A Diversified Integrated Model for Seasonal Product Demand Prediction

doi:10.21203/rs.3.rs-4897840/v1

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A Diversified Integrated Model for Seasonal Product Demand Prediction

https://doi.org/10.21203/rs.3.rs-4897840/v1

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Product demand forecasting is the core link of an intelligent supply chain. The article discusses the demand characteristics of seasonal fast-moving consumer goods and presents a diversified stacked regression model (RXOEL-X) that combines linear and multi-machine learning models. This model utilizes a model stacking strategy and adopts the ElasticNet model, combined with L1 and L2 regularization to handle complex relationships in the data and prevent overfitting. Empirical evaluation using real data from leading beverage companies demonstrates the model's superiority over other time series forecasting techniques in demand forecasting for smart supply chains.

Supply chain management

Demand forecasting

Diversified integration model

Machine learning

Robustness

As global economic patterns continue evolving and industrial structures innovate, enterprises are increasingly navigating a complex and volatile external environment. Prominent companies, such as Apple, Amazon, and Tesla, have encountered significant challenges in this context. For instance, inaccurate demand forecasting may lead to an overabundance or a shortage of Apple's newly launched products, such as the iPhone. This would impact the enterprise’s sales and brand reputation. Similarly, Amazon's difficulties in forecasting storage capacity in international facilities can result in stockpiling issues or logistical bottlenecks. For Tesla, despite the rapid expansion of the electric vehicle market, may still encounter growth impediments due to battery supply issues and forecast inaccuracies. Driven by environmental and market demand factors, efficient supply chain management has emerged as a crucial and indispensable business development component. Effective supply chain management helps companies minimize resource waste, reduce production and operational costs, and adjust the supply and demand structure. The primary objective of supply chain management is to optimize procurement and payment processes, production and inventory management, and sales and payment operations. Forecasting plays a pivotal role in supply chain management by enabling enterprises to estimate market demand, plan and deploy resources rationally and reduce inventory costs more accurately. At the same time, it can also prevent inventory backlogs resulting from overproduction and mitigate supply issues due to underproduction. Based on these insights, businesses can develop appropriate product distribution plans to enhance supply chain efficiency and operational stability. Enterprises require a demand forecasting model that is precise, flexible, and adaptable to market changes. Such a model should generate accurate forecasts amid shifting market conditions by incorporating historical sales data, market trends, seasonal factors, promotional activities, and other multidimensional factors.

In this study, we propose an innovative and diversified integrated model, RXOEL-X, which employs Blending linear regression as its foundation. The model is divided into a master model and a sub-model. The master model amalgamates the strengths of several primary models, including Random Forests (RF), XGBoost, Ordinary Least Squares (OLS), ElasticNet, and Long Short-Term Memory Networks (LSTMs), with XGBoost serving as the sub-model. By integrating the unique advantages of each model, RXOEL-X can more precisely estimate supply chain demand for enterprises. This model leverages the power of machine learning in big data analytics, combining the robustness of traditional statistical methods with the non-linear modeling capabilities of neural networks. It enhances overall predictive performance through model fusion. Blending linear regression provides a foundational prediction framework, while ensemble machine learning models such as RF and XGBoost offer substantial nonlinear fitting capabilities and stability against overfitting. OLS and ElasticNet, conversely, offer straightforward strategies for managing linear relationships. LSTM, as a deep learning algorithm, captures long-term dependencies in time series data, which are crucial for seasonal and trend-based demand forecasting. The choice of XGBoost as a sub-model is motivated by its excellent performance and adaptability to various data types, as well as its demonstrated strengths in handling complex non-linear patterns. By combining XGBoost's prediction results with those of other models, the accuracy and robustness of the predictions can be further enhanced. Additionally, this study emphasizes achieving a synergy between intelligent prediction and objective learning by incorporating the ElasticNet model. ElasticNet effectively manages complex relationships within the data in unstructured while preventing overfitting by combining the L1 and L2 regularization terms, thereby selecting relevant variables and stabilizing the model.

Seasonality and change points are essential factors affecting beverage sales. So, in this paper, we incorporate these elements as feature inputs into the integrated model. Machine learning techniques are employed to discern non-linear patterns in time-series data intelligently and to handle unstructured features inherent in the data objectively. Further, this paper empirically evaluates the forecasting methodology by applying it to a real dataset from a leading company in the beverage industry and comparing the proposed model with other time-series forecasting models. The results of the study indicate that the predictive accuracy of the proposed model is significantly superior to the other models.

The main innovations of the model include the development of a diversified linear stacking model explicitly designed for seasonal time series forecasting problems. Its superiority and effectiveness are verified by comparing it with various cutting-edge forecasting algorithms successfully applied to product demand forecasting. To enhance the model's accuracy, this study optimizes the ElasticNet model by employing validation and grid search methods to fine-tune its parameters. Additionally, the study emphasizes robustness, ensuring that the model maintains high performance across different scenarios. To comprehensively validate the effectiveness of the stacked models, we conducted experiments using different configurations and the same dataset, comparing the prediction results with several commonly used forecasting models. This study introduces an innovative approach by combining Blending linear regression with multiple Machine learning models and employing a model stacking strategy, thereby enhancing the intelligence of the predictions. The models demonstrate broad applicability and exceptional performance in practical applications.

This paper not only provides novel perspectives in theoretical research but presents efficient solutions to practical problems across various industries. The results demonstrate that the RXOEL-X model exhibits high accuracy and stability.

