Dynamic Optimization of Continuous Manufacturing of Pharmaceuticals

In this work the optimal dynamic operation of a continuous process for the production of a pharmaceutical product is investigated. The process includes reaction and several separations steps to produce an intermediate, based on a pilot plant previously tested at MIT. The mathematical formulation results in a hybrid, discrete-continuous, dynamical system, where the over whole on-specification production is explicitly optimized. This is done by enforcing the quality constraints only on an interior time interval (epoch) and optimizing its duration. This formulation, inspired by the turnpike property of optimal control, is guaranteed to be differentiable, thus we are able to use sensitivity analysis and local gradient-based optimization schemes to solve it. We solve for both the maximal yield and maximal productivity under a constant (short) time horizon. The solutions to these problems comprise the two extremes of a Pareto curve, which is constructed by adding a productivity constraint and solving for the maximal yield. It is demonstrated how changing the time horizon of the campaign affects these curves. This methodology should be used to produce valuable information to the decision makers responsible for the economics of the plant, in both the design stage and the operation stage of existing configurations.