Lessons Learned Applying Deep Learning Approaches to Forecasting Complex Seasonal Behavior

Accurate prediction of call center volumes is crucial for efficient staffing. Call center arrival processes are complex, influenced by day of week, time of day, holidays, and business conditions. Classical time series methods like Winters' Seasonal Smoothing and ARIMA have been used, but this paper explores the potential of deep learning methods, specifically RNNs, to improve forecasting accuracy. While doubly stochastic linear mixed models offer increased flexibility, they also introduce significant computational complexity. The study aims to improve the doubly stochastic approach and explore the practical aspects of applying RNNs to call center forecasting, comparing their performance to classical techniques. The research generalizes across sectors beyond financial services.

Existing literature demonstrates the effectiveness of various methods for modeling call center arrival processes. Winters' Seasonal Smoothing and ARIMA models are established techniques for handling seasonal and autocorrelated data. More recent advancements include doubly stochastic linear mixed models, which effectively account for additional complexities like intra- and inter-day correlation. RNNs have also been proposed as a deep learning approach for forecasting call volumes in various applications, offering flexibility in modeling complex arrival behaviors. However, this flexibility comes at the cost of increased computational and programming complexity and potential prediction variance. The review highlights the need to address the practical challenges in implementing and optimizing these advanced models.

The study uses a two-pronged approach. First, the authors modify the computational aspects of the doubly stochastic linear mixed model to improve convergence and flexibility, especially when dealing with numerous call streams (skills). They modify the original two-step estimation process to a joint optimization using SAS PROC MIXED, improving convergence by changing the convergence criterion and employing Fisher scoring. The square root transformation is applied to handle skewed data. Second, they investigate the use of RNNs (Elman, LSTM, GRU) for call center volume forecasting. A full factorial designed experiment is conducted to assess the performance of various RNN configurations, considering factors like model type, number of layers, number of nodes, L2 regularization, and the inclusion of predictions from other models (mixed.cheat). The experiment uses a five-week training period and five one-day-ahead predictions on a holdout dataset for three high-volume skills. The weighted absolute percentage error (WAPE) is used as the performance metric, and the model configuration is selected to minimize the upper 95% prediction interval on the testing error rate. The chosen RNN configurations are then evaluated over 60 one-day ahead predictions across 36 skills to compare performance to the doubly stochastic mixed model, ARIMA, and Winters' smoothing. The experiment uses a combination of one-hot encoding for categorical variables and lagged call volumes as input to the neural networks.

The modified doubly stochastic linear mixed model demonstrated improved convergence compared to the original approach. The designed experiment revealed that the GRU RNN generally outperformed other RNN architectures. The inclusion of predictions from other models (mixed.cheat) improved the GRU's performance. The analysis of variance models highlighted significant effects of model type, number of layers, mixed.cheat option, and number of nodes on the WAPE. The optimal RNN configuration was identified as a GRU with two layers, 50 nodes per layer, and the mixed.cheat option enabled. However, the L2 regularization parameter had little significant effect. In the comprehensive performance study across 36 skills and 60 days, the doubly stochastic model and GRU RNN showed the best overall performance. The GRU RNN's relative advantage was more pronounced for low-volume skills, whereas the doubly stochastic model performed better for high-volume skills. The GRU's performance could further be improved by using the doubly stochastic model's predictions as a covariate. Statistical tests confirmed the superiority of the GRU over other RNNs and the positive impact of the mixed.cheat option on GRU's performance. The authors observed increasing forecast error across all methods as call volumes decrease.

The findings highlight the value of both classical time series methods and deep learning approaches in call center forecasting. The doubly stochastic mixed model's strength in high-volume scenarios is likely due to its efficiency in capturing complex correlations within the data. Meanwhile, the GRU RNN's performance in low-volume scenarios demonstrates its flexibility to adapt to situations with more noise and less data. The effectiveness of using predictions from other models as covariates highlights the potential for combining different forecasting methods for better results. The study's findings have implications for choosing appropriate forecasting models based on data characteristics and computational constraints. For high-volume scenarios with strong correlations, the doubly stochastic model is a strong candidate. When dealing with low-volume data, the GRU RNN might be more effective. Using combined forecasts from multiple models can improve overall accuracy.

This study demonstrates that both doubly stochastic linear mixed models and GRU recurrent neural networks are effective approaches for forecasting call center volumes. The choice of method depends on data volume and computational resources. The study's findings offer valuable guidance for selecting and optimizing forecasting models in practice, emphasizing the importance of considering various factors like data characteristics and computational efficiency. Future research could explore more sophisticated architectures like stacked RNNs and more advanced optimization techniques.

The study's findings are based on data from a specific financial services company and may not generalize perfectly to other contexts. The five-week training period may not capture long-term trends or cyclical effects. Additional experiments with larger and more diverse datasets, longer training periods, and other input features are needed to further validate the findings. Although the authors used various strategies to prevent overfitting, the potential impact of overfitting, especially with the RNN models, should be carefully considered.