Smart Contract Adoption under Discrete Overdispersed Demand: A Negative Binomial Optimization Perspective

Effective supply chain management under high-variance demand requires models that jointly address demand uncertainty and digital contracting adoption. Existing research often simplifies demand variability or treats adoption as an exogenous decision, limiting relevance in e-commerce and humanitarian logistics. This study develops an optimization framework combining dynamic Negative Binomial (NB) demand modeling with endogenous smart contract adoption. The NB process incorporates autoregressive dynamics in success probability to capture overdispersion and temporal correlation. Simulation experiments using four real-world datasets, including Delhivery Logistics and the SCMS Global Health Delivery system, apply maximum likelihood estimation and grid search to optimize adoption intensity and order quantity. Across all datasets, the NB specification outperforms Poisson and Gaussian benchmarks, with overdispersion indices exceeding 1.5. Forecasting comparisons show that while ARIMA and Exponential Smoothing achieve similar point accuracy, the NB model provides superior stability under high variance. Scenario analysis reveals that when dispersion exceeds a critical threshold (r > 6), increasing smart contract adoption above 70% significantly enhances profitability and service levels. This framework offers actionable guidance for balancing inventory costs, service levels, and implementation expenses, highlighting the importance of aligning digital adoption strategies with empirically observed demand volatility.