Forecasting Intraday Arrivals at a Call Centre using Neural Networks: Forecasting Anomalous Days
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A key challenge for call centres remains the forecasting of high frequency call arrivals collected in hourly or shorter time buckets. These forecasts are required for decisions concerning the scheduling, hiring and training of staff. In addition to the high frequency nature of call arrival series and the complex seasonal patterns, including the multiple seasonal cycles, call arrival data often contain a large number of anomalies, driven by holidays, special events, promotional activities and system failures. This study presents an approach based on artificial neural networks (ANNs) for forecasting intraday call arrivals. In so doing, we empirically evaluate alternative methodologies for modelling and forecasting outliers in high frequency data, which span over several periods, addressing a gap in research of practical significance considering the difficulty and the cost associated with manual exploration and treatment of such data. We assess the performance of different ANN modelling methodologies in terms of the accuracy with which normal and outlying periods are modelled. Multi-period outliers are modelled using alternative encodings ranging from binary dummy variables to functional profiles, as well as segmenting the series to separate it into outlying and normal days. Results show that ANNs outperform conventional benchmarks and are capable of modelling high frequency outliers using relatively simple outlier modelling approaches.
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Forecasting Intraday Arrivals at a Call Centre using Neural Networks: Forecasting Anomalous Days
- 1. Forecasting Intraday Call Arrivals Modelling Special Days Devon K. Barrow Nikolaos Kourentzes 27th European Conference on Operational Research 12-15 July 2015 University of Strathclyde
- 2. 1. Research Questions 2. Call Arrival Data and 3. Experimental Design 4. Results 5. Conclusions and future work Outline Forecasting Intraday Call Arrivals Outline 2
- 3. • How do different forecasting methods perform when forecasting (high frequency) call centre arrivals? • What is the impact of coding or not coding of (functional) outlying periods on forecasting performance? Research Questions Research Questions 3Forecasting Intraday Call Arrivals
- 4. 1. Research Questions 2. Call Arrival Data and 3. Experimental Design 4. Results 5. Conclusions and future work Outline Forecasting Intraday Call Arrivals Call Centre Data 4
- 5. • High dimensional and sampled at a high frequency (Kourentzes and Crone, 2010). • Complex seasonal patterns – Intraday – Intraweek – interyear dependencies(De Livera et al., 2011) Call Arrival Data and Challenges Challenges 5Call Centre DataForecasting Intraday Call Arrivals
- 6. Call Arrival Data and Challenges Some call centre data 6 • Two series from a large UK service provider call centre • A leading entertainment company in Europe • Data is sampled at half-hourly intervals • Consists of 103 weeks and 3 days from 29 June 2012 to 23 June 2014 inclusive including bank holidays and weekends. Call Centre DataForecasting Intraday Call Arrivals
- 7. Call Arrival Data and Challenges Complex seasonal patterns 7 Intraday Intraweek Mean Median Monday Intrayear Call Centre DataForecasting Intraday Call Arrivals
- 8. • Development of new methods – Double seasonal exponential smoothing (Taylor, 2008) – Multiplicative double seasonal ARMA model (Taylor, 2003) – Exponential weighting (Taylor, 2008, 2010) – Regression (Tych et al., 2002; Taylor, 2010) – Singular vector decomposition (Shen and Huang, 2005, 2008; Shen, 2009) – Gaussian linear mixed-effects models (Aldor-Noiman et al., 2009; Ibrahim and L’Ecuyer, 2013) • Intraweek seasonal moving average performs well at medium to long horizons (Tandberg et al. 1995; Taylor, 2008; Taylor, 2010; Ibrahim and L’Ecuyer, 2013) Call Arrival Data and Challenges Handling high frequency complex seasonality 8Call Centre DataForecasting Intraday Call Arrivals !
