Optimal Campaign Continuous Manufacturing

Campaign continuous manufacturing (CM), characterized by relatively short operational windows such as a few weeks [1], is being explored as an alternative to traditional batch-wise manufacturing in the pharmaceutical industry. However, optimal operation in campaign CM can be challenging due to the significance of startup and shutdown phases, which can negatively affect on-specification production and plant economy. In this work, the effectiveness and computational tractability of several known optimization approaches when applied to campaign CM are investigated. Inspired by the turnpike property [2,3] in optimal control, a new approach is then proposed, which aims to maximize on-specification production directly rather than minimizing the startup/shutdown times as commonly adopted in high-volume industries. A main contribution in the new approach is that the resulting optimization formulation is guaranteed to be differentiable, despite the underlying hybrid dynamic system [4]. Thus, it can be solved reliably using gradient-based algorithms. Case studies are presented to demonstrate the effectiveness of the proposed approach.

[1] Ali M. Sahlodin, Paul Barton. Optimal Campaign Continuous Manufacturing, submitted.

[2] McKenzie, L. (1976). Turnpike theory. Econometrica, 44, 841–865.

[3] Zaslavski, A. J. (2006). Turnpike Properties in the Calculus of Variations and Optimal Control. volume 80 of Nonconvex Optimization and Its Applications. Springer.

[4] Galán, S., Feehery, W. F., & Barton, P. I. (1999). Parametric sensitivity functions for hybrid discrete/continuous systems. Applied Numerical Mathematics, 31, 17 – 47.