Over time, product demand has become increasingly critical to the development of businesses and society. Belvedere and Goodwin (2017) state that demand forecasting is vital for industries in a speedy fashion, as they are challenged with short-term and highly volatile sales time series. The importance of demand forecasting is not only in providing essential forecasts through statistical methods to provide a base forecast but in understanding and managing human factors in the forecasting process, such as the emotions and preferences of the forecasters and their knowledge of the product, which can affect the outcome of the forecast. Effective demand forecasting requires balancing these factors to ensure that the forecast is as close as possible to the actual sales situation, thus helping firms make informed inventory and production decisions in unstable markets. Fu and Chien (2019) propose that, in fact, demand forecasting provides key inputs for various strategic decisions in supply chain management, including capacity planning, inventory control, and demand fulfilment. Liang et al. (2024) point out that accurate and reliable demand forecasting is a vital presence for significant retailers today, as the results of demand forecasting will directly affect the retailers' assortment planning, store location, and production planning. Kück and Freitag (2020) point out that demand forecasting is more important than product quality, as it directly impacts the ability to manage inventory and operating costs. Trapero et al. (2023) state that demand forecasting is critical in supply chain management. Inventory control policies are directly affected by the accuracy of probabilistic demand forecasts. Punia and Shankar (2022) state that high-quality demand forecasts are essential for the future and growth of a business, so there is a need to ensure the accuracy and quality of the data when making demand forecasts for a product. Lee (2020) suggests that accurate demand forecasting is an essential and highly challenging problem. This is because the results of snowball forecasting will directly affect the organization's future growth and planning. Rodrigues et al. (2024) point out that inaccurate demand forecasting will directly affect society's future ecological and developmental status. Therefore, accurate product demand forecasting is a necessity for the development of society, which will help alleviate the burden on society and the environment in the future. Chien et al. (2023) point out that effective demand forecasting will help enterprises ensure customer satisfaction and minimize the enterprises' inventory stocking. It reduces the amount of stock available in the firm's inventory. At the same time, the highly variable demand size for products and time intervals makes the current demand forecasting problem challenging. Dou et al. (2018) pointed out that in the development of enterprises in various industries, the internal and external difficulties from the enterprise itself will increase the risk of supply and demand imbalance of the enterprise itself. This is because when the enterprise's supply chain is not able to produce the number of products to meet the demand of the customer, the enterprise's market share and customer satisfaction decline, making the enterprise lose its competitiveness in the market, and when the share of the production of the product is too much will increase the risk of the enterprise's inventory. An excess share of products produced will increase inventory risk and reduce the company's profitability, so accurate demand forecasting becomes essential for the company's future development. Tadayonrad and Ndiaye (2023) explored the importance of demand forecasting and safety stock determination in supply chain planning. Demand forecasting predicts future demand for a product or service by analyzing historical data and other external and internal factors to reduce inventories and overproduction. Xu et al. (2024) proposed a new double-layer grey prediction model to improve the performance of cold chain logistics demand prediction. This model adapts to data features and generates corresponding background sequences to adjust parameters. Merge the time response functions generated by the double-layer structure using a differential evolution algorithm. Compared with existing similar models, this model extends its applicability and can provide higher accuracy for data sequences with high development rates. This model outperforms classical grey models and their extensions in terms of prediction accuracy.

As more and more enterprises begin to pay attention to product demand forecasting, the methods of demand forecasting have started to increase gradually. Ni et al. (2022) pointed out that the comprehensive salesperson opinion method, expert opinion method, market experiment method, time series analysis method and statistical demand analysis method are the more common methods of demand forecasting in the market at present. With the progress of scientific research, scholars have been improving the biochemistry of demand forecasting methods, and there are currently three standard methods for predicting product demand: time series, deep learning, and combinatorial algorithms. Lee and Kim (2024) proposed a prediction model that combines dynamic simulation and regression models to better predict product demand. Steenbergen and Mes (2020) proposed a demand forecasting method called DemandForest by combining the demand forecasting methods of K-means clustering, Random Forest, and Quartile Regression Forest by clustering analysis of the demand patterns and introducing the intra-period. This machine learning method is capable of forecasting newly launched products using historical sales data and product characteristics to assist in the inventory management of new products. Selim Türkoğlu et al. (2024) proposed a robust short-term multivariate multistep forecasting framework for demand forecasting using temporal convolutional networks (TCNs) that are resistant to missing or erroneous data and can predict demand for new products. That can resist the shadow of missing or inaccurate data. Xu et al. (2017) proposed a six-step multistage combinatorial forecasting model to predict demand for product services with a hierarchical service structure. The model incorporates the advantages of method combination forecasting and information combination forecasting. Validated with an air compressor service prediction case study, the model's in-sample and out-of-sample test results show that it outperforms a single prediction model and its direct combination. The method can be flexibly customized for other product-service demand forecasting scenarios and is particularly suitable for dealing with stratified time series data. Ji Chen et al. (2024) proposed a prediction method that combines the Boruta algorithm (Boruta), bidirectional long short-term memory (BiLSTM), and convolutional neural network (CNN). Through comparative analysis, it is shown that the performance of the hybrid CNN BiLSTM model is superior to the benchmark model. Robustness testing and robustness testing confirm that the proposed model has appropriate generalization ability, which is of great help for demand prediction. Wu et al. (2024) proposed a novel dual correction model based on knowledge extraction called the Knowledge-Based Dual Correction Model (KbBcM). KbBcM utilizes prior and posterior knowledge to achieve effective lag-free prediction. Extract prior knowledge in the form of sequence and feature information using an autoregressive long short-term memory (AR-LSTM) network and a newly proposed lagged penalty attention (LPA) module. In addition, a hybrid stacked LSTM network is used to obtain preliminary prediction results, which are then corrected using a masked weighted Markov chain (MWMC) based on posterior knowledge. In response to the limitations of the current focus on absolute error indicators, we have also introduced a new mean prediction trend effectiveness (MPTE) to comprehensively evaluate the effectiveness of non-lagged prediction performance.

Machine learning demonstrates diverse approaches and comprehensive analytical capabilities in demand forecasting. It integrates traditional methods, such as salesperson opinion, expert opinion, market experiments, modern time series and statistical analysis techniques, with extensive data analysis using multidimensional metrics. Deep learning algorithms, particularly LSTM, capture complex patterns in time series data. In contrast, ensemble learning methods like XGBoost and RF enhance the accuracy and generalization of predictions. Existing research on machine learning has achieved notable progress in improving time series analysis and statistical demand forecasting. This includes enhancing forecast accuracy in small sample environments, accounting for the impact of related product demand, preventing overfitting in high-dimensional time series data, optimizing inventory management through cluster analysis and quantile regression, and developing multilevel combinatorial forecasting models to enhance forecasting performance for products with hierarchical service structures. However, challenges remain, such as overfitting issues, the inability of traditional methods to capture complex nonlinear relationships, difficulties in forecasting accuracy and inventory management for newly launched products, and the need for flexibility across different forecasting scenarios. To address these challenges, this paper proposes a diversified integrated model (RXOEL-X) that combines the strengths of Blending linear regression, RF, XGBoost, OLS, ElasticNet, and LSTM, with XGBoost serving as a sub-model. This model improves multi-product demand forecasting performance by enhancing accuracy, preventing overfitting, managing complex nonlinear patterns, flexibly adapting to market changes, and effectively analyzing high-dimensional data.

Guo et al. (2021) proposed a novel hybrid forecasting method for predicting seasonal manufacturing demand. The approach combines the strengths of the Prophet model, which is responsible for capturing seasonal fluctuations and determining the input variables for the SVR model, and the SVR model, which is used to identify nonlinear patterns. This hybrid PROPHET-SVR approach can customize holiday impacts and seasonal variations and effectively account for prediction residuals, thus improving prediction accuracy. The study results show that the hybrid method outperforms other traditional forecasting techniques in terms of forecasting performance. Joseph et al. (2022) explored the importance of accurate product demand forecasting for business decision-makers to formulate strategies in a changing market environment and developed a CNN BiLSTM framework incorporating the Lazy Adam optimizer to improve the accuracy of shop merchandise demand forecasting. He et al. (2023) used two LSTM-based networks as the basic framework for the demand forecasting model, on which horizontal and vertical sequential forecasting model improvements were carried out to forecast the relevant product demand. Li (2024) proposed A cascaded hybrid neural network commodity demand prediction model based on multimodal data, which integrates historical order information and product evaluation sentiment data by constructing multimodal data feature clustering and using a spatial feature fusion strategy. Thus, the advantages of bi-directional long- and short-term memory networks and bi-directional gated recurrent unit networks are combined to provide product forecasting accuracy for product inventory management. Ma and Liu (2024) proposed a CNN-LSTM-Attention algorithm to predict product demand and demonstrated through experiments that the CNN-LSTM Attention model outperforms 1DCNN-LSTM-Attention, CNN-LSTM, LSTM, SVR-based model, and BP neural network model in product demand prediction, with a prediction accuracy of 97.50%, verifying the practicality and effectiveness of the model.

