(667f) Investigation of Closed-Loop Optimal Process Scheduling Policies 

In the work of Lima et al., [1], the notion of inventory creep within a process scheduling context was introduced. In short, the inventory creep phenomenon is a gradual reduction of material inventory over time. To alleviate this myopic behavior, the authors of [1] advocate the use of larger prediction horizons, but quickly run into computational tractability issues. In our previous work [2], application of the Economic Model Predictive Control (EMPC) to a simple process scheduling problem (a single machine with two products), it was found that closed-loop performance (repeated rescheduling at each time-step) resulted in irregular performance as a function of horizon size. This is in contrast to most EMPC applications, where performance improves with each increase in horizon size [3, 4].

It has since been concluded that the open-loop EMPC problem does not converge as the horizon goes to infinity. In the current effort, we investigate the closed-loop EMPC problem using dynamic programming and the Hamilton-Jacobian-Bellman Equation (HJB). To avoid the curse of dimensionality a simple two state process scheduling example is used. Since the value function-results of the HJB depend on the objective function of the EMPC problem, a variety of (presumably equivalent) objective functions will be considered and compared.

[1] Lima, R. M.; Grossmann, I. E.; Jiao, Y. “Long-term scheduling of a single-unit multi-product continuous process to manufacture high performance glass.” Comp. Chem. Eng. 2011, 35 (3), 554−574.

[2] Aleissa, Y.M., Inventory Creep Phenomenon in Process Scheduling, Master’s Thesis, Illinois Institute of Technology (2016).

[3] Omell, B.P.; D.J. Chmielewski, "IGCC Power Plant Dispatch using Infinite-Horizon Economic Model Predictive Control" Ind. Eng. Chem. Res., 52(9) pp 3151-3164 (2013).

[4] Mendoza-Serrano, D.I.; D. J. Chmielewski, "Smart Grid Coordination in Building HVAC Systems: Computational Efficiency of Constrained ELOC " Sci. Tech. Built Env., 21, pp 812-823 (2015)