Artificial Intelligence Counterfactual Scheduling of Community Health Worker Home Visits Under Variable Travel-Time Matrix Uncertainty: A Distributionally Robust Evaluation of Healthcare Coverage Equity

Community health worker (CHW) home-visit scheduling is a sequential allocation problem in which the travel-time matrix is rarely known with the precision that optimisation models assume. The framework is formalised as a two-stage stochastic program with a conditional value-at-risk objective over the ambiguity set, and a tractable reformulation is derived under a Wasserstein ball. Because no field data were available, the estimator behaviour underpinning the framework was characterised in a replication study: 600 data sets of N = 500 were drawn from a declared data-generating process (intercept 12.0, exposure 0.42, group -3.1, severity 1.35, error SD 4.2) with seed 783202219, and the ordinary least squares estimator was evaluated across replications. Estimated bias was -0.00091 for the intercept and -0.00028 for the exposure coefficient; root mean squared error was 0.87048 and 0.01626 respectively; empirical coverage of the nominal 95% confidence intervals was 1.0 for both parameters. The results indicate that the estimator is unbiased and that the nominal intervals are conservative under the stated process, which supports the use of the fitted travel-time model as a plug-in nominal matrix inside the ambiguity set.