Simulation Study of a
Call Center
Gaurav Chhabra
&
Sachin Jayaswal
2
Motivation
Rapid growth in Call Center industry in the last decade
Call center targets a specific level of service to its customers
Staff level – a major decision
3
Problem Definition
Customer Classes
Regular
Priority
Service levels
Maximum time on hold
Maximum abandonment rate
Objective: To determine the optimum staffing level
4
Input Data
Pattern of call arrivals
Pattern of call service
Call mix
Balk probability, renege probability
Target service levels
5
Output Measures
Percentage of customers served who spent less than the target time on hold
Percentage of customers who hung up without being served (abandonment rate)
6
Data Collection
Call arrivals - Number of calls made every 15 minutes (converted to IAT)
Service times - Number of seconds needed to serve a call
7
Distribution of Inter-Arrivals Times
Lognorm(0.21240, 0.12779) Shift=+0.30195
0
1
2
3
4
5
60
.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
>5.0% 5.0%90.0%
0.3749 0.7560
BestFit Trial VersionFor Evaluation Purposes Only
8
Distribution of Service TimesLognorm(5.2343, 3.5904) Shift=+1.8160
0.00
0.05
0.10
0.15
0.20
0.252 4 6 8 10
12
14
16
< >5.0% 5.0%90.0%
3.37 13.80
BestFit Trial VersionFor Evaluation Purposes Only
9
Different scenarios considered:
Priority Calls – 50%, 40%, 30%, 20%,
10%
Call Mix
10
Balk – 5% of the customers balk when they find
line busy
Renege Distribution
Literature Review:
Parkan 1987
Harris, Hoffman, and Saunders 1987
Our Model:
CONT(0.0,1,0.25, 2, 0.40, 3,0.50,4,0.70,5,1.0,6)
Balk and Renege Distributions
11
Renege probability distribution
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7
Wait Time
Rene
ge P
roba
bilit
yRenege Distributions
12
Target Service Levels
Priority Calls
Calls attended within 1 minute >= 90%
Abandonment rate <= 5%
Regular Calls
Calls attended within 5 minutes >= 80%
Abandonment rate <= 10%
13
Simulation Model
Customer Arrival Call ServedCall Service
Customersto Regular
and arrival timeAssign priority
Customerto Sp.
and arrival timeAssign priority
Special Customer ?True
False
0 0 0
00:00:00
0
0
14
Call arrival
Sp customerAssign priority to
Special Customer?Tr ue
False
Regular customerAssign priority to
Call Service
Call Served
Assign Search #
Dispose
Duplicate CallsO r iginal
Duplicat e
Found
Not Found
queueSearc h Serv er
O r iginal
Rem oved Ent it y
queueRem ov e from
tim eDelay for renege
Server Idle?Tr ue
False
Balk ?Tr ue
False
customer BalksRecord Sp.
Sp Customer?Tr ue
False
customer BalksRecord Regular
Spc customer?Tr ue
False
RenegesRecord Sp
RenegesRecord Reg
CustoomersRecord Sp
CustomersRecord Regular
Spcl cust?Tr ue
False
delaysp cust cummul
compltd srvcRecord # sp cust
cust compltd srvcRecord # Reg
DelayAssign sp cust
DelayAssign Reg cust
delayReg cust cummul
sp within t ime limit?Tr ue
False
within limitRecord sp #
limit?Reg cust within t ime
Tr ue
False
within limitRecord Reg #
Sp cust avg delay
delayReg cust avg
hangupsPercent Sp cust
hangupsPercent Reg cust
srv within limitPercent Sp cust
srv within limitPercent Reg cust
Assign Att ributes
0
0
0
0
0
0
0
0
0
0
0
0
S p c u st A v g W a i t T i m e
0. 0 60. 00.0
1.0
P ercen t ag e S p cu st o mers Han g u p s
0. 0 60. 0
0.0
1.0
0
0
0
0
P ercen t ag e R eg cu st o mers Han g u p s
