Hybrid Forecasting Framework for Emergency Material Demand in Post-Earthquake Scenarios Integrating the Grey Model and Bayesian Dynamic Linear Models

Earthquakes are sudden and highly destructive events that severely disrupt infrastructure and logistics systems, making accurate and timely emergency material demand forecasting a critical challenge in disaster response. However, the scarcity of reliable data during the early stages of an earthquake limits the effectiveness of traditional forecasting methods. To address this issue, this study proposes a hybrid forecasting framework that integrates the Grey Model (GM(1,1)) with Bayesian Dynamic Linear Models (BDLMs), aiming to improve both the accuracy and adaptability of demand predictions. The approach operates in two phases: first, GM(1,1) generates preliminary forecasts using limited initial observations; second, BDLMs dynamically update these forecasts in real time as new data become available. The model is validated through a case study of the 2010 M7.1 Yushu earthquake in Qinghai Province, China. The results indicate that the hybrid method produces reliable forecasts even at the earliest stages of the disaster, with increasing accuracy as more observational data are incorporated. Our case study demonstrates that the integrated GM(1,1)-BDLM framework substantially reduces prediction errors compared to standalone GM(1,1). Using the first five days’ data to forecast fatalities and emergency material demand for days 6–10, the hybrid model achieves a 4.01% error rate—a 19.62 percentage point improvement over GM(1,1)’s 23.63% error rate. This adaptive forecasting mechanism offers robust support for evidence-based decision-making in emergency material allocation, enhancing the efficiency and responsiveness of post-disaster relief operations.