Liao et al. (2024) pointed out that in current demand forecasting, traditional models often face the challenge of capturing and analyzing complex time series data. To solve the dilemma better, they proposed an innovative co-training model based on empirical modal decomposition (EMD), which employs a two-layer optimization strategy and combines a differential evolutionary algorithm and interactive fuzzy planning to optimize the training of neural networks derived from EMD decomposition subsequences for neural network training. This co-training mechanism effectively overcomes the problem of capturing the complex relationships among subsequences, thus improving the prediction accuracy, and providing a new perspective for applying intelligent prediction in the field of tourism demand. Dong et al. (2023) pointed out that since human behaviours constantly change, the demand prediction will change as well, and therefore proposed a spatiotemporal feature enhancement model to ensure the completeness of the demand features and applied the steady-state analysis method to learn the spatiotemporal features, which is the best way to ensure the completeness of the demand features. Steady-state analysis was used to learn the spatial and temporal features, a convolutional filter was employed, and the feature sequences were transformed into image sequences, maintaining the correlation between the spatial and temporal features. Jin et al. (2024) proposed a hybrid forecasting method combining the System Dynamics (SD) model with the Power Generation Portfolio Planning (PGMP) model. This approach reduced the forecasting error and carried out the demand forecasting exercise by correcting the Markov chain state transfer matrix in the PGMP model. Ye et al. (2024) proposed a Fourier time-varying grey model (FTGM) to improve the accuracy of seasonal demand forecasting. The model combines the advantages of grey forecasting methods, i.e., the ability to process finite datasets efficiently, and the ability of the Fourier function to approximate time-varying parameters to capture and represent seasonal variations efficiently. The FTGM is characterized by a data-driven selection algorithm capable of adaptively determining the model without a priori knowledge. Fourier order of the model without a priori knowledge. Using the well-known M5 competitive dataset and comparing FTGM with state-of-the-art forecasting techniques based on grey models, statistical methods, and neural network approaches, experimental results show that FTGM outperforms other popular seasonal forecasting methods in terms of standard accuracy metrics.

In summary, intelligent forecasting has demonstrated the efficacy of integrating multiple modeling approaches to enhance accuracy. These approaches include global model training for linear and non-linear analysis and advanced neural network architectures, such as LSTM, for complex sequential data. Additionally, historical order data and product evaluation sentiment data are incorporated using multimodal data and cascading hybrid neural network models to improve forecasting accuracy. Intelligent forecasting also addresses complex time series through EMD and co-training mechanisms, utilizing spatiotemporal features to enhance the model's learning capabilities. This approach employs steady-state analysis methods, SD and PGMP to efficiently capture seasonal variations. Despite its ability to handle a wide range of complex scenarios, intelligent forecasting still faces challenges related to data quality, model generalizability and interpretability, and adapting to environmental dynamics. To address these challenges, this paper proposes a diversified integrated model (RXOEL-X), which combines the strengths of various forecasting techniques to enhance adaptability and robustness. This model optimizes data usage and improves interpretability, thereby overcoming the limitations of existing intelligent forecasting methods and providing more accurate, reliable, and interpretable forecast results.

Compared to other standard demand forecasting methods (e.g., Salesperson Opinion Method, Time Series Analysis, Statistical Demand Analysis), as well as models proposed in other studies (e.g., XGBoost-based models, Multi-Level Combined Forecasting Models, DemandForest, LSTM-based models), the RXOEL-X model stands out due to its integration of multiple forecasting techniques. This model offers a robust and precise framework, particularly adept at managing big data and high-dimensional time series data, thereby potentially optimizing inventory cost management.

Table 1 provides a summary of the forecasting models and their performance from the literature.

Table 1

List of related literature
Model	Contribution
XGBoost	Improving the accuracy of e-commerce product prediction in small sample data environments combines multidimensional metrics, fuses similar metrics using the entropy method, incorporates Logistic functions and regularization terms, and optimizes using a greedy algorithm.
AR	Considering the importance of associated product demand trends for forecasting, forecasting accuracy is improved by incorporating associated product demand as an additional predictor into the model, and a variable simplification scheme is introduced to prevent overfitting.
Demand Forest	Combines K-means clustering, RF, and quantile regression forests to optimize inventory management and predict new product launches with improved forecasting accuracy.
TCNs	Robust short-term multivariate multistep prediction framework that resists the effects of missing or erroneous data.
Multilevel Combined Prediction Model	The fusion approach combines the advantages of forecasting and information combination prediction and is suitable for dealing with product-service requirements in a hierarchical service structure. Validation has shown that it outperforms a single forecasting model and its combinations.
Co-Training Model Based on EMD	A two-layer optimization strategy, combining differential evolutionary algorithm and interactive fuzzy planning, is used to optimize neural network training, overcome the complex relationship between sub-sequences, and improve prediction accuracy.
Spatiotemporal Feature Enhancement Model	Spatiotemporal features are learned by means of a steady-state analysis method using a convolutional filter, and the sequence of features is transformed into a sequence of images, maintaining the correlation between spatial and temporal features.
SD&PGMP	Reducing prediction errors and correcting the Markov chain state transfer matrix in the PGMP model.
FTGM	To improve the accuracy of seasonal demand forecasting, a data-driven selection algorithm is used to adaptively determine the Fourier order of the model by combining the advantages of grey forecasting methods and Fourier functions.
PROPHET-SVR	Combine the strengths of the Prophet model and the Support Vector Regression (SVR) model to customize holiday impacts and seasonal variations and consider forecast residuals to improve accuracy.
CNN BiLSTM	A framework incorporating the Lazy Adam optimizer for improving the accuracy of forecasting demand for goods in shops.
Six-Step Multilevel Combinatorial Forecasting Model	It can be flexibly customized for other product-service demand forecasting scenarios and is particularly suitable for processing hierarchical time series data.
Two Horizontal and Vertical Sequence Prediction Models Based on LSTM	The correlations inherent in long-term series are skillfully captured, thus correcting the limitations of traditional algorithms in managing complex and irregular data patterns.
A Cascaded Hybrid Neural Network Commodity Demand Forecasting Model Based on Multimodal Data	Historical order information and product evaluation sentiment data are integrated by constructing multi-modal data feature clustering and utilizing spatial feature fusion strategies. The model combines the advantages of bi-directional long and short-term memory networks and bi-directional gated recurrent unit networks.
RXOEL-X	Integrating the strengths of Blending Linear Regression, RF, XGBoost, OLS, ElasticNet, and LSTM with XGBoost as a sub-model, it improves prediction accuracy, prevents overfitting, handles complex non-linear patterns, adapts to market changes, and effectively analyses high-dimensional data.

