Reinforced-count simulation for decision calibration under over-dispersed multi-type service demand

Service counts are often converted into capacity or inventory decisions with independent Poisson models, although clustering and latent heterogeneity can make the counts substantially more variable. We present reinforced-count simulation (RCS) as a low-parameter, pre-deployment stress test: it asks whether a decision calibrated under independence remains adequate when type shares persist. RCS is compared with independent Poisson, negative-binomial, empirical-residual and Scarf moment-robust decisions. The empirical analysis uses two public datasets. RAND Health Insurance Experiment physician-visit counts provide a cross-sectional held-out test (20,190 observations), and five categories of New York City 311 requests provide an external temporal test (1,096 days and 26 rolling origins). In the RAND analysis at a lost-event-to-holding-cost ratio of 20, over-dispersion-aware decisions reduced held-out cost relative to Poisson by 15.0% for RCS, 15.6% for negative binomial and 17.3% for the empirical quantile; fill rate increased from 76.5% to 88.2%–91.1%. In the NYC analysis at a ratio of 10, the RCS mean paired cost improvement was 18.7% (95% confidence interval, 12.4%–25.0%) and fill rate increased from 93.3% to 96.8%. A multi-type transfer experiment showed that each calibrated model was best in its matching environment; using a mismatched model produced 6.0%–20.0% regret. Joint sensitivity analysis, concentration-parameter learning curves and cost-ratio perturbations identify when the diagnostic is useful and when parameter error can dominate model choice. RCS is a reproducible check on mean-based decisions when composition dependence is uncertain, not a general demand model.