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

ArXiv ID: 2510.05487 “View on arXiv”

Authors: Jinho Cha, Sahng-Min Han, Long Pham

Abstract

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.

Keywords: Demand modeling, Negative Binomial, Smart contracts, Supply chain optimization, Inventory management, Supply Chain Logistics

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical modeling (Negative Binomial with autoregressive dynamics, maximum likelihood estimation, grid search optimization) and validates the framework using four real-world datasets with forecasting comparisons and scenario analysis.

  flowchart TD
    A["Research Goal: Optimize smart contract adoption under high-variance demand"] --> B["Methodology: Dynamic NB Demand Modeling with Endogenous Adoption"]
    B --> C["Data: Four real-world datasets\nDelhivery Logistics, SCMS Global Health, etc."]
    C --> D["Computations: MLE, Grid Search,\nScenario Analysis"]
    D --> E["Findings: NB outperforms benchmarks\nAdoption >70% boosts profit when dispersion >6"]
    A --> E