In this paper, we propose a diversified stacked regression model, RXOEL-X, which integrates LSTM, XGBoost, RF, and other models, combining them with a Blending multiple regression linear. This approach enhances the forecasting accuracy of seasonal time series. Unlike traditional time series forecasting models such as BP and ARIMA, this study initially employs a Bayesian-based curve-fitting method to smooth and forecast time series data. Subsequently, a demand forecasting system is constructed, incorporating models like LSTM, XGBoost, and RF, with further optimization achieved through Blending and model stacking techniques. By comparing the performance of each model with the integrated method, prediction accuracy is significantly improved. The Blending linear regression integration model consists of five primary models—RF, XGBoost, OLS, ElasticNet, and LSTM—and one secondary model, XGBoost.

3.1 Framework and process

In the RXOEL-X model, the predicted values from each primary model (RF, XGBoost, OLS, ElasticNet, LSTM) are initially combined using Blending linear regression. Subsequently, XGBoost serves as a secondary model to make the final prediction based on these combined values. This approach leverages the strengths of each model while mitigating the potential weaknesses of any single model. The objective is to enhance prediction accuracy by integrating the diverse strengths and characteristics of multiple models. Blending uses linear regression to merge the models' predictions, and the secondary model (XGBoost) refines the predictions by learning the residuals and patterns from the blended outputs, ultimately providing the final prediction.

In this study, a multi-model integration approach is adopted, in which a series of different master models, specifically RF, XGBoost, OLS, ElasticNet, and LSTM, are trained independently, based on which the prediction results of these master models are combined by linear regression using the Blending technique. In the Blending process, the predicted values of each master model are linearly combined to form an overall prediction that can be denoted as

$$\:{P}_{blend}={{\alpha\:}}_{1}{P}_{1}+{{\alpha\:}}_{2}{P}_{2}+\dots\:+{{\alpha\:}}_{n}{P}_{n}$$

where P denotes the predicted value of each of the leading models and $\:{{\alpha\:}}_{1},{{\alpha\:}}_{2},\dots\:,{{\alpha\:}}_{n}\:$are the linear regression coefficients, which are carefully selected by minimizing the prediction error.

Next, XGBoost is used as a secondary model which trains the secondary model by using the predictions obtained from the Blending technique as input features. The role of the secondary model is to further learn the residuals and patterns of the predictions from the primary model. Eventually, the output of the secondary model is used as the final prediction result as follows:

$$\:{P}_{final}=extXGBoost\left({P}_{blend}\right)$$

where $\:{P}_{blend}$ is the output of the Blending model.

The goal of the entire prediction process is to improve the overall accuracy of the predictions by combining the unique strengths and characteristics of multiple models. The Blending model effectively combines the predictions of the different models through linear regression, while the sub-model (XGBoost) builds on this by learning the residuals and patterns of these combined predictions in-depth, which results in a more accurate final prediction.

3.2 Modeling framework

Firstly, data were collected and cleaned, followed by a series of preprocessing operations, including handling missing values, feature encoding, and normalization or standardization, to ensure data quality and consistency. Subsequently, the data were split into training, validation and test sets for model training and evaluation. In this paper, various primary models were trained, including RF, XGBoost, a linear model with ordinary least squares, an ElasticNet linear regression model with L1 and L2 regularization, and LSTM for sequential data. The predictions of each model on the validation set were recorded and used as a new feature set to construct secondary training data. Next, a secondary XGBoost model was trained using these features, learning how to combine the predictions of the primary models best. After all primary models completed their predictions on the test set, these predictions were collected as input features for the secondary model, which then generated the final predictions. Finally, the models were evaluated and optimized using appropriate evaluation metrics to ensure optimal performance in real-world applications. The specific steps are shown in Fig. 1.

With the above methodology, this paper introduces diversified integration and evaluates the performance of the proposed integration model. The performance of the RXOEL-X model is also investigated from two perspectives. In section 4.1, the model proposed in this paper is compared with the models proposed in other studies using publicly available data (https://www.tipdmcup.cn/sszx/2019.jhtml). In the next section, a set of actual company data is applied to the proposed model, and the company data are processed and parameterized to produce the prediction results, which are analyzed accordingly. Meanwhile, section 4.2 presents the calculation results of six different models under the relevant data, and the robustness of these models is discussed and verified.

4.1 Comparison with traditional homogenized models

To assess the performance of the proposed model, this paper compares it with five commonly used and classical demand forecasting methods from the literature (Table 2 and Fig. 2). The selection criteria for these methods considered two key aspects. Firstly, raw data for training and testing was ensured. Secondly, the chosen methods were methodologically diverse to represent different prediction mechanisms and advantages. Specifically, LSTM, XGBoost, RF, Backpropagation Neural Networks (BP), and Autoregressive Integrated Moving Average (ARIMA) were selected as the traditional demand prediction models for this study. Each of these methods offers unique predictive capabilities. For instance, LSTM excels in handling long-term dependencies in time series data, while XGBoost and RF are advantageous in managing complex data relationships. ARIMA is a classical statistical model particularly suited for time series data with deterministic seasonal patterns. BP, as a typical neural network algorithm, is effective in modeling non-linear relationships.

This comparative study aims to provide a comprehensive assessment of the proposed model's performance in real-world demand forecasting tasks and to highlight its advantages and disadvantages relative to traditional methods. This paper will strictly follow the methodology provided in the literature and the operational methods of the underlying demand forecasting model to forecast the results of the data models and ensure the accuracy of the comparisons between the models. Firstly, a set of data model resources is used for data prediction, and the following table will show the difference between the results of the five basic demand forecasting models and the results of the proposed model. Finally, a comparison with the proposed model will be made.

Table 2

Comparisons between models
Model	RMSE	MAE	R²
RF	1.0940	0.8443	0.3922
XGBOOST	1.2204	0.9298	0.2543
LSTM	1.1500	0.8700	0.3400
ARIMA	1.0810	0.8140	0.4140
BP	1.5601	1.2828	-0.2221
RXOEL-X	1.0120	0.5230	0.8924

(1) Analysis of RMSE values

When comparing the RMSE values of different models, there is a significant difference in the prediction accuracy of each model. RMSE measures the magnitude of the model's prediction error, a lower RMSE metric implies that the model's prediction ability is better, and the error is more minor.

