Task assignment and restaurant output: a simulation analysis

Abstract

Purpose This study isolates the output contribution of productivity-based task assignment in a fixed workforce and examines how that contribution changes with worker heterogeneity, cross-group comparative advantage and the correlation between task productivities. Design/methodology/approach The analysis simulates fixed restaurant workforces of 1,000 workers in five 3,000-run Monte Carlo designs. Within each run, the output-maximizing cutoff assignment is paired with a random assignment that preserves exactly the same front- and back-of-house headcounts. Bivariate-normal productivity draws vary task dispersion, group means and within-worker task correlation; additional calculations vary the Cobb–Douglas task weights. A formula-driven Excel realization reproduces Figure 1, and the Stata materials reproduce the remaining simulation evidence. Findings Relative to random assignment with the same task headcounts, optimal sorting raises mean output by 7.6% in the low-dispersion design and 12.1% when front-of-house dispersion is doubled. Greater dispersion changes random-assignment output by only −0.2% but raises optimally assigned output by 4.0%. Assignment gains decline from 10.0 to 5.4% as within-worker task correlation rises from −0.5 to 0.5. A separate cross-advantage design produces incomplete group specialization without materially changing output relative to the fixed group-neutral benchmark. Research limitations/implications The results are comparative statics from assumed bivariate-normal productivity distributions. They remain conditional on fixed employment, perfect observation, costless reassignment, additive worker contributions within tasks and Cobb–Douglas aggregation across tasks. Originality/value This study does not propose a new theory of assignment, labor demand or immigration. Its value is a controlled computational decomposition that separates sorting from dispersion and group labels, makes the task-level mechanism visible and provides reproducible correlation and task-weight sensitivities.