In biopharmaceutical manufacturing, fermentation processes play a critical role on productivity and profit. A fermentation process uses living cells with complex biological mechanisms, and this leads to high variability in the process outputs. By building on the biological mechanisms of protein and impurity growth, we introduce a stochastic model to characterize the accumulation of the protein and impurity levels in the fermentation process. However, a common challenge in industry is the availability of only very limited amount of data especially in the development and early stage of production. This adds an additional layer of uncertainty, referred to as model risk, due to the difficulty of estimating the model parameters with limited data. In this paper, we study the harvesting decision for a fermentation process under model risk. In particular, we adopt a Bayesian approach to update the unknown parameters of the growth-rate distributions, and use the resulting posterior distributions to characterize the impact of model risk on fermentation output variability. The harvesting problem is formulated as a Markov decision process model with knowledge states that summarize the posterior distributions and hence incorporate the model risk in decision-making. The resulting model is solved by using a reinforcement learning algorithm based on Bayesian sparse sampling. We provide analytical results on the structure of the optimal policy and its objective function, and explicitly study the impact of model risk on harvesting decisions. Our case studies at MSD Animal Health demonstrate that the proposed model and solution approach improve the harvesting decisions in real life by achieving substantially higher average output from a fermentation batch along with lower batch-to-batch variability.
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