The manufacture of biological products from live systems such as bacteria, mammalian, or insect cells is called biomanufacturing. The use of live cells introduces several operational challenges including batch-to-batch variability, parallel growth of both desired antibodies and unwanted toxic byproducts in the same batch, and random shocks leading to multiple competing failure processes. In this article, we develop a stochastic model that integrates the cell-level dynamics of biological processes with operational dynamics to identify optimal harvesting policies that balance the risks of batch failures and yield/quality tradeoffs in fermentation operations. We develop an infinite horizon, discrete-time Markov decision model to derive the structural properties of the optimal harvesting policies. We use IgG1 antibody production as an example to demonstrate the optimal harvesting policy and compare its performance against harvesting policies used in practice. We leverage insights from the optimal policy to propose smart stationary policies that are easier to implement in practice.