From the data provided, the characteristics shown in Table 3 can be observed.

Table 3

RMSE value analysis
Model	Analysis
RF	On this dataset, the RF model has an RMSE value of 1.094, which shows a moderate level of prediction error. Although it is not optimal, it has a higher prediction accuracy than BP model.
XGBoost	The RMSE value of this model is 1.2204, which is slightly higher than that of the RF model, indicating that XGBoost's prediction performance in this dataset is slightly inferior. Nevertheless, it is still a relatively effective prediction tool, but further parameter tuning may be required to improve accuracy.
LSTM	The RMSE value of 1.15 for the LSTM model indicates a low prediction error when dealing with this dataset, which is better than XGBoost, but slightly inferior to the RF and ARIMA models. This reflects the strength of LSTM in capturing the long-term dependence of time series data.
ARIMA	The ARIMA model demonstrated the best single-model predictive power with the lowest RMSE value of all models at 1.081. This highlights the efficiency of ARIMA in dealing with such time series data, especially in capturing the linear trend of the data.
BP	The RMSE value of the BP model is 1.5601, which is the highest among all models, indicating that it has the worst prediction performance on this dataset. This may be due to the limitations of BP neural networks in dealing with complex data features, which require more refined network architecture design and parameter optimization.
RXOEL-X	The RMSE value of this model was significantly reduced to 1.012, which is the best among all the models, suggesting that the integrated approach may have a significant advantage in improving the prediction accuracy. The high accuracy of RXOEL-X may be attributed to the complementary feature-capturing capabilities of the different models, which effectively reduces the overall prediction error.

In summary, the integrated model is superior because it combines the strengths of multiple models and offsets the weaknesses of a single model, thus providing more accurate predictions. In this case, RXOEL-X notably surpasses all individual models, underscoring the potential and effectiveness of the integrated approach in addressing intricate prediction tasks, as illustrated in Fig. 3.

(2) Analysis of MAE values

When comparing the MAE values of different models, it is possible to assess the predictive accuracy of each model. MAE measures the average deviation between predicted and actual values, with lower MAE values indicating higher predictive accuracy, as shown in Table 4.

Table 4

MAE value analysis
Model	Analysis
RF	On this dataset, the RF model has an MAE value of 0.8443, showing a relatively low mean absolute error. Although it is not the lowest among all the models, it demonstrates better performance in terms of accuracy compared to the BP model.
XGBoost	The MAE value of this model is 0.9298, which is slightly higher than that of the RF model, indicating that XGBoost is slightly less accurate in its prediction when dealing with this dataset. Nonetheless, it is still an effective prediction method, but parameter tuning may be required to further improve its accuracy.
LSTM	The MAE value of the LSTM model is 0.87, which is slightly higher than the RF model but lower than the XGBoost model. This indicates that LSTM has an advantage in capturing the complex characteristics of time series, although there is still room for improvement in accuracy.
ARIMA	The ARIMA model exhibits the best predictive power of any single model with an MAE value of 0.814, which emphasizes the efficiency of ARIMA in dealing with time series data, especially those with significant linear trends and seasonality.
BP	The MAE value of 1.2828 for the BP model is the highest of all models, indicating that it has the worst prediction accuracy on this dataset. This may be related to the structure and parameter configuration of the BP neural network, and further optimization is required to improve its performance.
RXOEL-X	The MAE value of this model is significantly reduced to 0.523, which is the best among all the models, indicating that the integrated approach has a significant advantage in improving prediction accuracy. The high accuracy of RXOEL-X may be attributed to the complementary nature of the different models in capturing the features of the data, which effectively reduces the average deviation between the predicted and actual values.

Taking the above analyses together, the integrated model has a clear advantage in the MAE performance index, and its low error demonstrates the model's strong ability in prediction accuracy. In particular, the RXOEL-X model not only has the best performance on MAE but also implies that it can provide more trustworthy data support for decision-making in practical applications, as illustrated in Fig. 4.

(3) R² value analysis

When comparing the R² values of different models, we can assess each model's capability to explain data variability. A higher R² value approaching 1 indicates a better fit to the data and higher predictive accuracy. Table 5 provides the analysis of model R² values based on the given data.

Table 5

R² value analysis
Model	Analysis
RF	The R² value is 0.3922, which indicates that the RF model performs moderately well in fitting the variability of the dataset. Although it is not the best performer among all the models, the RF model still shows some ability in dealing with complex datasets, especially in avoiding overfitting.
XGBoost	The R² value is only 0.2543. This means that the XGBoost model has a poor fit in the prediction task and explains the variability of the data with a relatively weak fit that can better explain the variability of the data.
LSTM	The R² value is 0.34. This low R² value suggests that the LSTM model has limitations in capturing and predicting complex patterns in time series data and that more data or an improved network structure may be required to optimize performance.
ARIMA	The R² value of 0.414 is slightly higher than the RF model, which shows that the ARIMA model has some fitting ability on this dataset, especially when dealing with time series data with linear trends and seasonality.
BP	The actual R² value of the BP model is -0.2221, which indicates that on this dataset, the BP model not only fails to capture the variability of the data but instead exhibits a predictive trend that is opposite to the trend of the data. This may point to the need for significant adjustments to the structure of the model or the training process.
RXOEL-X	It has the closest R² value to 1 at 0.8924. This result highlights the excellent performance of the integrated model in explaining the variability of the data, fitting the data almost perfectly.

To summarize, all models exhibit R² values closer to 1, indicating that they can all explain the variability of the dataset well to varying degrees. However, the RXOEL-X model performed the best in this round of analyses, having the closest R² value to 1, demonstrating its excellent ability to predict accuracy and explain the data(Fig. 5). This further demonstrates that integrating different prediction models can improve overall model performance, especially in complex prediction tasks.

Based on the comparison of the above three values, the following conclusions are drawn that the RMSE, MAE of this RXOEL-X model are lower than the other methods and the R² value is closest to 1. Therefore, this model is better than the comparative methods regarding prediction accuracy.

4.2 Applied research on modeling

Demand forecasting for beverage companies faces seasonal and cyclical challenges and is significantly affected by seasonal variations and holiday promotions. The study analyzes daily sales data by using a listed beverage company from 2015 to March 2022, with a total of 2602 observations. The data shows that sales have seasonal fluctuations, with solid sales in the summer and reduced demand in the winter and are closely related to weather conditions. To address these challenges, a time series decomposition technique was used to split the sales data into trend, seasonal, and stochastic components so that the model could learn sales patterns across seasons and weather. A comparison of the 10 combined models and the single model revealed that the XGBoost-based model and the integrated model performed well in terms of accuracy and stability. Sensitivity analyses showed that the RXOEL-X model had the most negligible impact on predictive accuracy under data variations and exhibited the highest robustness. Temporal analysis points out that the RXOEL-X model outperforms the other models in terms of time efficiency, despite the high computational cost of the integrated model.

