In biopharmaceutical manufacturing, fermentation processes play a critical role in productivity and profit. A fermentation process uses living cells with complex biological mechanisms, and this leads to high variability in the process outputs, namely, the protein and impurity levels. 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 the industry is the availability of only a 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 (i.e., when to stop the fermentation and collect the production reward). 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.

翻译：在生物制药制造业中,发酵过程在生产力和利润方面发挥着关键作用。发酵过程使用生物机理复杂的活细胞,这导致过程产出的高度变异性,即蛋白质和杂质水平。通过利用蛋白质和杂质增长的生物机制,我们引入了一种随机模型,以说明发酵过程中蛋白质和杂质水平积累的特点。然而,该行业的一个共同挑战是,仅提供非常有限的数据数量,特别是在生产的发展和早期阶段。这增加了一层不确定性,称为模型风险,因为难以用有限的数据估计模型参数。在本文中,我们研究了模型风险下发酵过程的收成决定(即何时停止发酵并收集生产奖励)。我们采用了一种巴伊斯式方法,更新基于增长率分布的模型未知的模型参数,并使用由此得出的海市分布表来说明模型风险对发酵结果的影响。我们通过在分析数据分析模型中采用分析结果,通过分析结果分析结果,将分析结果纳入我们的决策流程。