(26g) Evaluation of Local Solvers for Flexibility Analysis of Dynamic Pharmaceutical Processes

Authors: 
Laky, D., Vanderbilt University
Vaidyaraman, S., Eli Lilly and Company
Laird, C., Purdue University
Successful operation of any industrial process requires an understanding of the operating conditions that are necessary to provide product quality, as well as the impact of uncertainty on this operating space. In pharmaceutical manufacturing, the design space defines the flexibility region in the operating parameters where critical quality attributes are guaranteed to meet performance constraints. The probabilistic design space extends this concept to include consideration of uncertain parameters and seeks to identify the flexibility region that guarantees product quality over a specified confidence. Traditionally, sample-based approaches such as Monte Carlo simulation have been used to identify such a probabilistic design space. However, the cost of such methods are extremely high, and new methods are required to reduce the computational burdened while allowing for rigorous treatment of large-scale models. In this work, we present algorithms based on flexibility analysis for efficient computation of the probabilistic design space.

We have demonstrated that flexibility analysis is a practical tool for analyzing the design space of steady-state pharmaceutical processes. We developed two tailored flexibility analysis approaches and compared them with the traditional Monte Carlo sampling approach in terms of computational cost and quality of the computed probabilistic design space. In this presentation, we will show that such flexibility analysis approaches can reduce computational time by as much as two orders of magnitude in certain cases. We wish to extend these concepts to dynamic models and analyze the practicality of utilizing similar techniques to mitigate the large cost of identifying the design space of dynamic pharmaceutical processes.

In this presentation, an example of batch pharmaceutical process will be analyzed to identify the probabilistic design space. Batch systems inherently require the consideration of process dynamics which increases the model scale significantly. Moreover, providing solutions with provable guarantees requires global solution of the flexibility analysis formulations, and all of these methods become computationally challenging on large-scale problems. To overcome these computational challenges, we extend these approaches to include a progressive refinement strategy based on relaxations that produces a sequence of inner and outer bounding regions. We compare this approach with both Monte Carlo techniques and local solution strategies coupled with simulation-based testing on boundaries of the design space.