Call centre forecasting using

temporal aggregation

Devon K. Barrow| Nikolaos Kourentzes |Bahman Rostami-Tabar

ISF 37th International Symposium on Forecasting

Cairns, Australia, June 25-28, 2017

Agenda

1. Call centre industry in numbers

2. Call centre operations

3. Evaluation: The data

4. Multiple seasonalities and temporal aggregation

5. Evaluation: The experimental setup

6. Results

7. Conclusions

The Call Centre Industry in Numbers

US$337.8 BillionGrowth in global call centre market

by 2018

49%Customer service

Sales (21%); Sales and service (30%)

78%Inbound calls

75% Agents working in call centres that

have 230 total employees or more

10% Average growth per year.

Exceptions: India (89%);

Brazil (38%) and Poland (23%)

70% Costs due to labour

Source: The Global Call Centre Report; Global Industry Analysts

The Call Centre Industry in Numbers

Source: UNISON

1 MillionJobs

5,000Call centres

3%Workforce

Agenda

1. Call centre industry in numbers

2. Call centre operations

3. Evaluation: The data

4. Multiple seasonalities and temporal aggregation

5. Evaluation: The experimental setup

6. Results

7. Conclusions

Call Centre Operations: Resources

Resources

• Personnel

• Computers

• Telecommunication equipment

Functions

• Customer service

• Help desk

• Emergency response services

• Telemarketing

• Order taking

Call Centre Operations: Decisions• Strategic decisions concern the role of the contact centre in the company, the

type of service that is to be delivered, etc.

2 to 5 Years

• Tactical decisions concern how the resources are to be used. Decisions about structure (e.g., skill-based routing) and organization are taken at this level, as well as decisions about the hiring and training of agents.

Weekly to Monthly to 1 Year

• Planning decisions concern scheduling of agents on a weekly basis also called workforce management.

Half-hourly to Weekly

• Daily control shift leaders monitor service levels and productivity on a daily basis and can react to that.

Half-hourly to 1 day

• Real-time control concern real-time decisions by software, for example decisions about the assignment of calls to available agents.

Agenda

1. Call centre industry in numbers

2. Call centre operations

3. Evaluation: The data

4. Multiple seasonalities and temporal aggregation

5. Evaluation: The experimental setup

6. Results

7. Conclusions

0

2000

4000

1 224 447 670 893

Arrivals

Half-hours

Evaluation: The Data

• Data• Half-hourly arrivals at the call center of a

major retail bank in the United Kingdom (Taylor 2008)

• Opening hours: 7 A.M. – 11 P.M.

• Recorded interval: Half-hourly

• Experiment Setup• Size of estimation sample: 5600

• Size of evaluation: 3040

• Rolling origin: 10 origins (each shifted weekly)

Intraday cycle, 𝑠1= 32,

Intraweek cycle, 𝑠2 = 7×32 = 224

Agenda

1. Call centre industry in numbers

2. Call centre operations

3. Evaluation: The data

4. Multiple seasonalities and temporal aggregation

5. Evaluation: The experimental setup

6. Results

7. Conclusions

Multiple Seasonalities

Day half-hour

Week half-hour

Day half-hour Week half-hour

Seasonal

Matrix

Seasonal

Distribution

Multiple Seasonalities:Temporal aggregation

Multiple Seasonalities:Temporal Aggregation

Morning-evening

(aggregate 16)

Morning-evening

(aggregate 16)

Daily

(aggregate 32)

Agenda

1. Call centre industry in numbers

2. Call centre operations

3. Evaluation: The data

4. Multiple seasonalities and temporal aggregation

5. Evaluation: The experimental setup

6. Results

7. Conclusions

0

2000

4000

1 224 447 670 893

Arrivals

Half-hours

Evaluation: Experiment Setup

• Data• Half-hourly arrivals at the call center of a

major retail bank in the United Kingdom (Taylor 2008)

• Opening hours: 7 A.M. – 11 P.M.• Recorded interval: Half-hourly• 38 Weeks long

• Experiment Setup• Size of estimation sample: 5600• Size of evaluation: 3040• Rolling origin: 10 origins (each shifted weekly)

