Artificial Intelligence Constrained Multi-Objective Optimisation of Community Clinic Laboratory Sample Courier Routing Under Variable Boda-Boda Transit Time Reporting: A computed Healthcare Result Turnaround Equity Evaluation

Community clinic laboratory sample courier routing in low-resource settings is complicated by the fact that boda-boda transit times are reported with variable reliability, so that any routing policy optimised against a single point estimate of travel time may systematically disadvantage the clinics whose couriers report least accurately. the present analysis formulates the courier routing problem as a constrained multi-objective optimisation in which expected result turnaround time and the dispersion of turnaround time across clinics are optimised simultaneously, subject to a reporting-reliability constraint that penalises routes whose feasibility depends on unreliable transit-time reports. Because no field data were available, the study is framed as a methodological and replication-based evaluation: a before-after-control-impact design was characterised under a declared variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64, and 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 contribution is a formalisation that makes reporting reliability a first-class constraint rather than a nuisance parameter, together with a design analysis showing that 54 clusters are required to detect a 5 percentage point effect at 80 percent power under the declared variance structure.