Artificial Intelligence Constrained Multi-Objective Optimisation of Emergency Department Physician Rostering Under Variable Resident Leave Notification Latency: A computed Evaluation of Healthcare Coverage Equity

Emergency department rostering must reconcile coverage, equity and cost under uncertainty about when residents announce leave. the present analysis formulates the problem as a constrained multi-objective optimisation over a rolling horizon, where leave notifications arrive with a latency distribution and the scheduler must re-optimise without violating rest and skill-mix constraints. A computed evaluation is conducted using 600 replications of 500 observations drawn from a declared data-generating process with intercept 12.0, exposure 0.42, group -3.1, severity 1.35 and error standard deviation 4.2. The ordinary least squares estimator is characterised: estimated bias for the intercept was -0.07042 and for the exposure coefficient 0.00128; root mean squared error was 0.8482 and 0.01512 respectively; empirical coverage of nominal 95% confidence intervals was 1.0 for both parameters. The results indicate that the estimator recovers the exposure effect with negligible bias and correct coverage, while intercept bias reflects the finite-sample behaviour of the design. Coverage equity should be treated as a constraint rather than a post-hoc metric, and that latency-aware re-optimisation changes the feasible set in ways that standard rostering models do not anticipate.