# Sustainable Cold Chain Management: An Evaluation of Predictive Waste Management Models
## 4 Data Analysis
### Model Evaluation and Performance Metrics
#### 4.4.2 MLR Model  
The MLR model, trained on the same dataset, incorporated three independent variables: temperature, product type, and promotional activity. The results for 2023 predictions were as follows:  
* Mean Absolute Error (MAE): 5.1%
* Root Mean Squared Error (RMSE): 7.4%  
While the MLR model provided accurate insights into the relationships between demand and the selected variables, its prediction precision was similarly affected by the lack of real-time environmental data inputs. This highlights the potential for IoT integration to improve predictive performance further.  
Both models demonstrated reliable baseline predictions, with MAE and RMSE values indicating acceptable levels of accuracy for demand forecasting in cold chain logistics. These metrics validate the use of ARIMA and MLR as practical tools for mid-sized operations. Future research should incorporate IoT-enabled environmental metrics to reduce error rates and enhance forecasting precision, aligning with evidence from the literature that IoT data integration significantly improves model performance [22].  
Figure 10 provides insight into the ARIMA model's predictive performance, capturing general demand trends but showing limitations in accurately forecasting short-term fluctuations due to missing environmental data. For example, during May 2021, the ARIMA model over-predicted demand by approximately 15% compared to actual sales. This deviation can be attributed to several factors:  
* Lack of Real-Time Data: The ARIMA model relies solely on historical sales data and does not incorporate real-time external factors such as unrecorded promotional activities or sudden market shifts, which could significantly influence demand.
* Residual Error Propagation: Errors from previous periods may accumulate and amplify deviations during specific timeframes, as observed in May 2021.
* Seasonal Component Anomalies: Atypical variations in the seasonal component during this period likely contributed to the over-prediction.  
Similar deviations, including instances of under-prediction, were observed during periods of sudden demand spikes. These findings highlight the model's limitations and emphasize the importance of integrating additional data sources, such as IoT-enabled real-time metrics, to enhance its accuracy and robustness.  
Figure 11 suggests potential overproduction risks in the absence of refined adjustments. Although ARIMA is effective for capturing seasonal trends, incorporating IoT metrics such as temperature and spoilage indicators could enhance the model's responsiveness to real-time demand shifts, reducing waste by enabling more precise inventory adjustments.  
Figure 12 illustrates the relationship between the observed data (scatter points) and the predictions made using the Multiple Linear Regression (MLR) model (red line). The MLR model predicts the dependent variable (YYY) based on the independent variable (X1X_1 \(\times\) 1) using the equation:  
\[\text{Y}=10+2.5\times 1\text{Y}=10+2.5\text{X}\_1\text{Y}=10+2.5\text{X}\text{1}\]  
Here:  
* Intercept (10): Represents the value of YYY when X1 = 0X_1 = 0X1 = 0, serving as the baseline prediction.
* Slope (2.5): Indicates the rate at which YYY changes for every unit increase in X1X_1X1.  
Figure 11: Future Demand Forecast Using ARIMA.  
Figure 10: ARIMA Predictions vs. Actuals with Confidence Interval (Historical data (2021 and 2022) and ARIMA prediction for 2023 demand).  
The scatter points represent the observed data showcasing real-world variability around the predicted trend line. The proximity of these points to the regression line demonstrates the accuracy and reliability of the MLR model in capturing the relationship between the variables. The computational efficiency and simplicity of the MLR model make it a practical choice for demand forecasting and analysis in cold chain logistics.  
This figure highlights the effectiveness of the MLR model in explaining the data trends and providing actionable insights for inventory and supply chain management.