Phase Aggregation in a Markov Switching Model of Manufacturing Workforce–Automation Dynamics Under Poisson Approximation

Modern manufacturing systems operate under substantial uncertainty because automation modes, machine states, and workforce capabilities evolve across different time scales. Classical deterministic models often fail to capture rare disruptions, rapid switching between automation states, and stochastic variability in production systems. To address these limitations, we extend a Lotka–Volterra interaction model by incorporating fast Markov-switching for automation-mode transitions and Poisson-jump perturbations for rare operational shocks. Using phase-space aggregation and ergodic averaging, we derive a reduced limit system that preserves the main long-term behavior of the original multiscale process while remaining suitable for simulation and statistical analysis. Numerical experiments show that the aggregated model reproduces cyclical workforce-automation interactions, switching-dependent variability, and sensitivity to automation intensity and shock frequency. The proposed framework provides a tractable stochastic model for studying uncertainty, automation dynamics, and disruption effects in manufacturing systems.