Demand Forecasting for Industrial Gas Distribution in Small and Medium Enterprises: Evaluating Model Suitability under Different Demand Characteristics

2.1 Forecasting methods: Statistical vs. machine learning

The debate between traditional statistical methods and machine learning approaches in time-series forecasting has been extensively studied. Cerqueira et al. [8] conducted a comprehensive study which showed that statistical methods consistently outperformed machine learning on small datasets. Their research using 90 time series with a minimum of 1000 observations revealed that while statistical methods excel on small datasets, machine learning methods show better performance as data size increases. This finding emphasizes the importance of considering dataset size when selecting forecasting approaches.

In the SME manufacturing context, research by Aidoo-Anderson et al. [9] examining demand forecasting practices in pharmaceutical SMEs showed that most companies still rely on judgmental forecasting and simple methods due to limited historical data, human resources, and low technology adoption. The study confirmed that SME demand is often volatile, sporadic, and exhibits intermittent demand characteristics, making stable historical patterns difficult to identify.

A benchmark study across industries by Syberg et al. [10] comparing statistical and machine learning methods in make-to-order production environments characterized by highly fluctuating demand and limited historical data found that no single method consistently outperformed others under all conditions. Simple statistical methods such as ARIMA, Seasonal Naïve, and exponential smoothing often provided more stable performance compared to machine learning models.

2.2 Extreme Gradient Boosting in forecasting applications

XGBoost has emerged as a powerful tool for forecasting tasks due to its ensemble tree-based approach. Martinović et al. [11], in their study on predicting innovation outcomes at the company level, compared various machine learning algorithms, including Random Forest, XGBoost, CatBoost, SVM, and ANN. Results showed that boosted decision tree models, particularly XGBoost, excelled in accuracy, F1-score, and ROC-AUC metrics. The study emphasized the importance of using corrected cross-validation techniques and Bayesian-based hyperparameter optimization.

Acar and Gardner [6] conducted a case study of forecasting method selection for a global manufacturer, comparing exponential smoothing methods against optimization and simulation techniques to minimize total supply chain cost. Their results showed that the choice of forecasting method has a direct, measurable impact on downstream supply chain cost and service level, reinforcing that method selection should be driven by empirical performance on the specific demand pattern rather than by model sophistication alone.

2.3 Prophet for business forecasting

Facebook Prophet has gained widespread adoption in business forecasting due to its ability to model long-term trends, seasonality, and calendar/holiday effects within a relatively easy-to-implement additive model framework. Prophet's main advantage lies in its flexibility in handling trend changes (changepoints), multi-seasonality, and robustness to non-stationary data commonly found in industrial and SME sales data.

Žunić et al. [12] developed a retail sales forecasting framework based on Prophet, equipped with rolling back-testing procedures to evaluate forecast reliability at the product (SKU) level. The study showed that Prophet can provide stable performance across various forecasting horizons and offers good interpretability through trend and seasonal component decomposition.

Petropoulos et al. [13] evaluated forecasting method performance across thousands of real time series and found that no single method, however sophisticated, consistently outperforms others across all data patterns. Their findings support a "horses for courses" approach in which the choice between methods such as Prophet, SARIMA, or simple exponential smoothing should be guided by the specific characteristics of the data at hand, such as volatility and trend or seasonal strength, rather than by a default preference for model complexity.

Furthermore, Prophet has been combined with other algorithms in hybrid approaches. Guo et al. [14] showed that combining Prophet with Support Vector Regression (SVR) can improve forecasting accuracy by leveraging Prophet's strength in capturing trends and seasonality, along with machine learning's capability in modelling non-linear relationships not captured by Prophet's additive structure.

2.4 Seasonal autoregressive integrated moving average in industrial applications

SARIMA remains one of the most widely used statistical methods for time-series forecasting, particularly for data with strong seasonal patterns. The model's ability to capture both short-term dependencies and long-term seasonal cycles makes it suitable for various industrial applications.

Falatouri et al. [4] compared SARIMA and LSTM in retail supply chain management, finding that SARIMA provided competitive performance with easier interpretability and lower computational requirements compared to deep learning approaches. The study emphasized SARIMA's effectiveness in capturing regular seasonal patterns without requiring extensive computational resources.

However, SARIMA's performance depends heavily on data characteristics. The model requires sufficient historical data to estimate parameters accurately and assumes linear relationships between variables. In contexts with high noise levels or irregular patterns, simpler methods may outperform SARIMA despite its theoretical sophistication.

2.5 Industrial gas forecasting and B2B demand prediction

Giannopoulos et al. [15] reviewed machine learning approaches for intermittent and lumpy demand forecasting, covering hyperparameter tuning, feature engineering, and training strategies across 124 peer-reviewed studies. Their review highlighted that ML methods for intermittent demand require careful handling of overfitting and the risk of treating noise as signal on short, volatile series. Zhou et al. [16] presented a predictor with denoising features and information combination to guide contrastive representation learning for gas forecasting. Sanchez-Ubeda and Berzosa [17] captured the trend and combined it with the Linear Hinges Model and a transitory component to predict gas consumption.

