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# Modelling alternatives for scheduling mixed batch/continuous process plants with variable cycle time

Nott, Helen P. (1998) Modelling alternatives for scheduling mixed batch/continuous process plants with variable cycle time. PhD thesis, Murdoch University.

## Abstract

The efficient scheduling of mixed-batch/continuous plants in the process industry has the potential for high economic returns. This study examines such a scheduling problem, with batch cycle times modelled as independent decision variables. Various mathematical models are developed, incorporating realistic system objectives and physical constraints. Results are applied to a case study in the sugar milling industry. The presence of both batch and continuous processes and the independence of the batch cycle times complicate this problem.

Systems incorporating both batch and continuous processes lead to a more difficult scheduling problem. The traditional solution approach is to divide the solution horizon into time units of fixed specified length. The solution consists of a value for each decision variable at each unit of time. The size of each time interval and hence the number of time intervals is determined by characteristics of the continuous processes. The domain of each decision variable is much larger than purely batch systems where only batch starts/finishes need to be considered.

Permitting batches to process for a variable length of time results in a large number of binary variables and boolean constraint-relationships in the model. This results in a substantial increase in the complexity of the resultant mixed integer linear programming problem. Thus the traditional model is unsuitable when batch processes are modelled with variable batch cycle times within the mixed-batch/continuous construct.
The critical issues considered when developing alternative models are as follows:
• Representation of time in the model. Time may be represented in alternate ways to the traditional uniform discretisation. However, the quality of the solution produced may be degraded.
• Optimisation of batch cycle times. The traditional model witlT variable batch cycle times produces a superior quality solution. However the solution algorithm complexity is also increased. Alternative models optimise the cycle time by nontraditional means. For example, optimising the cycle times as an outer objective to the remainder of the model.
• Representation of the batch components of the schedule. At the centre of the traditional model is the way in which the batch schedules are represented. At each discrete time point the batch schedule is determined by one of four choices: start a batch, continue a batch, finish a batch or a period of idleness. Alternate models involve more efficient representations of the batch scheduling decisions
• Solving the mixed integer linear programming problem. The solution path to the optimum can be carefully controlled. Additional resources are required to prove a solution is optimal, when often a “good" solution may be acceptable.

Two methods that are the most successful in reducing the solution complexity for a particular class of mixed-batch continuous problems both involve representing batch schedules by nontraditional means.

The first, a sets method which is based on generating feasible batch sub-schedules prior to the mixed-integer linear programming model. The batch scheduling decision is then to select which sub-schedules, where each sub-schedule represents the processing of a single batch, will constitute the overall solution. This model reduces the time required to solve the problem by 99.2%.

The second method is a multi-stage method based on optimal control theory. This method solves a relaxed form of the traditional model where the batch operations are represented as if they were continuous operations. This determines a reference trajectory for the ‘production’ through each ‘batch’ unit. The complete model is then used to ‘track’ this batch production curve. This method results in close to 99.9% reduction in the time required to solve the examined class of mixed-batch/continuous process scheduling problems.

When applying these two methods to the sugar milling case study, the sets method maintains its excellent performance. However, the optimal control method performance is only comparable to the traditional scheduling approach. The differences between the test problem and the actual sugar mill scheduling problem have been shown to be accountable for these performance differences.

This thesis has developed alternate models for mixed-batch/continuous systems and these have shown to have considerable impact on the solution algorithm performance. A very large reduction (more than 99%) in the resources required to solve problems has been achieved by alterate representations of the batch schedule within the model.

Item Type: Thesis (PhD) School of Engineering Note to the author: If you would like to make your thesis openly available on Murdoch University Library's Research Repository, please contact: repository@murdoch.edu.au. Thank you. Lee, Peter http://researchrepository.murdoch.edu.au/id/eprint/52661 Item Control Page