A Gray Model and Single Exponential Smoothing Approach for Predicting Insulin Demand in Diabetic Patients

Diabetes mellitus, a prevalent metabolic disorder with no known cure, requires continuous insulin management. Challenges such as reduced imports of foreign insulin and limited adoption of domestic alternatives have created supply-demand imbalances in pharmacies. This study proposes an optimized predictive model.

Sales data for two insulin pen types were collected monthly and weekly (May–October 2024) from pharmacies in western Mazandaran, Iran. Single exponential smoothing, double exponential smoothing, and the Gray model were applied, with accuracy evaluated via mean absolute error (MAE) and mean square error (MSE).

Testing different alpha values revealed optimal performance at α=0.7 for endogenous insulin and α=0.9 for exogenous insulin. Therefore, forecasting was performed using the smoothing method, and after modeling using the Gray method, the results were compared. Finally, the prediction results using the Single Smoothing were compared with it.

The results demonstrate that the Gray model provides more accurate insulin demand predictions than exponential smoothing models and can enhance demand prediction performance, offering a better framework for managing supply-demand balance.