Gauss–Hermite metabolism GM(1,1) model to predict emergency material demand: a novel forecasting method

Purpose The main goal of this improvement is to enhance the prediction accuracy of GM(1,1) model to facilitate its application in the prediction of emergency material demands and enhance the existing GM(1,1) by incorporating the Gauss–Hermite integral, thereby deriving a novel model termed the Gauss–Hermite metabolism GM(1,1) (GHM-GM(1,1)). Design/methodology/approach The image equation of the metabolism GM(1,1) is improved using the Gauss–Hermite integral. First, based on the properties of this integral method, a new time-response equation is derived, and the GHM-GM(1,1) is constructed. To further optimize the model’s performance, a new parameter, “δ” is introduced. This parameter adjusts the amount of data supplementation and deletion each time. Additionally, a selector is equipped to determine the optimal window size, ensuring that the result with the minimum prediction error is selected and output during each data prediction process. Subsequently, to verify the model’s validity, we compare it with other GM(1,1) models through a simulation experiment and two practical cases. We objectively evaluate the characteristics and advantages of GHM-GM(1,1) through specific performance indicators and evaluation criteria. Finally, using the new model, the population affected by natural disasters in China was predicted to complete the emergency material demand prediction. Findings The new prediction model has demonstrated higher prediction accuracy in three comparative experiments, verifying the validity and practical application potential of the model. Results show that the model more accurately predicts emergency material demand by capturing data trends and fluctuations, outperforming other models in accuracy. Originality/value In this study, a new GM(1,1) is proposed, which integrates the Gauss–Hermite integral and metabolism GM(1,1), which significantly improves the accuracy and reliability of gray prediction. The introduction of the optimal window “δ” not only further enhances the prediction accuracy of the metabolism GM(1,1) but also increases the adaptability of the model.