Efficient Scheduling of Discrete Industrial Processes through Continuous Modeling

The resource-task network (RTN) model has been widely applied to represent the technical constraints of complex industrial processes (IPs) such as steel-making, providing the basis for industrial demand response. However, the legacy RTN model contains numerous binary variables and applies different formulations for non-flexible and flexible processes, restricting its computational efficiency and applicability. To systematically improve the computational performance of IP models, we propose continuous RTN model (cRTN), a novel modeling approach that uses continuous variables to represent production tasks and progresses, which are then integrated into unified as well as computationally favorable formulations for the technical constraints in discrete IPs, including resource balance, task execution, waiting time limits, and production targets. Compared to the legacy models, cRTN features fewer binary variables, shorter solving time, and better scalability while maintaining the same accuracy. Numerical tests based on a steel plant demonstrate that cRTN is in typical cases 10 times faster than legacy models and remains tractable with increasing batch sizes, which in legacy models leads to larger problem scales and infeasible solving time. cRTN also achieves a reduction in energy costs by resolving the issue of rounding errors reported in legacy models.