Artificial Intelligence Constrained Multi-Objective Optimisation of Community Hypertension Medication Synchronisation Under Variable Pharmacy Stock Reconciliation Error: A computed Healthcare Adherence Equity Evaluation

Community hypertension medication synchronisation programmes align refill dates across a patient panel, but their adherence benefits depend on pharmacy stock records that are reconciled with variable error. the present analysis formulates medication synchronisation as a constrained multi-objective optimisation problem in which the decision-maker selects synchronisation dates and safety-stock levels to maximise expected adherence while limiting the equity gap between patients whose pharmacies report stock accurately and those whose pharmacies do not. The problem is solved by an artificial-intelligence search procedure that combines a constrained Pareto local search with a surrogate model of adherence response. Because no field data are available, the evaluation is a replication study: a before-after-control-impact design is 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 is 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 design achieves 80% power at 52 clusters for a 5-percentage-point effect. Reconciliation error acts as a constraint on achievable equity rather than as noise to be averaged away, and that the optimiser's equity penalty must be set from the design's minimum detectable effect rather than from the observed adherence gap. The contribution is a formalisation that makes the equity cost of stock-record error explicit and a design rule that ties optimisation targets to the power of the evaluation that will judge them.