Models to predict client’s phone

calls to Iberdrola Call Center

VI Modelling Week UCM

PARTICIPANTS (UCM): Cazallas Piqueras, Rosa Gil Franco, Dolores M Gouveia de Miranda, Vinicius Herrera de la Cruz, Jorge Inoñan Valdera, Danny Javier Advisor: Ivorra, Benjamin

Outlook

1. Problem description

2. Data analysis

3. Modelling

4. Validation and prediction

5. Conclusions and perspectives

1. Problem description

Iberdrola is a company that provides electricity and/or gas to the customers.

Customers can contact Iberdrola, for instance, by letters, internet and Phone calls (Call Center).

In a Call Center: to avoid over-staff and under-staff

Iberdrola needs a good prediction about the number of operators.

Objective: Find a model to predict the volume of customer calls.

Problem description

Forecasting methodology: for operational reasons,

we need to predict the volume of calls for next month, six weeks in advance.

Problem description

2. Data analysis

Data analysis

Weekly data

Portfolio 1: regulated market Portfolio 2: free market Portfolio 3: gas market (since 01/2007) Bill type 1: estimated consumption Bill type 2: real consumption Bill type 3: fixed quota without consumption Bill type 4: other (corrections, material, etc.)

Daily data

Calls: number of calls target variable

Transformed to daily data

Data analysis

0

2000000

4000000

6000000

8000000

10000000

12000000

14000000

16000000

18000000

20000000

2_2

00

4

23

_20

04

44

_20

04

12

_20

05

33

_20

05

2_2

00

6

23

_20

06

44

_20

06

13

_20

07

34

_20

07

3_2

00

8

24

_20

08

45

_20

08

14

_20

09

35

_20

09

3_2

01

0

24

_20

10

45

_20

10

14

_20

11

35

_20

11

4_2

01

2

25

_20

12

46

_20

12

Portfolio1

Portfolio2

Portfolio3

suma

2009 2012

EVOLUTION

Data Analysis

0

100000

200000

300000

400000

500000

600000

700000

800000

2_2

00

4

21

_20

04

40

_20

04

6_2

00

5

25

_20

05

44

_20

05

11

_20

06

30

_20

06

49

_20

06

16

_20

07

35

_20

07

2_2

00

8

21

_20

08

40

_20

08

7_2

00

9

26

_20

09

45

_20

09

11

_20

10

30

_20

10

49

_20

10

16

_20

11

35

_20

11

2_2

01

2

21

_20

12

40

_20

12

BillType1

BillType2

BillType3

BillType4

suma

2009: Change due to an European regulation (monthly bills instead of twice-monthly bills).

Data Analysis

1 2 3 4 5 6 7 8 0

50.000

100.000

150.000

200.000

250.000

300.000

350.000

400.000

1 6 11 16 21 26 31 36 41 46 51

Calls seasonality pattern Calls distribution during weeks and holidays

0 20000 40000 60000 80000

100000 120000 140000 160000 180000 200000

1-1

-20

08

1-2

-20

08

1-3

-20

08

1-4

-20

08

1-5

-20

08

1-6

-20

08

1-7

-20

08

1-8

-20

08

1-9

-20

08

1-1

0-2

00

8

1-1

1-2

00

8

1-1

2-2

00

8

1-1

-20

09

1-2

-20

09

1-3

-20

09

1-4

-20

09

1-5

-20

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1-6

-20

09

1-7

-20

09

1-8

-20

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1-9

-20

09

1-1

0-2

00

9

1-1

1-2

00

9

1-1

2-2

00

9

M T W Th F S Su H

Holidays

Special Events

3. Modelling

SARIMA Model

SARIMA MODEL (1,1,1)(0,1,1)7

White noise

calls

0

10000

20000

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50000

60000

70000

80000

90000

100000

110000

120000

fecha

01/02/2012 16/02/2012 01/03/2012

mes=2

PLOT calls Predicción para logcalls

Límite de confianza superior 95% Límite de confianza inferior 95%

SARIMA Model

Example of a forecast:

Forecast

Real data

C.I. 95%

SARIMA Model

Example of forecast error:

SARIMA Model

33,0%

Low precision for long run predictions

24,9% ARIMA models are generally suited for short

run forecasts, but fail in long term predictions!!!