Qin et al. [18] addressed data scarcity through a Federated Contrastive Pretraining-Local Clustered Fine-tuning paradigm. Pu et al. [19] used a spatial-temporal Bayesian model to predict gas demand through time-varying spatial graphs, considering gas-pipeline connectivity and co-movement. Syntetos et al. [20] critically reviewed the gap between forecasting theory and supply chain practice, noting that academic research has often neglected practical issues such as data quality and the operational translation of theoretical forecasting gains.

2.6 Research gap

While extensive research exists on comparing forecasting methods, few studies specifically address the SME industrial gas distribution context characterized by: (1) limited historical data availability, (2) high demand volatility without clear seasonal patterns, (3) B2B customer relationships creating dependency on client business activities, and (4) resource constraints limiting complex model implementation.

This research contributes by evaluating how different forecasting approaches perform across products with varying demand characteristics (measured by coefficient of variation (CV)) in a real SME setting, providing practical insights for similar businesses facing comparable challenges.

4.1 Data characteristics

Based on descriptive statistical analysis, five main products showed different variability levels reflected in their CV values. Table 1 presents descriptive statistics for the five products based on weekly aggregation.

Oxygen shows the highest transaction volume, with 44,553 transactions (approximately 65% of the combined total for the top five products, or 58.5% of the full 76,200-transaction dataset), with an average of 284.64 transactions per week. Besides high volume, this product shows relatively good demand stability, reflected in the lowest CV value of 24.29% among the five analyzed products.

Conversely, Argon UHP shows the highest volatility with CV reaching 73.80%, although transaction volume is relatively small at 1,987 transactions or approximately 2.9% of total transactions. High volatility is closely related to Argon UHP usage characteristics, as high-purity industrial gas is generally used in laboratory testing activities and precision analytical instrument operation.

Time series decomposition results using the STL method showed that all gases have Seasonal Strength significantly more dominant than Trend Strength. Trend Strength values for all gases are in the low to very low category (below 0.2), while Seasonal Strength values range between 0.40 and 0.48. The seasonal strength value is likely influenced by the Eid al-Fitr holiday cycle, which, as a moving holiday, causes a total operational shutdown, recorded as a drastic sales volume reduction to zero in the observed data.

ACF and PACF analysis results showed that the weekly industrial gas demand time series exhibits relatively weak autocorrelation characteristics. Most ACF and PACF values at various lags are within statistical confidence bounds, with only a few small spikes appearing sporadically. This condition indicates that the relationship between current demand values and previous period values does not show strong and systematic temporal dependency.

In summary, for low-volatility products like Oxygen and Argon, demand was stable and symmetrical, as indicated by near-identical mean and median values. SARIMA was the optimal model for these two because its linear and parametric structure relied on strong autocorrelation and Gaussian residual distributions.

As volatility increases in Nitrogen and Acetylene, the widening gap between mean and median values indicated right-skewed demand. For these products, Prophet served as the best solution due to its additive piecewise linear regression, which automatically detected trend change points and multi-period seasonality. It also remains resilient to demand spikes.

For highly volatile and lumpy demand profiles like Argon UHP, neither the statistical time-series models nor XGBoost were effective. In this scenario, the simple Mean baseline was actually the best-performing approach (MAPE 57.66%, Table 2), outperforming XGBoost, SARIMA, and Prophet. This indicates that when demand approaches white noise with no learnable structure, added model complexity provides no benefit and can instead amplify overfitting to spurious patterns.

Table 2. Summary of the best model performance for each product

4.2 Model performance

Table 2 presents a summary of the best model performance for each product. For Oxygen, the Prophet model showed the best performance with a MAPE of 16.82% when using 2022-2023 training data to predict 2024. However, quarterly evaluation revealed significant performance degradation in Q2 (MAPE increased to 30.82%) due to the Eid al-Fitr holiday shift, which the model without external holiday variables could not anticipate. Prophet's relatively good performance is supported by low data fluctuation levels (CV 24.29%), indicating sales tend to be around their average value. Rolling forecast evaluation with weekly retraining showed Prophet achieved a MAPE of 15.05%, demonstrating strong performance for short-term operational predictions when using the most recent data patterns.

To address all four experimental scenarios described in Section 3.5, Table 3 consolidates the training period, testing period, and best-performing model (lowest MAPE) for each product across the three fixed-window train-test splits. The fourth scenario (quarterly granularity) is summarized narratively above and in Section 4.3, since its results are reported per quarter rather than as a single best model.

Table 3. Summary of best-performing model across the three fixed train-test scenarios (Section 3.5, Scenarios 1–3)

Across all three scenarios, the best-performing model varies by product and by training window: Oxygen is consistently best served by Prophet or, when only one year of recent data is available, by the Naïve baseline; Argon and Nitrogen alternate between SARIMA, Naïve, XGBoost, and Prophet depending on the period; and Acetylene and Argon UHP, the two highest-CV products, are best served by simple baselines (Mean, Naïve) or, in one scenario, XGBoost, but never consistently by a single complex model. This instability across scenarios reinforces that no single algorithm generalizes across training windows for this dataset, and that reported “best models” should be read as scenario-specific rather than as a fixed model recommendation per product.

