Artificial Intelligence Constrained Multi-Objective Optimisation of Laboratory Sample Referral Networks Under Variable Courier Transit Time Reporting: A computed Evaluation of Healthcare Diagnostic Turnaround Equity

Laboratory sample referral networks in low-resource health systems must reconcile three competing objectives: minimising diagnostic turnaround time, containing courier and processing costs, and distributing service quality equitably across catchment populations. Courier transit times are typically reported as interval-censored or sporadically missing values, which complicates both the optimisation and the evaluation of equity. the present analysis formulates the referral-network design problem as a constrained multi-objective optimisation over a directed graph whose edge weights are random variables with interval-censored observations, and it proposes an artificial-intelligence solution architecture that couples a distributionally robust transit-time estimator with a non-dominated sorting genetic algorithm and an explicit equity constraint on the upper tail of the turnaround-time distribution. Because no field data were available, the design was evaluated through a replication-based replication study using a before-after-control-impact estimator with a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64). Power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis indicates that 56 clusters are required to detect a 5-percentage-point equity improvement at 80% power, and that the intraclass correlation of 0.64 dominates the detectable-effect curve. The contribution is a formalisation of equity-constrained referral-network design under transit-time uncertainty, together with a design-level power analysis that specifies the evidence a field evaluation would need to produce.