- 9. • Data is context sensitive – Effects of holidays, special events and promotional activities • Prone to quite sizeable unexplained variations (outliers) – E.g. due to system failures and data processing Call Arrival Data and Challenges Challenges 9Call Centre DataForecasting Intraday Call Arrivals
- 10. Call Arrival Data and Challenges Anomalies (outliers) 10 Series 1 Series 1I Call Centre DataForecasting Intraday Call Arrivals
- 11. Call centre data Seasonal profile 12 4 8 12 16 20 0 100 200 300 400 Calls Monday 4 8 12 16 20 Tuesday 4 8 12 16 20 Wednesday 4 8 12 16 20 Hour Thursday 4 8 12 16 20 Friday 4 8 12 16 20 Saturday 4 8 12 16 20 Sunday Median 25-75% 10-90% 05-95% 4 8 12 16 20 0 10 20 30 40 Calls Monday 4 8 12 16 20 Tuesday 4 8 12 16 20 Wednesday 4 8 12 16 20 Hour Thursday 4 8 12 16 20 Friday 4 8 12 16 20 Saturday 4 8 12 16 20 Sunday Median 25-75% 10-90% 05-95% Series 1 Series 1ILarge variation from the middle Call Centre DataForecasting Intraday Call Arrivals
- 12. Call centre data Outliers vs. median pattern Call Centre Data 13 4 8 12 16 20 0 100 200 300 400 Monday Calls 4 8 12 16 20 Tuesday 4 8 12 16 20 Wednesday 4 8 12 16 20 Thursday Hour 4 8 12 16 20 Friday 4 8 12 16 20 Saturday 4 8 12 16 20 Sunday Profile Outliers 4 8 12 16 20 0 10 20 30 40 Monday Calls 4 8 12 16 20 Tuesday 4 8 12 16 20 Wednesday 4 8 12 16 20 Thursday Hour 4 8 12 16 20 Friday 4 8 12 16 20 Saturday 4 8 12 16 20 Sunday Profile Outliers Series 1 Series 1IRegular profile very different from outliers Forecasting Intraday Call Arrivals
- 13. • Approaches to handling ‘special days’: – Information is either available and/or data is pre- cleansed – The forecaster has an external methodology for tackling ‘special days’ (Jongbloed and Koole, 2001; Avramidis et al., 2004; Taylor, 2008a; Pacheco et al., 2009; Taylor, 2010b) – Removing such days altogether (Taylor et al. 2006) – Singular vector decomposition for automatic outlier detection (Shen and Huang, 2005) • Kourentzes (2011) demonstrates that there are substantial accuracy benefits to be had from modelling irregular load patterns. Call Arrival Data and Challenges Handling ‘special days’ 14Call Centre DataForecasting Intraday Call Arrivals !
- 14. 1. Research Questions 2. Call Arrival Data and 3. Experimental Design 4. Results 5. Conclusions and future work Outline Forecasting Intraday Call Arrivals Experimental Design 15
- 15. Experimental Design Functional outlier modelling 16 • We evaluate seven alternative methodologies for modelling functional outliers • These are based on extensions of conventional outlier modelling and novel approaches • We assume that the data generating process of normal observations is captured adequately and the outliers are already labelled Control Single Binary Dummy Multiple Binary Dummy Single Integer Profile Dummy Trigonometric Dummy Model Separately Experimental DesignForecasting Intraday Call Arrivals
- 16. Experimental Design Functional outlier modelling 17 • Control/benchmark – A set of autoregressive lagged inputs (past values) are identified using stepwise regression – Outliers are not modelled • Single Binary Dummy Variable – Indicator variable s.t. one = outlier; zero otherwise • Multiple Binary Dummy Variable – S is the seasonal length (S=48) – 48 (S) dummy variables to code each observation – 47 (S – 1) dummy variables to code each observation – Stepwise selection, s = {1,…,S=48} s.t. s is significantly different from normal observations Experimental DesignForecasting Intraday Call Arrivals