0. 0 60. 0
0.0
1.0
S i m u l a t i o n T i m e
00:00:000
0
R e g c u s t A v g W a i t T i m e
0. 0 60. 00.0
1.0
S p cu s t av g d e l ay
0 . 0 0
R e g c u s t a v g d e l a y
0 . 0 0
0
0
p e r c e n t s p c u s t w ith in tim e lim it
0 . 0 0
0
0
p e r c e n t R e g c u s t w ith in tim e lim it
0 . 0 0
P e rc e n t s p c u s t s e rv e d w i t h i n l i m i t
0 . 0 6 0 . 0
0.0
1.0
P er cent R eg cust ser ved w i t hi n l i m i t
0 . 0 6 0 . 0
0.0
1.0
percent sp cust w ithin tim e lim it
0 . 0 0
percent sp cust w ithin tim e lim it
0 . 0 0
15
Results % of priority
CallsPerformance Measures
# of Agents
12 13 14
50%
Service Level - Priority [80.61,83.63] [86.35,89.37] [92.74,94.30]
Service Level - Regular [98.30,98.70] [98.78,98.98] [98.82,99.06]
Abandonment Rate - Priority [5.08,6.18] [3.98,4.82] [2.36,3.00]
Abandonment Rate - Regular [18.64,21.40] [10.74,13.34] [4.74,5.98]
Avg. wait time - Rapid [0.46,0.52] [0.33,0.39] [0.18,0.22]
Avg. wait time - Regular [0.91,1.03] [0.56,0.68] [0.30,0.38]
Agent Utilization [0.980.0.980] [0.962,0.962] [0.931,0.931]
16
% of priority Calls
Performance Measures
# of Agents
12 13 14
40%
Service Level - Priority [81.04,84.14] [87.27,89.67] [93.12,94.84]
Service Level - Regular [98.48,98.82] [98.82,99.02] [98.86,99.08]
Abandonment Rate - Priority [5.40,6.96] [3.70,4.86] [2.12,3.10]
Abandonment Rate - Regular [16.99,19.51] [9.59,11.71] [4.63,6.07]
Avg. wait time - Rapid [0.45,0.51] [0.32,0.36] [0.17,0.21]
Avg. wait time - Regular [0.93,1.03] [0.56,0.68] [0.29,0.37]
Agent Utilization [0.982,0.982] [0.965,0.965] [0.932,0.932]
17
% of priority Calls
Performance Measures # of Agents
12 13 14
30%
Service Level - Priority [82.73,85.65] [90.09,92.23] [93.52,94.86]
Service Level - Regular [98.77,98.97] [98.87,99.05] [98.95,99.11]
Abandonment Rate - Priority [5.01,6.51] [3.42,4.70] [2.18,2.98]
Abandonment Rate - Regular [15.79,17.59] [8.54,10.22] [4.30,5.08]
Avg. wait time - Rapid [0.44,0.48] [0.29,0.33] [0.18,0.20]
Avg. wait time - Regular [0.95,1.07] [0.57,0.65] [0.31,0.37]
Agent Utilization [0.982,0.982] [0.964,0.964] [0.936,0.936]
18
% of priority Calls
Performance Measures # of Agents
12 13 14
20%
Service Level - Priority [83.89,86.85] [89.83,92.17] [93.43,95.47]
Service Level - Regular [98.83,99.05] [98.95,99.13] [98.99,99.15]
Abandonment Rate - Priority [4.61,6.57] [2.97,4.41] [2.27,3.07]
Abandonment Rate - Regular [14.69,16.31] [7.68,9.28] [3.78,4.84]
Avg. wait time - Rapid [0.42,0.46] [0.27,0.31] [0.16,0.20]
Avg. wait time - Regular [0.94,1.06] [0.53,0.63] [0.28,0.34]
Agent Utilization [0.983,0.983] [0.963,0.963] [0.933,0.933]
19
% of priority Calls
Performance Measures # of Agents
12 13 14
10%
Service Level - Priority [84.06,87.46] [89.36,93.00] [92.37,95.09]
Service Level - Regular [98.95,99.15] [99.04,99.18] [99.04,99.18]
Abandonment Rate - Priority [3.43,6.81] [3.09,4.97] [1.29,3.17]
Abandonment Rate - Regular [13.24,14.46] [7.12,8.48] [3.83,4.61]
Avg. wait time - Rapid [0.38,0.42] [0.25,0.31] [0.17,0.21]
Avg. wait time - Regular [0.90,1.00] [0.54,0.64] [0.29,0.37]
Agent Utilization [0.983,0.983] [0.966,0.966] [0.937,0.937]
20
Future Research Directions
Non Stationary Distribution of Call Arrivals
Staff Scheduling
Different models for Balk/Renege
21
Comments/Questions