# (298c) A Novel Technique for Prediction of Time Points in Scheduling of Multipurpose Batch Plants

Authors:
University of Pretoria
University of Pretoria

In recent years, Batch plants have attracted much attention due to their flexibility in producing different products using the same facility. The profitability of the Batch plant is highly dependent on the way the production is optimized. In this regard, modelling the process is important to maximize resource utilization. Previous models based on the state sequence network representation (SSN) gave few binary variables when compared to the state task network representation (STN). The formulation resulted in a mixed integer linear programming (MILP) problem that can be solved in reasonable computational time. The computational time of the developed mathematical model depends on the nature of the problem (complexity of the batch operation), the number of binary variables and time points. Time points are used to denote the use or production of a particular state at a particular point in time. In solving the model, the optimal number of time points is determined by iteration, with the computational or CPU time required to get the optimal solution being the summation of CPU times for each iteration. If the problem is complex or the number of time points large, a high CPU time is required in solving the problem. The implication is that complex scheduling problems require long time to iterate and obtain the optimum number of time points related to the optimum objective value. This is the main challenge in scheduling Batch plants on a daily or weekly basis. This paper presents a mathematical technique for prediction of the optimal number of time points in short term scheduling of multipurpose Batch plants. The mathematical formulation is based on SSN representation. The developed method is based on the principle that the optimal number of time points depends on how frequent the critical unit is used throughout the time horizon. In the context of this work, a critical unit refers to a unit that is most frequently used and it is active for most of the time points when it is compared to other units. Linear model is used to predict how many times the critical unit is used. In conjunction with knowledge of recipe, this information is used to determine the optimal number of time points. The statistical R-squared value obtained between the predicted and actual number of time points in all the problems considered was 0.98, which suggests that the developed method is accurate in predicting optimal number of time points. Consequently this avoids costly computational times due to iterations. The presentation will demonstrate the application of this technique to several problems in literature where it is proved consistently accurate.

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