In biopharmaceutical manufacturing, fermentation processes play a critical role in productivity and profit. A fermentation process uses living cells with complex biological mechanisms, leading 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 stages 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 (i.e., when to stop the fermentation and collect the production reward) under model risk. 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. 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：在生物制药制造中，发酵过程对生产效率和利润起着至关重要的作用。发酵过程利用具有复杂生物机制的活细胞，导致过程产出（即蛋白质和杂质水平）具有高度可变性。基于蛋白质和杂质生长的生物机制，我们引入了一个随机模型来表征发酵过程中蛋白质和杂质水平的积累。然而，该行业面临的一个普遍挑战是仅有非常有限的数据可用，尤其是在开发和早期生产阶段。由于难以用有限的数据估计模型参数，这增加了额外的不确定性层，称为模型风险。本文研究了在模型风险下发酵过程的收获决策（即何时停止发酵并收集生产收益）。我们采用贝叶斯方法来更新生长率分布的未知参数，并利用得到的后验分布来表征模型风险对发酵产出变异性的影响。收获问题被表述为一个具有知识状态的马尔可夫决策过程模型，这些知识状态总结了后验分布，从而将模型风险纳入决策过程。我们在MSD Animal Health的案例研究表明，所提出的模型和解决方法通过实现发酵批次平均产出的显著提高以及批次间变异性的降低，改进了现实中的收获决策。