Analyzing Retailer Ordering Decisions in Emergency Supply Chains Under an Uncertain Random Environment Based on Chance Theory

Public health emergencies create demand environments in which routine demand can be estimated from historical observations, whereas emergency demand is often characterized by limited data and expert assessments. To address this challenge, this study develops an uncertain-random newsvendor model for emergency supply chains based on chance theory. Routine demand is modeled as a random variable, while emergency demand is represented as an uncertain variable, enabling both stochastic and epistemic uncertainties to be incorporated within a unified analytical framework. The model is analyzed under decentralized and centralized decision-making modes, and closed-form optimal ordering policies are derived. The results show that the proposed framework generalizes both stochastic and uncertain newsvendor models as special cases. Residual value, shortage cost, expected emergency demand, and belief degree significantly affect inventory decisions and supply chain performance. Higher residual values and larger emergency demand expectations encourage inventory expansion, while centralized decision-making consistently generates higher order quantities and expected profits than decentralized decision-making. Moreover, the efficiency loss associated with decentralized decision-making increases with the belief degree, indicating that supply chain coordination becomes increasingly important when decision-makers place greater confidence in emergency demand forecasts. The findings highlight the importance of inventory incentives, demand forecasting, and coordinated decision-making in emergency operations. This study provides a theoretical foundation for emergency procurement and inventory planning when historical data are limited and demonstrates the value of integrating chance theory into emergency supply chain management under uncertain-random demand environments.