4.2.1 Data description and pre-processing

Demand for products in the beverage industry is often significantly affected by seasonal changes and holidays. This article collects data from one of the leading beverage companies in China. The beverage industry exhibits significant seasonality and some cyclicality. Seasonality is mainly reflected in consumers' seasonal preferences for different types of beverages (e.g., carbonated beverages, fruit juices, tea beverages, etc.); for example, summer is the peak season for the sale of cold beverages, while demand is usually lower in winter. Meanwhile, holidays such as the Chinese New Year, National Day and Mid-Autumn Festival can also have a significant impact on beverage sales, with promotional activities around different holidays often driving sales spikes.

The sales periodicity of beverage products is affected by consumer buying behaviors and marketing activities. During specific holidays or events, such as music festivals and sports events in summer, beverage companies launch various promotional activities to attract consumers. In addition, beverage sales are closely related to weather conditions, with warmer weather conditions increasing sales of cold beverages.

Faced with the uncertainty and volatility of seasonal commodity demand, beverage companies face significant challenges in inventory management and production decisions. To reduce operating costs and meet market demand, companies must optimize supply chain management and production planning based on external factors such as consumer buying habits, market trends and weather.

For this purpose, this paper has selected the daily sales of a listed beverage company from 2015 until mid-March 2022 with its related factors, totaling 2602 observations, as shown in Fig. 6.

4.2.2 Comparison of models and parameter settings

To better evaluate the performance of the RXOEL-X model, this study contrasts it with 10 combination models: LSTM-OLS, LSTM-ElasticNet, RF-OLS, RF-ElasticNet, XGBoost-OLS, XGBoost-ElasticNet, (RF, OLS)-ElasticNet, (XGBoost, OLS)-ElasticNet, (RF, XGBoost, OLS, ElasticNet, LSTM)-ElasticNet, and (RF, XGBoost, OLS, ElasticNet, LSTM)-OLS. Additionally, trend and residual components obtained from individual LSTM, RF, and XGBoost models serve as inputs to the sub-modules in the ensemble model. The experiments are conducted in Python.

Table 6 provides a concise description of these ten models. Each model employs different technical combinations to enhance prediction accuracy and mitigate overfitting risks, aiming to optimize forecasts for corporate needs. Given the lengthy names of the comparison models, referenced by numerical identifiers in Fig. 7–11.

Table 7 outlines the correspondence between the 11 models and their respective identifiers, while Table 8 presents the computational results for these models.

Table 6

10 combination models
Model	Analysis
LSTM-OLS	It combines LSTM with traditional OLS regression. The LSTM is responsible for capturing long-term dependencies and non-linear patterns in the time-series data, whereas the OLS provides parameter estimations on top of the LSTM outputs, aiming to optimize the prediction accuracy.
LSTM-ElasticNet	Like LSTM-OLS, this model uses LSTM to deal with sequence dependence but applies ElasticNet regression to the output of LSTM. ElasticNet combines L1 and L2 regularization for feature selection (like Lasso regression) and model stabilization (like Ridge regression).
RF-OLS	Combines RF and OLS regression. RF is an integrated decision tree-based learning method capable of handling high-dimensional data and non-linear relationships. OLS is used as a post-processing step for parameter estimation using the output of RF.
RF-ElasticNet	The predictions from RF are used as inputs and ElasticNet regression is used as the predictor in the second stage. This leverages RF's ability to handle complex data structures while improving the generalization of the model through ElasticNet regularization.
XGBoost-OLS	Combines XGBoost with OLS regression. XGBoost provides accurate predictions and handles all data problems, while OLS fits a linear regression on the model output.
XGBoost-ElasticNet	Like the XGBoost-OLS model, this model uses the XGBoost algorithm for initial prediction and then uses ElasticNet regression to optimize based on the XGBoost results, combining the advantages of both techniques.
(RF, OLS)-ElasticNet	Predictions are first made by combining Random Forest and OLS regression, and then ElasticNet is used as the second stage model to further process the output of RF + OLS, with the aim of exploiting the regularization properties of ElasticNet to improve the stability of the final predictions.
(XGBoost, OLS)-ElasticNet	Like the (RF, OLS) -ElasticNet model, this model first combines XGBoost and OLS to get one prediction and then makes a second prediction via ElasticNet. This captures the power of XGBoost in handling complex patterns while reducing overfitting with the help of ElasticNet.
(RF, XGBoost, OLS, ElasticNet, LSTM)-ElasticNet	This is a multi-level stacked model that first integrates the predictive power of RF, XGBoost, and LSTM combines the linear regression results from OLS and ElasticNet, and then optimizes the fully integrated results using ElasticNet again. This is a complex model that is theoretically capable of combining the strengths of various prediction models.
(RF, XGBoost, OLS, ElasticNet, LSTM)-OLS	Like the previous model, this is an integrated model, except that in the final stage, it uses OLS to fit the integrated results. By doing this the model can be expected to have good predictive power, while the OLS provides a clear interpretation of the model parameters.

Table 7

Numbering correspondence of the 11 models
Model	NO.
LSTM-OLS	1
LSTM-ElasticNet	2
RF-OLS	3
RF-ElasticNet	4
XGBoost-OLS	5
XGBoost-ElasticNet	6
(RF, OLS)-ElasticNet	7
(XGBoost, OLS)-ElasticNet	8
(RF, XGBoost, OLS, ElasticNet, LSTM)-ElasticNet	9
(RF, XGBoost, OLS, ElasticNet, LSTM)-OLS	10
RXOEL-X	11

Table 8

Calculations for 11 models
Model	RMSE	MAE	R²
LSTM-OLS	12.8289	7.9523	0.9668
LSTM-ElasticNet	12.8302	7.9529	0.9668
RF-OLS	15.3126	6.5875	0.9527
RF-ElasticNet	15.3188	6.5866	0.9527
XGBoost-OLS	6.1295	3.6567	0.9924
XGBoost-ElasticNet	6.1297	3.6567	0.9924
(RF, OLS)-ElasticNet	8.5384	5.6060	0.9853
(XGBoost, OLS)-ElasticNet	9.4232	5.0905	0.9924
(RF, XGBoost, OLS, ElasticNet, LSTM)-ElasticNet	9.4244	5.097	0.9923
(RF, XGBoost, OLS, ElasticNet, LSTM)-OLS	6.1298	3.6569	0.9924
RXOEL-X	5.9876	3.3242	0.9924

By comparing the values of RMSE, MAE and R² of the different models, the predictive performance of the models can be fully assessed. Table 9 presents an analysis of the comparative results based on the provided data.