A Structural model

The purpose is to estimate the relationship among some relevant inputs and the output:

Using a dynamical model for inputs. Adding some seasonal events. Estimating an additional model for the error term.

In order to simplify the inputs, we have created two

relevant variables:

NetBill2: the difference between Billtype2 and Billtype1 Neterror: the sum of Billtype3 and Billtype4

Could be due to measure errors in our daily generation of weekly inputs.

Structural Model We have found strong contemporary relation among

target and inputs

0

20000

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60000

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-20000 20000 40000 60000 80000100000

NETABILL2

CA

LL

S

CALLS vs. NETABILL2 (iters = 4)

0

20000

40000

60000

80000

100000

-20000 20000 40000 60000 80000100000

NETABILL2_1

CA

LL

S

CALLS vs. NETABILL2_1

0

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40000

60000

80000

100000

0 10000 30000 50000 70000

NETABILLERROR

CA

LL

S

CALLS vs. NETABILLERROR (iters = 4)

0

20000

40000

60000

80000

100000

0 10000 30000 50000 70000

NETABILLERROR_1

CA

LL

S

CALLS vs. NETABILLERROR_1 (iters = 4)

Structural Model

Variable Coefficient (lag) Explanation

Target variable

0.20 (0) An increase of 1% in billtype 3 or 4 increases 0.20% the calls

-0.285(0) 0.141 (1)

An increase of 1000 billtype 2 over billtype1, decreases 1.4% the calls

Long term seasonality

Is a parsimonious way to take long run cyclical movements

Daily pattern Dummy variables to catch deterministic daily fluctuations

Error term Capturates autocorrelation pattern

Structural Model

0

20

40

60

80

100

120

140

160

-1.0 -0.5 0.0 0.5

Series: Residuals

Sample 9/05/2009 5/13/2011

Observations 616

Mean -0.007341

Median -0.000487

Maximum 0.559416

Minimum -1.066512

Std. Dev. 0.154450

Skewness -1.341027

Kurtosis 12.80172

Jarque-Bera 2650.525

Probability 0.000000

We obtain a white noise residual correlogram…

…however…

…residuals are not normal. Squared residual correlogram are

not white noise

In a next step, we should study the posibility of any GARCH-ARCH structure for error term to model the error volatility.

Some Naïves Models

Consider the number of calls of previous Year (Y-1)

Adjust the Y-1 model with a coefficient proportional to the difference with the real data (A-1)

Apply the same variation (%) of the number of calls from Y-1 to Y-0 than from Y-1 to Y-2 (Diff) 35000

40000

45000

50000

55000

60000

65000

70000

75000

80000

10/17/2011 10/18/2011 10/19/2011 10/20/2011 10/21/2011

Real

A-1

Y-1

Y-2

Diff

4. Validation and prediction

Validation and prediction

Structural SARIMA Diff A-1 Y-1

9,31 14,97 12,40 10,32 11,68

Mean relative error

30000

35000

40000

45000

50000

55000

60000

65000

70000

75000

80000

26/12/2011 27/12/2011 28/12/2011 29/12/2011 30/12/2011

Structural

SARIMA

Differential

PY-1

Y-1

Real

A-1

Structural

SARIMA

Y-1

Diff

Weightened Models

Following Clements and Hendry we have considered a model based on the weigths of the solutions generated by all the models (Structural, SARIMA, Differential, A-1).

We define Jerr(α1, α2 ,α3 ,α4 ) the relative error function which is computed considering the weights (α1, α2 ,α3 ,α4 ) ϵ ϴ=[0,1]4.

We minimize Jerr in ϴ by considering a Newton method. Then, we obtain:

Mean Error : 8,45 (vs. 9,31 for Structural)

Structural SARIMA Diff A-1

α1 =0.6 α2 =0 α3 =0 α4 =0.4

Validation and prediction

0

10000

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60000

70000

Pond

Min

Max

We have predicted from 28/05/2012 to 30/12/2012. For instance, a week obtained from inputs generated by Iberdrola.

Weight

5. Conclusions and perspectives

Conclusions and perspectives

Conclusions

We have generated models with error values between 8%-15%.

In addition, we have generated a prediction for future number of calls from an unknown time interval.

Perspectives

Compare our solution with the real data when available.

We would like to have additional variables such as

campaigns, discretional events, etc.

Thank You!