Artificial Intelligence Distributionally Robust Optimisation of Insulin Cold-Chain Allocation Under Variable Solar Refrigerator Autonomy Telemetry: A computed Healthcare Spoilage Equity Evaluation

Solar-powered refrigerators have extended insulin cold-chain reach in off-grid health facilities, but their autonomy telemetry is intermittent and heterogeneous, so allocation rules that assume reliable state-of-charge reporting can systematically misallocate stock toward facilities whose data look favourable rather than whose need is greatest. the present analysis formulates insulin cold-chain allocation as a distributionally robust optimisation problem in which the ambiguity set is defined over telemetry-conditional spoilage distributions, and it characterises the operating characteristics of a before-after-control-impact evaluation of the resulting allocation rule under a declared variance structure. The design uses between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64, with 2000 replications per design cell across cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. Power curves, minimum detectable effect curves and coefficient plots are derived analytically from the variance structure rather than from field observation.54 clusters are required to detect a 5 percentage point spoilage-equity effect at 80 per cent power, and that the intraclass correlation of 0.64 dominates the design's sensitivity. The contribution is a formal bridge between distributionally robust allocation and equity-oriented cold-chain evaluation, together with a transparent statement of the design conditions under which such an evaluation can and cannot identify an effect.