For Argon and Nitrogen: with CV values around 30% and 40% respectively, machine learning models did not show significant forecasting performance improvement compared to baseline methods. Simple benchmark approaches such as Naïve forecasting were able to produce accuracy levels comparable to more complex models. This indicates that although demand variability levels are relatively high, fluctuations are not accompanied by consistent patterns learnable by complex models. For Argon, the best-performing model (Mean method) achieved a MAPE of 24.85% and MAE of 10.79 cylinders per week. Nitrogen followed a similar pattern, with SARIMA marginally outperforming other approaches at MAPE 28.48%, though the improvement over simpler methods was modest. The relatively similar performance across models for both products can be attributed to the nature of their customer base: these gases serve a wider variety of industries and use cases than Oxygen, resulting in demand that is more fragmented and harder to predict from historical patterns alone. Quarterly analysis further revealed that Q2 performance degraded for all models across both products, consistent with the Eid al-Fitr disruption observed in Oxygen.

For Acetylene and Argon UHP: with the highest CV values of 52% and 70%, respectively, both products present difficulties for both machine learning models and baseline methods in producing accurate forecasts. This is reflected in high MAPE values, ranging from above 50% to even exceeding 100% in most forecasting models. High fluctuation levels in Acetylene products are caused by customer company characteristics, where most customers do not use Acetylene as the main material in production processes, making demand uncertain and without consistent patterns. For Argon UHP, extreme volatility is driven by its role as a specialty gas primarily used in laboratory and precision analysis contexts, where purchasing is project-driven rather than routine, meaning demand spikes are largely unpredictable without external context. In both cases, even the best-performing model (Mean method) produced MAPE values of 96.85% for Acetylene and 57.66% for Argon UHP, indicating that these products may be better managed through safety stock policies or order-point systems rather than traditional time-series forecasting. These results align with findings in the broader literature that products with near-white-noise demand patterns are better served by inventory buffering strategies than by predictive modelling.

4.3 Impact of training window

Experiments with various training data durations, namely two years and one year, showed that using two years of training data did not produce significant forecasting performance improvement compared to using one year of training data. This finding indicates that forecasting based on more recent historical data provides a more relevant representation of actual demand conditions.

For example, in Oxygen product forecasting, Prophet training using only 2023 data produced an MAE of 44.90 and a MAPE of 17.06%, almost identical to training results using two years of data (2022–2023). Very small performance differences show that data recency has a more dominant role than historical horizon length.

Taken together, the cross-product results reveal a clear relationship between demand predictability and model suitability. As illustrated in Table 2, MAPE values increase substantially as the CV of the product rises, from 16.82% for Oxygen (CV 24.29%) to 96.85% for Acetylene (CV 49.10%). This gradient underscores that no single model consistently dominates; rather, forecasting strategy should be tailored to each product’s demand structure. From a practical standpoint, this finding has direct operational implications. SME industrial gas distributors with a mixed product portfolio comparable to the one studied here would benefit from a tiered forecasting approach: deploying statistical models such as Prophet for stable, high-volume products, while relying on simpler safety-stock policies for high-volatility items. Furthermore, the consistent Q2 performance degradation across all models and products highlights that model-agnostic external information, such as holiday calendars or B2B customer activity schedules, could substantially improve forecast reliability during disruption-prone periods.

Qualitative inspection of the forecast plots showed generally wide nominal 95% forecast intervals, particularly for more volatile products and longer forecast horizons. This pattern indicates substantial uncertainty and limited forecast precision, but interval width alone cannot establish whether nominal 95% coverage was achieved. Formal evaluation of interval coverage and sharpness is therefore outside the scope of this study.

4.4 Key findings

Several important findings from the study can be obtained. Model complexity does not always guarantee better accuracy. On products with high fluctuation levels and weak time-series structure or approaching white noise, complex models like SARIMA and XGBoost did not show significant superiority over baseline methods. In such conditions, simple statistical methods like Mean and Naïve provided more stable and competitive forecasting results.

When time-series data exhibits high fluctuation and weak temporal structure, simple methods exceed complex models because they avoid overfitting to random noise and directly align with underlying stochastic processes. High-capacity architectures like SARIMA and XGBoost require stable signals to estimate autoregressive parameters or feature split thresholds. By assuming minimal structural form, these baseline methods eliminate parameter estimation instability and maintain robust predictive performance.

CV shows its importance as a predictability indicator. The higher a product's CV value, the more difficult it is for forecasting models to produce accurate predictions. This is caused by the company's data characteristics: high CV values are not driven by strong, recurring seasonal patterns, but rather by the data's fluctuating and unstructured nature.

Data recency is important. Using more recent training data provides a better representation of current market conditions compared to longer historical data, which may contain patterns that are no longer relevant.

There is a need for external variables. Significant performance degradation in Q2 across all models emphasizes the need to integrate external variables such as national holiday calendars or holiday regressors to improve prediction accuracy, especially during religious holiday periods.