Personnel scheduling models in industrial engineering typically represent fatigue as a static counter computed from schedule structure, ignoring the time-dependent dynamics of homeostatic sleep debt and circadian-modulated recovery documented in the biomathematical literature. This paper proposes a system dynamics model that integrates the two-process homeostatic-circadian formulation, circadian-phase-dependent sleep efficiency, and chronotype heterogeneity within an explicit stock-and-flow structure with two feedback loops. The model is implemented in Vensim with hourly resolution and applied to four canonical shift patterns under three chronotypes. The contribution is methodological: it brings the system dynamics framework to a problem domain dominated by closed-form ODE models and provides a transparent policy-evaluation tool aligned with the conference theme From Data to Policy.