Intraday cycle, 𝑠1= 32,

Intraweek cycle, 𝑠2 = 7×32 = 224

0

2000

4000

1 224 447 670 893

Arrivals

Half-hours

Evaluation: MethodsMeasure

• Method:• Base Model = ES (TSTools R Package)

• Top Down

• Bottom Up

• MAPA (Kourentzes et al., 2014)

• MAPA [Decision Level]

• Middle Out

• Thief (Athanasopoulos et al., 2017)

• Measure• Relative Mean Absolute Error (RMAE)

Intraday cycle, 𝑠1= 32,

Intraweek cycle, 𝑠2 = 7×32 = 224

Agenda

1. Call centre industry in numbers

2. Call centre operations

3. Evaluation: The data

4. Multiple seasonalities and temporal aggregation

5. Evaluation: The experimental setup

6. Results

7. Conclusions

Results – RMAE AverageDecision

Level Base Model

Bottom

Up MAPA

MAPA-to-

DL

Top

Down

Middle

Out

Half-hourly AL-1 1.00 1.00 1.22 1.00 1.06 0.96

Hourly AL-2 1.00 0.96 1.16 0.95 1.01 0.92

2 Hourly AL-4 1.00 1.01 1.23 1.91 1.10 0.97

3.5 Hourly AL-7 1.00 1.07 1.25 2.52 1.18 1.01

4 Hourly AL-8 1.00 1.01 1.10 2.18 1.15 0.94

7 Hourly AL-14 1.00 1.09 1.21 1.53 1.25 1.00

Half-daily AL-16 1.00 1.01 1.07 1.33 1.20 0.91

14 Hourly AL-28 1.00 1.10 1.13 1.22 1.43 1.01

Daily AL-32 1.00 1.09 1.16 1.18 1.41 1.01

28 Hourly AL-56 1.00 1.30 1.31 1.28 1.54 1.14

56 Hourly AL-112 1.00 0.83 0.82 0.82 0.93 0.79

Weekly AL-224 1.00 2.18 1.78 1.72 1.00 2.72

Table 1: Average across 10 origins, each origin beginning the following week

Results – RMAE Ranks

Decision Level Base Model

Bottom

Up MAPA

MAPA-to-

DL

Top

Down

Middle

Out

Half-hourly AL-1 3.30 3.30 5.80 3.30 3.10 2.20

Hourly AL-2 3.40 3.40 5.60 3.00 3.10 2.50

2 Hourly AL-4 2.70 2.60 4.70 5.90 3.00 2.10

3.5 Hourly AL-7 2.40 2.90 4.60 6.00 2.80 2.30

4 Hourly AL-8 2.60 2.90 4.20 6.00 3.20 2.10

7 Hourly AL-14 2.60 3.30 4.20 5.30 3.00 2.60

Half-daily AL-16 2.90 3.10 4.20 4.90 3.60 2.30

14 Hourly AL-28 2.90 3.40 3.70 4.50 3.50 3.00

Daily AL-32 3.20 2.90 3.80 4.40 3.60 3.10

28 Hourly AL-56 3.20 3.60 3.80 4.20 3.80 2.40

56 Hourly AL-112 4.10 3.40 3.30 3.70 3.70 2.80

Weekly AL-224 3.80 4.00 3.25 3.05 3.80 3.10

Table 2: Average rank across 10 origins, each origin beginning the following week

Variance stabilisation

• We apply a variance stabilization transformation method to transform the time series toimprove performance.

𝑉𝑗,𝑘 = 𝑁𝑗,𝑘 +1

4

• The number of arrivals in each half hour for each day as 𝑁𝑗,𝑘, where 𝑗 is the day index and 𝑘 is

the half hour of the day index (𝑘 = 1,… , 32).

𝑁𝑗,𝑘 ∼ 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 (Λ𝑗,𝑘)

• Time-dependent inhomogeneous Poisson process, where Λ𝑗,𝑘 is the Poisson arrival rate for day 𝑗

and half hour slot 𝑘.

