Artificial Intelligence Constrained Multi-Objective Optimisation of Community Clinic Sputum Smear Microscopy Batching Under Variable Staining Reagent Degradation Reporting: A computed Healthcare Diagnostic Yield Equity Evaluation

Sputum smear microscopy remains the primary tuberculosis diagnostic in many community clinics, yet its yield depends on batching decisions that balance reagent economy against turnaround time and equitable case detection. the present analysis formulates the batching problem as a constrained multi-objective optimisation over slide batches, incorporating stochastic staining reagent degradation as a state variable that couples batch size to diagnostic sensitivity. A non-dominated sorting genetic algorithm (NSGA-II) is adapted to generate batch schedules that trade off expected diagnostic yield against reagent consumption and equity of access across patient subgroups. The evaluation is a replication study: no observational data are used or claimed. The design is a before-after-control-impact (BACI) estimator evaluated across 2000 replications per cell, with cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The intraclass correlation is 0.64, between-cluster standard deviation 6.0 and residual standard deviation 4.5. Power analysis indicates that 52 clusters are required to detect a 5 percentage point effect at 80% power. The contribution is a formalisation of reagent-degradation-aware batching as a constrained multi-objective problem and a demonstration that equity constraints alter the attainable yield-reagent frontier. The framework is proposed as a decision-support tool; empirical validation is required before clinical deployment.