A Service-Constrained Two-Stage Stochastic Programming Framework for Hospital Pharmacy Medication Supply Under Demand Uncertainty: Heterogeneous Demand, Conditional GARMA Scenarios, and Longitudinal Validation

Background/Objectives: Hospital pharmacies must maintain medication availability despite heterogeneous and time-varying demand. Statistical fit alone may not yield well-calibrated future scenarios or the best replenishment decision. This study prospectively evaluates a decision-support framework combining probabilistic demand modelling, conditional temporal adaptation, explicit service requirements, and stochastic inventory optimization. Methods: Forty-eight monthly requested-demand observations for 13 anonymized medicines from a Chilean public hospital were evaluated through 12 expanding-window origins, yielding 156 prospective medicine-month decisions. A focused contextual consultation with three pharmacist experts was added to interpret the observed growth, decline, and intermittency patterns. Recurrent-positive and intermittent demand were modelled using normal, gamma, negative binomial type II (NBII), zero-inflated NBII (ZINBI), and hurdle negative-binomial models. When training data indicated trend or serial dependence, time-trend generalized linear models (GLMs) and generalized autoregressive moving average (GARMA) models were additionally considered as conditional scenario generators. The selected model supplied scenarios to a service-constrained two-stage stochastic inventory model with joint cycle-service and fill-rate requirements of 95% (SC95) and 99% (SC99). Results: Four of five recurrent-positive series favored the normal distribution; among intermittent series, seven showed numerical AIC ties between ZINBI and hurdle-NB and one favored normal. Four medicines showed positive temporal trends under the prespecified screen and two showed negative trends; eight had intermittent zero-request months, and M09 was both increasing and intermittent. Expert consultation indicated that growth and intermittency can arise from multiple clinical, organizational, inventory, and supply mechanisms rather than representing mutually exclusive demand types. A temporal model ultimately replaced the marginal generator in 46 of 156 origins, including GARMA in 19. Temporal adaptation increased central 90% held-out coverage from 84.0% to 88.5% overall and from 73.3% to 83.3% for recurrent-positive demand. SC95 achieved realized fill rate 0.991 and cycle service 0.929, whereas SC99 achieved 0.997 and 0.962, respectively. Scenario-expected versus realized cost MAPE was 2.4% and 0.7%, respectively. In a separate 900-case diagnostic simulation, 74.0% of cases were operational ties and AIC agreed with the operational winner in 13.7% of unique-winner cases. Conclusions: Hospital pharmacy replenishment should not rely on a single probability model or on statistical fit alone. Growth or decline in temporal direction and intermittency in demand occurrence should be interpreted as complementary dimensions, with pharmacist context used to avoid assigning unsupported causal meaning to anonymized series. Distributional heterogeneity and temporal dependence should guide scenario generation, while explicit service requirements and prospective validation should govern their translation into replenishment decisions.