• The square root transformed of the half-hourly arrival counts time series 𝑉𝑗,𝑘 become a

Gaussian process observations with an approximately mean 𝜃𝑗,𝑘 = Λ𝑗,𝑘 and variance 𝜎2 =1

4.

(Brown et al., 2005)

Results – RMAE AverageDecision

Level

Base

Model

Bottom

Up MAPA

MAPA-to-

DL

Top

Down

Middle

Out

Half-hourly AL-1 1.00 1.00 0.98 1.00 1.01 1.06

Hourly AL-2 1.00 0.98 0.96 0.98 0.99 1.03

2 Hourly AL-4 1.00 0.97 0.96 0.87 0.98 1.03

3.5 Hourly AL-7 1.00 0.95 0.94 0.84 0.96 1.01

4 Hourly AL-8 1.00 0.95 0.94 0.85 0.96 1.00

7 Hourly AL-14 1.00 0.95 0.94 0.89 0.96 1.00

Half-daily AL-16 1.00 0.96 0.96 0.91 0.97 1.02

14 Hourly AL-28 1.00 0.95 0.94 0.92 0.96 1.00

Daily AL-32 1.00 0.95 0.95 0.93 0.96 1.00

28 Hourly AL-56 1.00 0.96 0.96 0.95 0.97 1.02

56 Hourly AL-112 1.00 0.98 0.98 0.97 0.99 1.04

Weekly AL-224 1.00 0.99 0.99 0.99 1.00 1.05

Table 3: Average across 10 origins, each origin beginning the following week

Results – RMAE Ranks

Table 4: Average rank across 10 origins, each origin beginning the following week

Decision

Level

Base

Model

Bottom

Up MAPA

MAPA-to-

DL Top Down

Middle

Out

Half-hourly AL-1 3.30 3.30 1.80 3.30 3.60 5.70

Hourly AL-2 4.70 2.50 1.60 3.30 3.40 5.50

2 Hourly AL-4 4.70 3.30 2.40 1.00 3.90 5.70

3.5 Hourly AL-7 5.30 3.20 2.60 1.00 3.70 5.20

4 Hourly AL-8 5.20 3.20 2.70 1.00 3.60 5.30

7 Hourly AL-14 5.20 3.20 2.70 1.00 3.70 5.20

Half-daily AL-16 4.40 3.10 3.00 1.10 3.70 5.70

14 Hourly AL-28 5.00 3.10 3.00 1.10 3.50 5.30

Daily AL-32 4.70 3.10 3.10 1.10 3.60 5.40

28 Hourly AL-56 4.40 3.20 3.10 1.70 3.20 5.40

56 Hourly AL-112 4.00 3.10 3.10 2.20 3.20 5.40

Weekly AL-224 3.30 3.20 2.55 3.25 3.30 5.40

Agenda

1. Call centre industry in numbers

2. Call centre operations

3. Evaluation: The data

4. Multiple seasonalities and temporal aggregation

5. Evaluation: The experimental setup

6. Results

7. Conclusions

Conclusions

• Middle out is best when there is high variance

• MAPA performs well [after stabilising variance]

• MAPA to Decision Level outperforms all other approaches

• Suggestion that selecting the appropriate level for a given decision level is important (series has not trend so why aggregate to highest level)

References

• Taylor, J. W. 2008. A comparison of univariate time series methods for forecasting intradayarrivals at a call center. Management Science, 54, 253-265.

• Brown, L., Gans, N., Mandelbaum, A., Sakov, A., Shen, H. P., Zeltyn, S. & Zhao, L. 2005.Statistical analysis of a telephone call center: A queueing-science perspective. Journal of theAmerican Statistical Association, 100, 36-50.

• Kourentzes, N., Petropoulos, F. and Trapero, J.R., 2014. Improving forecasting by estimatingtime series structural components across multiple frequencies. International Journal ofForecasting, 30(2), pp.291-302.

• Athanasopoulos, G., Hyndman, R.J., Kourentzes, N. and Petropoulos, F., 2017. Forecastingwith temporal hierarchies. European Journal of Operational Research, 262(1), pp.60-74.