Mendez et al., 2001). These sequence-based formulations typically include assignment and sequencing constraints expressed in terms of batches: each batch has to be assigned to exactly one unit at each stage/operation and the batches assigned to the same unit have to be sequenced. In addition to exploiting the sequential structure of the process, most sequence-based approaches are based on a series of restricting assumptions (e.g. unlimited utilities and storage capacity) which lead to highly specialized but computationally effective formulations.

On the other hand, the approaches developed for network processes are rather general (Kondili et al., 1993; Pantelides, 1994). These network-based formulations can be used to address problems with storage as well as resource constraints. The main idea behind these approaches is the partition of the scheduling horizon into (discrete or continuous) time periods and the enforcement of i) material balance, ii) unit assignment and iii) resource constraints for each period. Importantly, these constraints are expressed similarly to flow balance constraints in networks. One of the limitations of this ?flow? representation, however, is that it does not keep track of batches. Therefore, network-based approaches cannot be used to address problems in sequential processes.

Therefore, there is no single approach that can be used to represent and address all scheduling problems. Furthermore, problems in facilities with different material routing restrictions (which are quite common in many sectors) are decomposed into simpler (sequential and network) subproblems, leading to suboptimal solutions.

Proposed Work

The goal of this work is the development of a methodology that accounts for sequential and network as well as continuous processes in a unified manner. The advantage of the proposed approach is that it can be used to address problems in facilities that include both sequential and network structures, e.g. process where batch identity has to be preserved in early stages for quality control purposes, but bulk (i.e. network-like) processing is allowed in later stages (e.g. packing). Furthermore, the proposed mixed-integer programming model considers batching and scheduling decisions simultaneously, and accounts for utility and storage constraints. To our knowledge, this is the first work that addresses this integrated problem. First, we present the basic components that enable the representation of all processes in a unified manner: 1) A systematic method for the representation of a mixed facility (i.e. a facility with batch sequential and network, and continuous substructures) as a purely network-like facility. This is achieved via the definition of different classes of states and tasks. 2) A systematic method for the transformation of a problem in a sequential process (i.e. expressed in terms of batches, stages and units) into a problem expressed in terms of a network-based formulation (i.e. in terms of tasks, states, and units). 3) A global discrete-time representation to ensure that material balance constraints and utility constraints are seamlessly enforced. Second, we discuss two new modeling concepts that allow us to enforce sequential processing in the unified network structure resulting from the previous step: 1) We introduce ?unit-connection? and material flow variables among process units/vessels to enforce connectivity constraints in the sequential subsystems. 2) We develop novel storage constraints that ensure that batches are neither mixed nor split in storage vessels in the sequential subsystems. Third, we discuss the development of tightening constraints to enhance the solution process. The key concepts underlying the development of tightening constraints are twofold. First, we estimate some key parameters based on customer demands, bill of materials and other process details. We backtrack the demand amounts and estimate the minimum production amount of each material state as well as the minimum number of tasks. To achieve this, we develop a general algorithm that estimates the above parameters for a given process network. Second, based on the above parameters, we express tightening constraints that are specific to different subsystems.

Finally, we present a number of example problems to illustrate how various sub-classes of the general scheduling problem can be solved effectively using our framework. Further, we illustrate how the proposed tightening constraints reduce the solution time to several orders of magnitude.

Reference:

1. Mendez, C.A.; Cerda, J.; Grossmann, I.E.; Harjunkoski, I.; Fahl, M. State-of-the-art review of optimization methods for short-term scheduling of batch processes. Comput. Chem. Eng., 2006, 30, 913-946.

2. Pinto, J.M.; Grossmann, I.E. A Continuous Time Mixed Integer Linear Programming Model for Short Term Scheduling of Multi-stage Batch Plants. Ind. Eng. Chem. Res., 1995, 34, 3037-3051.

3. Hui, C.H.; Gupta, A. A novel MILP formulation for short-term scheduling of multistage multiproduct batch plants. Comput. Chem. Eng., 2000, 24, 1611-1617.

4. Méndez, C.A.; Henning, G.P.; Cerdá, J. An MILP continuous-time approach to short-term scheduling of resource constrained multi-stage flowshop batch facilities. Comput. Chem. Eng., 2001, 25, 701-711.

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

6. Pantelides, C.C. Unified frameworks for the optimal process planning and scheduling. In proceeding on the second conference on foundations of Computer Aided operations; AIChE: New York, 1994, pp 253-274.