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OR54 Conference, Edinburgh, Sept US Energy Provider: Daily call volumes to call centre (Winter)
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OR54 Conference, Edinburgh, Sept 2012.
When to use Virtual Hold Technology in Call Centre Operations
Dave Worthington, Chris KirkbrideDepartment of Management Science,Lancaster University, UK.d.worthington@lancaster.ac.ukc.kirkbride@lancaster.ac.uk
(Thanks to Zubin Sethuraman, MSc student, Lancaster University).
OR54 Conference, Edinburgh, Sept 2012.
Outline Energy provider call centre context Previous work on balking queues Do our models fit? Model predictions Implications for call centre management.
2
OR54 Conference, Edinburgh, Sept 2012.
US Energy Provider:Daily call volumes to call centre (Winter)
0
500
1000
1500
2000
2500
3000
3500
0 30 60 90 120 150 180
Days
Daily
Cal
lss
ACQUISITIONS CARE PAYG
OR54 Conference, Edinburgh, Sept 2012.
Hourly: call volumes & ASAs (mins)
0
50
100
150
200
250
300
8 9 10 11 12 13 14 15 16 17 18 19
Time of day
CARE ACQUISITIONS PAYG
0.0
5.0
10.0
15.0
20.0
25.0
30.0
8 9 10 11 12 13 14 15 16 17 18 19
Time of day
CARE ACQUISITIONS PAYG
OR54 Conference, Edinburgh, Sept 2012.
Hourly: ASAs (mins) & abandonment %s
0.0
5.0
10.0
15.0
20.0
25.0
30.0
8 9 10 11 12 13 14 15 16 17 18 19
Time of day
CARE ACQUISITIONS PAYG
0
10
20
30
40
50
60
8 9 10 11 12 13 14 15 16 17 18 19
Time of day
CARE ACQUISITIONS PAYG
OR54 Conference, Edinburgh, Sept 2012.
The problem posed Virtual hold technology (VHT) gives
callers opportunity to be called back without losing their place in the queue (accept /stay in queue/ balk)
When should they use VHT? Should they use it differently for
different queues?
OR54 Conference, Edinburgh, Sept 2012.
7
Reminder
OR54 Conference, Edinburgh, Sept 2012.
Time-dependent queues with balking Balking can be used to represent balking and reneging We investigate M(n(t))/G/S and assume geometric balking, i.e.
SnbtSnt
t Snn )( )(
)( 1
Impact of balking on Arrival Rates
0
2
4
6
8
10
12
0 10 20 30 40 50
no. in system
arriv
al ra
te Strong
Medium
Weak
Time-dependent arrival rate (t)
0
2
4
6
8
10
12
0 6 12 18 24 30 36 42 48
Time
arriv
al ra
te
OR54 Conference, Edinburgh, Sept 2012.
Results: Easy-to-use approximation Queue length behaviour of M(n(t))/G/S
can be approximated (well) by a Normal distribution with:
)1ln(1
(t))variance(n
)1ln(
))(ln(5.0E(n(t))
b
b
St
S
OR54 Conference, Edinburgh, Sept 2012.
Self Validation Property Approximation works well when Prob (n<S) is
small, which we can check using standard Normal tables, e.g. Prob(n<S) < 0.05 if mean is >=1.645 SDs above S, i.e.:
)1ln(645.1))(ln( i.e.
)1ln(645.1))(( i.e.
bSt
bStnE
OR54 Conference, Edinburgh, Sept 2012.
Results: Easy-to-use approximation Anticipated Queueing Time (AQT):
Sb
St
)1ln(
))(ln(5.0
(t))AQTE(
)(S served customers of Percentage t
Abandonment behaviour:
OR54 Conference, Edinburgh, Sept 2012.