Table 9

Comparison results of 11 combination models
Model	Analysis
LSTM-OLS & LSTM-ElasticNet	The performance of these two models on the three metrics is very close to each other with little difference. The RMSE and MAE are relatively high, while the R² values are better, indicating that the models fit the data relatively well and have more significant prediction errors.
RF-OLS & RF-ElasticNet	Similarly, in the case of LSTM, the performance of these two models is very close. They have the worst performance in terms of RMSE, medium MAE, fair but still low R² values, and overall average performance.
XGBoost-OLS & XGBoost-ElasticNet	Both models performed very well on all metrics, with the lowest RMSE and MAE of all models and the highest R² values. This indicates that the XGBoost base model is accurate and well fitted in prediction.
(RF, OLS)-ElasticNet	The model performs in the medium range, with RMSE and MAE better than the RF and LSTM variants, but worse than the XGBoost variant. The R² values are better but still do not exceed the XGBoost correlation model.
(XGBoost, OLS)-ElasticNet & RXOEL-X	The two models performed comparably with extremely high R² values, but they did not outperform the XGBoost model alone in terms of RMSE and MAE metrics.
(RF, XGBoost, OLS, ElasticNet, LSTM)-OLS	Like XGBoost-OLS and XGBoost-ElasticNet, the model outperforms all metrics, suggesting that XGBoost may be a key driver of performance in this combination.
RXOEL-X	This integrated model demonstrates strong performance across all metrics, showing a slight improvement in RMSE. It ranks among the best-performing models, highlighting the efficacy of the integrated learning approach in enhancing overall performance by leveraging the strengths of various models.

Overall, both the XGBoost-based model and the integrated model exhibit high prediction accuracy and data fitting ability across the three metrics: RMSE, MAE, and R². Notably, the RXOEL-X model, which stands out as the overall optimal model after considering all metrics, demonstrates the potential of integrating multiple models and techniques to effectively enhance prediction performance. Conversely, RF and LSTM-based models performed poorly in this comparison, particularly in the RMSE metric. In practice, selecting the best model also requires considering computational cost, model training and inference time, and task-specific requirements.

4.3 Sensitivity analysis

Sensitivity analysis is an essential tool for evaluating how sensitive a model's outputs are to changes in input parameters. Through sensitivity analysis, we can gain a deeper understanding of how the model processes inputs to generate outputs, thereby enhancing the model's transparency and interpretability. Conducting sensitivity analysis during model development and application not only improves our understanding of model behavior but also significantly enhances the model's performance and reliability, making it more suitable for practical applications. In this study, we tested the sensitivity of the models by randomly removing 11 data points from each of the 11 models, as shown in Table 10. The comparison of RMSE before and after removal is illustrated in Fig. 10.

Table 10

Sensitivity analysis results
Model	Previous RMSE	Current RMSE	Change Rate(%)
LSTM-OLS	313530.09	368935.73	18%
LSTM-ElasticNet	123344.55	217322.32	76%
RF-OLS	213573.42	299423.92	40%
RF-ElasticNet	192446.99	252861.35	31%
XGBoost-OLS	156351.93	213234.8	36%
XGBoost-ElasticNet	145708.26	185347.54	27%
(RF, OLS)-ElasticNet	216538.05	253563.32	17%
(XGBoost, OLS)-ElasticNet	126738.08	181325.52	43%
(RF, XGBoost, OLS, ElasticNet, LSTM)- ElasticNet	135785.097	191326.62	41%
(RF, XGBoost, OLS, ElasticNet, LSTM)-OLS	245786.097	297844.64	21%
RXOEL-X	12335.47	12521.01	2%

From the sensitivity analysis results, the following points can be analyzed regarding the sensitivity of the different models, as shown in Table 11.

Table 11

Comparison of the sensitivity of 11 models
Model	Analysis
LSTM-OLS	The RMSE of the model increased from 313530.09 to 368935.73 with a change of 18%. This indicates a decrease in the predictive accuracy of the model.
LSTM-ElasticNet	The RMSE of the model increased from 123,344.55 to 217,322.32, a change of 76%, which is the largest change of all the models, suggesting that it is extremely sensitive and may be particularly sensitive to changes in certain parameters or data.
RF-OLS	Increased from 213573.42 to 299423.92, a change of 40%, indicating that this model is also more sensitive relative to the other models.
RF-ElasticNet	The RMSE increased from 192446.99 to 252861.35 with a change of 31%, indicating that it was relatively stable in the model, but still had significant changes.
XGBoost-OLS	The RMSE of the model increased from 156,351.93 to 213,234.8 with a change of 36%, showing moderate sensitivity.
XGBoost-ElasticNet	The RMSE increased from 145708.26 to 185347.54 with a change of 27%, which makes this model less sensitive compared to the other models.
(RF, OLS)-ElasticNet	The RMSE increased from 216538.05 to 253563.32 with a change of 17%, indicating that the portfolio model is relatively stable.
(XGBoost, OLS)-ElasticNet	The RMSE increased from 126738.08 to 181325.52, a change of 43%, indicating that this portfolio model is more sensitive.
(RF, XGBoost, OLS, ElasticNet, LSTM)-ElasticNet	The RMSE increased from 135,785.097 to 191,326.62 with a change of 41%, showing a high sensitivity.
(RF, XGBoost, OLS, ElasticNet, LSTM)-OLS	The RMSE increased from 245786.097 to 297844.64 with a change of 21%, indicating better stability.
RXOEL-X	The RMSE showed the slightest change, increasing from 12335.47 to 12521.01 with a change of only 2%, showing very high stability and low sensitivity.

In summary, the RXOEL-X model exhibits optimal performance, as evidenced by its minimal change in RMSE. The model's previous RMSE was 12,335.47, and its current RMSE is 12,521.01, reflecting a change of only 2%. This is the slightest change compared to the other models, indicating that its predictive accuracy has been the least affected. The RXOEL-X model's meagre percentage change in RMSE signifies a very high level of robustness.

In practice, data are often influenced by various factors, including measurement errors, randomness in the data collection process, and changes in external conditions. A robust model can effectively withstand these variations, ensuring the stability and reliability of its output. The RXOEL-X model combines multiple Machine learning techniques, including RF, XGBoost, OLS, ElasticNet regularization, and LSTM. This multi-model integration approach leverages the strengths of each model while mitigating their respective shortcomings, thus enhancing the overall model's robustness and predictive accuracy. Including XGBoost as the final layer further optimizes the model's performance, as XGBoost excels in handling diverse data types, automatically managing missing values, and offering good scalability and the ability to handle large-scale data.

The model demonstrates excellent robustness due to its low variability and strategy of integrating multiple models, making it the optimal choice in the comparison. This high level of robustness ensures that the model maintains stable performance across different datasets and application scenarios, making it ideal for practical applications.

4.4 Temporal analysis

Temporal analysis typically focuses on the time overhead required by the model during the training and prediction phases. When selecting a suitable predictive model, the speed at which the model runs is an essential factor besides accuracy considerations. Lower temporal analysis results indicate higher model efficiency. Primary temporal analysis in this experiment was conducted on daily data. Based on the temporal analysis results, the following conclusions can be drawn:

The RXOEL-X model demonstrated the best temporal efficiency, with a temporal analysis result of 0.9852, making it the fastest model in the analysis. This indicates that this composite model was highly successful in optimizing time despite integrating multiple models.

