A Screening Tool for Construction Automation: Efficiency Bounds and a Labour-Time Envelope under Variability

Construction firms still lack a simple way to estimate how much labour time automation could save before committing to an investment. This paper proposes such a tool by rewriting the Kingman G/G/1 waiting-time approximation as a closed-form efficiency bound, η(CV, ρ) = 1/(1 + CV 2 °§ ρ/(1 − ρ)), based on only two quantities: process variability (CV ) and utilisation (ρ). The bound distinguishes between losses that can be closed through better planning and coordination and losses that can only be closed by lowering variability through standardisation, mechanisation, or automation. Four contributions follow. First, we introduce the Kingman-derived bound as a compact analytical tool for construction processes under variability. Second, on a controlled 32-case test grid, it explains R2 = 0.66 of the variance in a replicated discrete-event simulation used as an internal numerical reference rather than external ground truth, it is statistically unbiased, and it outperforms deterministic, i.i.d. stochastic, and PERT-style planning baselines (all R2 < 0). A project-specific DES at the research frontier reaches R2 = 0.94 at much higher modelling cost, so the disclosed trade-off is predictive accuracy per unit of modelling effort. Third, against approximately 10,000 data points from nine secondary sources, with estimated rather than measured ρ and GAN-synthetic TBM CV, nine construction sectors are placed along the variability–utilisation plane in the order predicted by the bound, as an external consistency check rather than an empirical validation. Fourth, the efficiency gain from lower variability becomes a labour-time envelope: an upper bound on the crew-hour savings that automation could in principle deliver at assumed ρ. This envelope is intentionally narrow. It is neither a business case nor a return-on-investment model, but a first-pass screening tool, computable on a spreadsheet from two measurable parameters before more detailed simulation or investment analysis is undertaken. First-party field measurement of ρ on real construction sites is the next empirical step, and the subject of a companion methods paper in preparation.