Call centre forecasting using temporal...
Transcript of Call centre forecasting using temporal...
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.