On the nature and validity of the clearing function

Clearing functions are valuable tools for production planning because they capture the relationship between workload—specifically work in progress (WIP)—and expected throughput (yield). However, the use of steady-state queueing models to derive these functions is often criticized given the finite nature of actual planning periods. This study addresses this limitation by proposing a mechanistic model for a single-resource factory, drawing the Industrial-Metabolism-based analogy between machine operations and enzyme kinetics. By framing the system as a singularly perturbed model with slow (WIP) and fast (busy machines) variables, we demonstrate that the clearing function emerges as an asymptotic expansion of the slow invariant manifold. Ultimately, we demonstrate that the validity of this approximation in non-steady states depends on the ratio of active machines to WIP; a sufficiently low ratio justifies the use of clearing functions even when steady-state conditions are not met.