The (RF, XGBoost, OLS, ElasticNet, LSTM)-OLS and (RF, XGBoost, OLS, ElasticNet, LSTM)-ElasticNet models also showed better temporal efficiency, with results of 1.1242 and 1.752, respectively. Their relatively low temporal performance may be attributed to effective model optimization and time management.

The (XGBoost, OLS)-ElasticNet model is also highly time-efficient, with a temporal analysis result of 2.38521. This suggests that even composite models can be carefully designed for faster runtimes.

Other single models such as RF-ElasticNet, (RF, OLS)-ElasticNet, and XGBoost-ElasticNet also scored relatively low in temporal analysis, with results of 152.242, 126.8721, and 120.756, respectively. This indicates that integrating ElasticNet regularization techniques into these models did not significantly increase their time overhead.

Conversely, the XGBoost-OLS, LSTM-ElasticNet, and LSTM-OLS models ranked lower in temporal performance, with temporal analysis results of 173.123, 165.872, and 186.863, respectively. This may be due to the inherent complexity of the models or longer runtimes resulting from inadequate optimization.

In summary, despite the expectation that integrated models generally have higher computational costs, this analysis found that some integrated models, particularly the RXOEL-X model, outperformed or even surpassed single models in terms of temporal performance. This may be related to the model implementation's optimization strategy and hardware acceleration. In practical applications, if computational resources are limited or a quick model response is required, a model with good temporal performance should be preferred. It is also essential to be aware of the possible trade-off between a model's temporal performance and its prediction accuracy.

4.5 Results and Discussions

Firstly, this paper evaluates 5 single models and 11 integrated models using the most recent datasets, which were constructed with different input methods. The predictive performance of these 16 models was evaluated by computing statistical metrics on the test set. The results of the prediction evaluation show that there are significant differences in the performance of the models. For each model, the optimal results have been shown in bold.

Among the models compared, the XGBoost-OLS and XGBoost-ElasticNet models excelled in the three statistical metrics of RMSE, MAE, and R², demonstrating their superior prediction accuracy and data-fitting capabilities. Additionally, the hybrid model RXOEL-X, which combines RF, XGBoost, OLS, ElasticNet, and LSTM, also exhibited excellent performance across all metrics. It maintained the smallest variation rate of only 2% in the sensitivity analyses, indicating that this integrated model achieves the highest stability.

The results of the sensitivity analysis reveald that the LSTM-ElasticNet model has a 76% rate of change in RMSE, the highest among the models, indicating a high sensitivity to data variations. The RF-OLS, RF-ElasticNet, XGBoost-OLS, and (RF, XGBoost, OLS, ElasticNet, LSTM)-OLS models also exhibit higher rates of change, suggesting potential instability when faced with data fluctuations. In contrast, the RXOEL-X model demonstrates the lowest rate of change, indicating superior adaptability to input changes and making it the most reliable and robust model in the analysis.

In this evaluation, the XGBoost-based models excel in prediction accuracy and data fitting, while the integrated RXOEL-X model stands out for its stability. The findings underscore that combining machine learning methods with traditional prediction techniques enhances the model's ability to adapt to complex data patterns and improves the robustness of the predictions. Therefore, in practical applications, choosing an integrated model as a prediction tool may be more effective when dealing with nonlinear data and high variability.

In the current complex and dynamic global economy, effective supply chain management is crucial, particularly for beverage companies that need to swiftly adapt to market changes. This study proposes an innovative diversified integration model to accurately predict market demand and optimize resource allocation. The model leverages intelligent forecasting and objective learning concepts to handle the unstructured processing of seasonal and nonlinear patterns in time series data. By integrating linear regression, LSTM, XGBoost, and RF models, and employing model stacking techniques, this approach effectively captures these complex patterns.

In this paper, we conduct an in-depth analysis to derive the key advantages and limitations of the proposed model. The strengths of the model lie in its integration of the unique advantages of several mainstream models, including RF, XGBoost, OLS, ElasticNet, and LSTM, which collectively achieve highly accurate predictions. By combining the powerful data processing capabilities of machine learning with the robustness of traditional statistical methods, the model enhances stability through the overfitting resistance provided by RF and XGBoost. Additionally, the LSTM's ability to capture long-term dependencies is crucial for handling seasonal and trending demand forecasts. The introduction of ElasticNet further strengthens robustness against overfitting and improves model performance through optimal parameter selection. This study emphasizes the model's accuracy and robustness, ensuring reliable forecasting capability in variable environments. However, the limitations of the models cannot be ignored. Complex multi-model fusion may lead to a complicated model structure, increasing computational cost and difficulty understanding. The model's performance is highly dependent on the quality and quantity of data, and it may be difficult to perform optimally for poor quality or limited data quantity. In addition, tuning model parameters can be very time-consuming, especially when optimizing using cross-validation and grid search methods. Predictors' affective biases and product engagement may also impact the model's judgmental adjustments, thus affecting the accuracy of the predictions. Finally, although the model has demonstrated a good application in the beverage industry, its ability to generalize to other industries or domains requires further validation and testing.

In conclusion, the integrated model proposed in this study offers a cutting-edge solution to the demand forecasting challenges in the beverage industry and broader corporate supply chain management. It employs intelligent tools and methods to enhance companies' responsiveness to market changes, improve overall supply chain flexibility, reduce costs, and minimize inventory backlogs. Future research can build on this foundation by exploring forecasting models tailored to different industry contexts and investigating how these capabilities can be integrated with strategic enterprise decisions to promote efficient and intelligent development.

Competing Interests- There is no interest conflict for all authors.

Authors contribution statement- All authors contributed to the study conception and design. The Implementations, Material preparation and data collection were performed by Ding Hao and Liu Bin. The first draft of the manuscript was written by Ding Hao and thanks to Liu Bin and Yun Qiaoyun for their revision of the manuscript. All authors read and approved the final manuscript.

Funding Declaration- This paper is supported by NSFC with grants number 71971134.

Ethical and informed consent for data used- Not applicable.

Data availability and access- The data that support the findings of this study are available from the corresponding author, Dr. & Professor Liu Bin, upon reasonable request.

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No competing interests reported.

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A Diversified Integrated Model for Seasonal Product Demand Prediction

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Abstract

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1. Introduction

2. Related Literature

3. Methodology

3.1 Framework and process

3.2 Modeling framework

4. Performance analysis of models and applied research

4.1 Comparison with traditional homogenized models

4.2 Applied research on modeling

4.2.1 Data description and pre-processing

4.2.2 Comparison of models and parameter settings

4.3 Sensitivity analysis

4.4 Temporal analysis

4.5 Results and Discussions

5. Conclusions

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References

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