- 17. Experimental Design Functional outlier modelling 18 • Single Integer Dummy Variable – Monotonically increasing variable from 1 to 48 if outlier; zero otherwise • Profile Dummy Variable – This variable is equal to the profile if there is an outlier; zero otherwise • Trigonometric Dummy Variables – Sine and cosine if there is an outlier; zero otherwise • Model Separately – Create a new series containing only outliers – Replace outliers in original series with normal observations Experimental DesignForecasting Intraday Call Arrivals
- 18. Experimental Design Experimental setup Experimental design 19 • Neural network setup – Inputs based on backwards regression + dummies + seasonal dummies. – Mode ensemble of 50 networks trained by scaled conjugate gradient descent – Hidden nodes identified experimentally for each set of inputs • Forecast creation – Forecast horizon is set to 1 day ahead (1-48 half hourly steps ahead) – Test set of 100 days (4800 data points x 48 forecasted horizons) • Forecast evaluation – Mean Absolute Error (MAE) – Relative Mean Absolute Error (RMAE) i.e. MAE_{Method} / MAE_{Control} AE = |Yt - Ft| Forecasting Intraday Call Arrivals
- 19. 1. Research Questions 2. Call Arrival Data and 3. Experimental Design 4. Results 5. Conclusions and future work Outline Forecasting Intraday Call Arrivals Results 20
- 20. Results Neural networks versus benchmarks 21 Time Series 1 Overall Outlier Normal Naïve 1 3.930 2.711 4.269 Naïve Day 1.417 1.211 1.475 Naïve Week 1.333 1.057 1.410 MA Day 1.238 1.278 1.226 MA Week 1.233 0.845 1.341 ETS Day 1.887 1.438 2.013 ETS Week 1.529 1.165 1.630 ETS Double 1.086 0.857 1.149 MAPA Day 1.522 1.362 1.566 MAPA Week 1.484 1.274 1.542 NN Control 1.000 1.000 1.000 ResultsForecasting Intraday Call Arrivals
- 21. Results Neural networks versus benchmarks Time Series II Overall Outlier Normal Naïve 1 2.236 1.770 2.500 Naïve Day 1.415 1.119 1.582 Naïve Week 1.433 1.157 1.590 MA Day 1.415 1.119 1.582 MA Week 1.129 0.973 1.217 ETS Day 1.600 1.368 1.731 ETS Week 1.479 1.288 1.587 ETS Double 1.151 0.990 1.242 MAPA Day 1.347 1.242 1.406 MAPA Week 1.280 1.201 1.325 NN Control 1.000 1.000 1.000 22ResultsForecasting Intraday Call Arrivals
- 22. Results Outlier modelling versus control Time Series 1 Overall Outlier Normal NN Control 1.000 1.000 1.000 NN Bin1 0.996 0.933 1.013 NN BinS 0.884 0.822 0.901 NN BinS-1 0.873 0.831 0.885 NN Bin Step 0.897 0.858 0.908 NN Bin Back 0.895 0.850 0.907 NN Int 0.935 0.913 0.941 NN SinCos 0.980 0.865 1.012 NN Profile 0.986 0.953 0.995 NN Replace 1.002 1.019 0.997 23ResultsForecasting Intraday Call Arrivals
- 23. Results Outlier modelling versus control Time Series II Overall Outlier Normal NN Control 1.000 1.000 1.000 NN Bin1 0.956 0.930 0.970 NN BinS 0.922 0.866 0.954 NN BinS-1 0.923 0.870 0.954 NN Bin Step 0.929 0.876 0.958 NN Bin Back 0.931 0.875 0.963 NN Int 0.957 0.940 0.966 NN SinCos 0.951 0.912 0.972 NN Profile 0.963 0.936 0.979 NN Replace 1.030 1.090 0.996 Results 24Forecasting Intraday Call Arrivals
- 24. 1. Research Questions 2. Call Arrival Data and 3. Experimental Design 4. Results 5. Conclusions and future work Outline Forecasting Intraday Call Arrivals Conclusion and future work 25
- 25. Conclusion and future work Conclusion and future work 26 • Conclusion – Neural networks are good for call centre data for two reasons: • They can do complex structures • They can do complex outliers with relatively simple modelling • Future work – Automatic functional outlier detection and modelling for call centre arrival data Forecasting Intraday Call Arrivals
- 26. Devon K. Barrow Coventry Business School Coventry University, Priory Street, Coventry, CV1 5FB Direct line: + 44 024 7765 7413 Skype: devon.k.barrow Email: devon.barrow@coventry.ac.uk