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