A computationally efficient method for the scheduling of complex batch processes
This dissertation presents an improved continuous time, unit-specific event-based Mixed-Integer Linear Programming formulation for the optimal scheduling of general network-represented batch plants, based on the State-Task Network representation. The formulation draws on and combines the strengths of previous works in order to incorporate rigorous conditional sequencing, pre- and post-processing unit wait and task splitting while ensuring the integrity of the Finite Intermediate Storage policy. Task splitting is simulated without requiring potential problem truncation and nested iteration which may result from the utilization of a splitting parameter ∆𝑛 and threeindex binary and continuous variables to represent the start and end events of tasks. Additionally, the proposed formulation allows for the fractional extraction of produced states from their producing unit at multiple events, thereby increasing the flexibility of resulting schedules. Computational performance is compared against reimplementations of four recent task splitting formulations through solution of 22 example problems using the GAMS CPLEX solver in order to demonstrate the effectiveness of the proposed approach and highlight its advantages. It is shown how the proposed formulation is the most reliable due to its ability to converge in all of the considered problem instances and not get trapped at suboptimal solutions due to iterative procedures relating to task splitting. The proposed model performed the fastest during solution in 16 of these examples, while in the other six (Examples 4.1 and 10.4 to 10.8.), the solution time was very comparable to the other formulations investigated. The proposed model demonstrated a best-case CPU time reduction of more than 90%.
A dissertation submitted in fulfilment of the requirements for the degree of Master of Science in Engineering to the Faculty of Engineering and the Built Environment, School of Chemical and Metallurgical Engineering, University of the Witwatersrand, Johannesburg, 2022