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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, [email protected]@lancaster.ac.uk
(Thanks to Zubin Sethuraman, MSc student, Lancaster University).
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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
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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
Dai
ly C
alls
s
ACQUISITIONS CARE PAYG
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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
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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
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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?
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OR54 Conference, Edinburgh, Sept 2012.
7
Reminder
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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.
Snbt
Sntt Snn )(
)()( 1
Impact of balking on Arrival Rates
0
2
4
6
8
10
12
0 10 20 30 40 50
no. in system
arriva
l rat
e
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
arri
val ra
te
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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
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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
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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:
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OR54 Conference, Edinburgh, Sept 2012.
‘Sub-optimal’ behaviour is frequent
100%100%% S_util
20%20%% balked
1.253.41AQT0.95
0.642.25E(AQT)
11.844.0E(Q)Perf’mancemeasures
0.9820.995B
2020S
2525System Parameters
BASystem
100%100%% S_util
20%20%% balked
1.253.41AQT0.95
0.642.25E(AQT)
11.844.0E(Q)Perf’mancemeasures
0.9820.995B
2020S
2525System Parameters
BASystem
Impatience is a virtue!
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OR54 Conference, Edinburgh, Sept 2012.
CARE: non-balking % V queue length/server
Queue length/server
Non-b
alk
ing %
100%
6.0
50%
0.0
b*(off) =0.8205
b*(on) = 0.8578
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OR54 Conference, Edinburgh, Sept 2012.
ACQU’: non-balking % V queue length/server
Queue length/server
Non-b
alk
ing %
100%
2.5
50%
0.0
b*(off) =0.6773
b*(on) = 0.7361
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OR54 Conference, Edinburgh, Sept 2012.
PAYG: non-balking % V queue length/server
Queue length/server
Non-b
alk
ing %
100%
6.0
20%
0.0
b*(off) =0.7807
b*(on) = 0.8091
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OR54 Conference, Edinburgh, Sept 2012.
Performance prediction tool:
Sb
St
)1ln(
))(ln(5.0
(t))AQTE(
… based on:
ASA
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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
ute
s
Actual
Predicted
Predicted (+1)
Predicted (-1)
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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
ute
s
Actual
Predicted
Predicted (+1)
Predicted (-1)
Pred (+VHT)
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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
ute
s
Actual
Predicted
Predicted (+1)
Predicted (-1)
Pred (+VHT)
Pred (+VHT+1)
Pred (+VHT-1)
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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
ute
s
Actual
Predicted
Predicted (+1)
Predicted (-1)
Pred (+VHT)
Pred (+VHT+1)
Pred (+VHT-1)
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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
ute
s
Actual
Predicted (S)
Predicted (S+1)
Predicted (S-1)
Pred (+VHT)
Pred (+VHT+1)
Pred (+VHT-1)
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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
ute
s
ACQ
CARE (S)
CARE (S+1)
PAYG (S)
PAYG (S-1)
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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
ute
s
ACQ
CARE (S)
CARE (S-1)
PAYG (S)
PAYG (S+1)
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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
ute
s
ACQ
CARE (S)
CARE (&VHT)
PAYG (S)
PAYG (&VHT)
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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 …………………?