Abstract
Mathematical models in process systems engineering (PSE) are widely used to support decision-making in design and operation, but they are mostly limited to deterministic models. For biochemical systems, the biological variability can give rise to stochastic dynamics. This work addresses the question of when to act in such processes, as the stochastic dynamics affect the timing of important events. We consider the case of batch production of malic acid using Ustilago trichophora. The goal is to predict when the substrate concentration falls below a predefined threshold. We extend an existing deterministic model of the process to a stochastic differential equation (SDE) formulation by introducing a Monod-like noise term. Simulations of the SDE model reveal a distribution of substrate depletion times and a deviation between the mean of the stochastic trajectory and the deterministic solution due to nonlinear effects. To determine optimal intervention times under uncertainty, we formulate a finite-horizon optimal stopping problem and solve it using the Longstaff-Schwartz algorithm, also known as the Least-Squares Monte Carlo (LSMC). The resulting distribution of optimal stopping times from the LSMC algorithm is shown to closely match the actual first threshold hitting times obtained from a posteriori analysis of the stochastic simulations, as confirmed by a two-sample Kolmogorov-Smirnov test. The results demonstrate that optimal stopping provides a framework for decision-making in stochastic biochemical processes, enabling risk-aware operational strategies beyond deterministic optimisation.