(769e) Optimal Online Batch Process Scheduling: Definition, Computations, and Role of State Estimation in Scheduling

In this work, we propose a novel approach to incorporate real-time plant information in online scheduling of batch processes. In a dynamic environment, disturbances or new information could lead to sub-optimality or infeasibility of the computed schedule, necessitating rescheduling (Gupta et al, 2016). One source of new information that may necessitate rescheduling is the plant’s automation system, which makes discrete decisions that guide the plant’s behavior. For example, a batch reaction maybe modeled as a single task with a fixed duration in the scheduling problem, while the automation system considers it as a sequence of 10 or more distinct steps with the transitions between the steps dependent on certain logic conditions. Therefore, a schedule computed using the coarser model may not actually be feasible when executed in the plant. An initial effort to address the mismatch between the model of the plant in the scheduling problem and actual plant behavior, driven by the automation system has been undertaken (Rawlings et al, 2018).

In addition to the step information derived from the automation system, online scheduling models also benefit from real-time plant information about flow rates, yield losses and the availability of various resources needed to execute a batch. Building upon previous work (Subramanian et al., 2012), we present an online scheduling algorithm based on a state-space discrete-time resource task network (RTN) model, and “update equations” used to calculate, at each iteration, the initial state of the system based on real-time data from the plant. In the RTN model, we generalize the definition of a task to account for the inherent sequence of steps involved in the process. The resource interactions (consumption/release) in the RTN representation are associated with these individual steps. Furthermore, we develop a systematic method to introduce common schedule disruptions such as processing delays into the scheduling model through (1) the estimation, at each iteration, of the initial state (state estimation), and (2) the update of resource-task interaction coefficients. While the former is routinely performed in control systems, the second is a novel concept, necessary when dealing with real-time scheduling problems.

Next, we discuss how the update of the RTN parameters is performed. In the RTN model, its state variables represent, among others, the “progress status” of a batch. We discuss how real-time information, can be used to estimate the state of the plant and from there determine the progress status of all currently executed batches. For example, if a step is delayed, then all subsequent steps in the sequence will be (typically) also delayed, resulting in an increase in the batch end time. We then discuss how such delays trigger a re-computation of the resource-task interaction coefficients. Specifically, we present an algorithm that calculates resource consumption/release at discrete time points depending on the start/end time of the step associated with that resource.

Finally, to fully exploit the real-time knowledge of the “state” of a batch, we introduce features that have not been examined before, such as considering delays in processing times of tasks as decisions taken by the optimizer. Delays as optimization decisions may be triggered due to delays in other tasks; for example, when the steps in different tasks require the same shared resource at a given point in time, one of the steps will have to be delayed avoiding schedule infeasibility.

Generally speaking, if online scheduling is viewed as an MPC problem, then the proposed methods (new state-space RTN model, estimation of current plant state, algorithm for resource-task interaction coefficients update, and introduction of new optimization decisions at the scheduling level) allow us, together, to generalize the concept of state estimation to scheduling, and then exploit the new information to obtain better solutions.

We illustrate the advantages of our methods through a case study that involves batch processes, and multiple equipment units and products. The tasks are composed of various steps including material filling and withdrawing, heating, reaction, and quality control. We show how the incorporation of real-time plant information into the RTN model developed in this work leads to a better estimate of the batch end time, resulting in superior quality closed-loop schedules over existing models.

References

1. Gupta, D., Maravelias, C. T., and Wassick, J.M. (2016) From rescheduling to online scheduling. Chemical Engineering Research and Design, 116, 83-97.
2. Rawlings, B. C., Avadiappan, V., Lafortune, S., Maravelias, C. T., and Wassick, J. M. (2018) Incorporating automation logic in the online scheduling of batch chemical plants. Computer Aided Chemical Engineering, 44, 2053-2058.
3. Subramanian, K., Maravelias, C. T., and Rawlings, J.B. (2012) A state-space model for chemical production scheduling. Computers & Chemical Engineering, 47, 97-110.