‘Sub-optimal’ behaviour is frequent
100%100%% S_util20%20%% balked1.253.41AQT0.95
0.642.25E(AQT)11.844.0E(Q)Perf’mance
measures
0.9820.995B2020S2525System
Parameters
BASystem
100%100%% S_util20%20%% balked1.253.41AQT0.95
0.642.25E(AQT)11.844.0E(Q)Perf’mance
measures
0.9820.995B2020S2525System
Parameters
BASystem
Impatience is a virtue!
OR54 Conference, Edinburgh, Sept 2012.
CARE: non-balking % V queue length/server
Queue length/server
Non-
balk
ing
%100%
6.0
50%
0.0
b*(off) =0.8205b*(on) = 0.8578
OR54 Conference, Edinburgh, Sept 2012.
ACQU’: non-balking % V queue length/server
Queue length/server
Non-
balk
ing
%100%
2.5
50%
0.0
b*(off) =0.6773b*(on) = 0.7361
OR54 Conference, Edinburgh, Sept 2012.
PAYG: non-balking % V queue length/server
Queue length/server
Non-
balk
ing
%100%
6.0
20%
0.0
b*(off) =0.7807b*(on) = 0.8091
OR54 Conference, Edinburgh, Sept 2012.
Performance prediction tool:
Sb
St
)1ln(
))(ln(5.0
(t))AQTE(
… based on:
ASA
OR54 Conference, Edinburgh, Sept 2012.
ASA analysis: CARE calls
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
8.00 10.00 12.00 14.00 16.00 18.00 20.00
Hour of day
min
utes
Actual
PredictedPredicted (+1)Predicted (-1)
OR54 Conference, Edinburgh, Sept 2012.
ASA analysis: CARE calls
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
8.00 10.00 12.00 14.00 16.00 18.00 20.00
Hour of day
min
utes
Actual Predicted
Predicted (+1)Predicted (-1)
Pred (+VHT)
OR54 Conference, Edinburgh, Sept 2012.
ASA analysis: CARE calls
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
8.00 10.00 12.00 14.00 16.00 18.00 20.00
Hour of day
min
utes
Actual
PredictedPredicted (+1)
Predicted (-1)Pred (+VHT)
Pred (+VHT+1)Pred (+VHT-1)
OR54 Conference, Edinburgh, Sept 2012.
ASA analysis: PAYG calls
0.0
10.0
20.0
30.0
40.0
50.0
60.0
8.00 10.00 12.00 14.00 16.00 18.00 20.00
Hour of day
min
utes
Actual Predicted
Predicted (+1)Predicted (-1)
Pred (+VHT)Pred (+VHT+1)
Pred (+VHT-1)
OR54 Conference, Edinburgh, Sept 2012.
ASA analysis: ACQUISITION calls
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
8.00 10.00 12.00 14.00 16.00 18.00 20.00
Hour of day
min
utes
Actual Predicted (S)Predicted (S+1)Predicted (S-1)Pred (+VHT)Pred (+VHT+1)Pred (+VHT-1)
OR54 Conference, Edinburgh, Sept 2012.
ASA analysis: What if …….. 1?
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
8.00 10.00 12.00 14.00 16.00 18.00 20.00
Hour of day
min
utes
ACQCARE (S)
CARE (S+1)PAYG (S)
PAYG (S-1)
OR54 Conference, Edinburgh, Sept 2012.
ASA analysis: What if …….. 2?
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
8.00 10.00 12.00 14.00 16.00 18.00 20.00
Hour of day
min
utes
ACQCARE (S)
CARE (S-1)PAYG (S)
PAYG (S+1)
OR54 Conference, Edinburgh, Sept 2012.
ASA analysis: What if …….. 3?
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
8.00 10.00 12.00 14.00 16.00 18.00 20.00
Hour of day
min
utes
ACQCARE (S)
CARE (&VHT)PAYG (S)
PAYG (&VHT)
OR54 Conference, Edinburgh, Sept 2012.
Management implications VHT is not necessary for Acquisition calls For other call types VHT reduces
abandonments and therefore increases ASAs!
So do current results suggest that VHT is a bad idea? Depends how many customers accept VHT Maybe depends on call centre agent
allocation software And …………………?
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