Artificial Intelligence Constrained Multi-Objective Optimisation of Teleophthalmology Screening Appointment Slots Under Variable Retinal Camera Uptime: A computed Evaluation of Healthcare Diabetic Retinopathy Access

Teleophthalmology diabetic retinopathy screening programmes schedule appointments against retinal cameras whose uptime is uncertain, so that slot allocation must trade off access volume against the risk of a cancelled or degraded screening session. the present analysis formulates slot allocation as a constrained multi-objective optimisation problem in which camera availability is a random variable and the decision variables are appointment assignments across a finite horizon. A computed evaluation is conducted using a before-after-control-impact design with 8, 16, 24 and 32 clusters, effect sizes of 3, 5 and 8 percentage points, and 2000 replications per design cell; the variance structure assumes a between-cluster standard deviation of 6.0, a residual standard deviation of 4.5 and an intraclass correlation of 0.64. The analysis characterises the operating characteristics of the design rather than estimating effects from observational data. Power curves, minimum detectable effect curves and coefficient plots are reported for the declared design grid. The results indicate that 54 clusters are required to detect a 5 percentage point improvement at 80 per cent power under the stated variance structure, and that the before-after-control-impact estimator's precision degrades sharply below 24 clusters. The contribution is a formalisation of camera-uptime-aware slot allocation together with a design-level power analysis that specifies the cluster counts at which a field evaluation would be informative.