forecasting intraday arrivals at a call centre using neural networks: forecasting anomalous days

Forecasting Intraday Call Arrivals

Modelling Special Days

Devon K. BarrowNikolaos Kourentzes

27th European Conference on Operational Research

12-15 July 2015

University of Strathclyde

1. Research Questions2. Call Arrival Data and

Challenges3. Experimental Design4. Results5. Conclusions and future work

Outline

Forecasting Intraday Call Arrivals Outline 2

• 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



Outline

Forecasting Intraday Call Arrivals Call Centre Data 4

• 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 ChallengesChallenges

5Call Centre DataForecasting Intraday Call Arrivals

Call Arrival Data and ChallengesSome 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

Call Arrival Data and ChallengesComplex seasonal patterns

7

Intraday Intraweek

MeanMedian

Monday

Intrayear


• 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


!

• 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 ChallengesChallenges


Call Arrival Data and ChallengesAnomalies (outliers)

10

Series 1

Series 1I


Call centre dataSeasonal profile

12

4 8 12 16 200

100

200

300

400

Cal

ls

Monday

4 8 12 16 20

Tuesday

4 8 12 16 20

Wednesday

4 8 12 16 20Hour

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 16 200

10

20

30

40

Cal

ls

Monday

4 8 12 16 20

Tuesday

4 8 12 16 20

Wednesday

4 8 12 16 20Hour

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 middleCall Centre DataForecasting Intraday Call Arrivals

Call centre data Outliers vs. median pattern

Call Centre Data 13

4 8 12 16 200

100

200

300

400

Monday

Cal

ls

4 8 12 16 20

Tuesday

4 8 12 16 20

Wednesday

4 8 12 16 20

Thursday

Hour4 8 12 16 20

Friday

4 8 12 16 20

Saturday

4 8 12 16 20

Sunday

Profile

Outliers

4 8 12 16 200

10

20

30

40

Monday

Cal

ls

4 8 12 16 20

Tuesday

4 8 12 16 20

Wednesday

4 8 12 16 20

Thursday

Hour4 8 12 16 20

Friday

4 8 12 16 20

Saturday

4 8 12 16 20

Sunday

Profile

Outliers

Series 1

Series 1I

Regular profile very different from outliers


• 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’


!



Outline

Forecasting Intraday Call Arrivals Experimental Design 15

Experimental DesignFunctional 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


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



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 DesignExperimental 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|




Outline

Forecasting Intraday Call Arrivals Results 20

ResultsNeural 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 1.000ResultsForecasting Intraday Call Arrivals

ResultsNeural 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 1.00022ResultsForecasting Intraday Call Arrivals

ResultsOutlier 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 0.99723ResultsForecasting Intraday Call Arrivals

ResultsOutlier 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 0.996Results 24Forecasting Intraday Call Arrivals



Outline

Forecasting Intraday Call Arrivals Conclusion and future work 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


Devon K. Barrow Coventry Business SchoolCoventry University, Priory Street, Coventry, CV1 5FBDirect line: + 44 024 7765 7413Skype: devon.k.barrowEmail: [email protected]

Questions?

forecasting intraday arrivals at a call centre using neural networks: forecasting anomalous days

Data & Analytics

centre arrivals

arrival data

centre data seasonal

challenges challenges

europe data

data processing

forecasting performance

challenges anomalies