Khudyakov Polina
Designing a Call Center
with an IVR
MSc. Seminar
Advisor: Professor Avishai Mandelbaum
Call centers around the world
Call center operators represent:
• 4% of the workforce in USA
• 1.8% of the workforce in Israel
• 1.5% of the workforce in Great Britain
• 0.5% of the workforce in France
More than $300 billion is spent annually on call centers around the world
All Fortune 500 companies haves at least one call center, which
employs on average 4,500 agents
Quality of service
• 92% of U.S. consumers form their image of a company based
on their experience using the company’s call center
• 63% of the consumers stop using a company’s products based
on a negative call center experience
• almost 100% of the consumers between ages 18 and 25 stop
using a company’s products based on a negative call center
experience
Future of call centers
Self-services
• Interactive Voice Response (IVR)
• Outbound Voice Messaging (OVM)
• The Web
• Outbound Email
• Speech Recognition
Three sound reasons for using IVR
• Improved customer satisfaction
• reduce queue times
• extended service hours
• offer privacy
• Increased revenue
• extended business hours
• unload trained agents from routine requests and simple service
• Reduced cost
• typical service phone call involving a real person costs 7$
• an Internet transaction, with a person responding, costs 2.5$
• a “self-service” phone call with no human interaction costs 50 cent
Background
• Halfin and Whitt (1981) (M/M/S)
• Massey and Wallace (2004) (M/M/S/N)
• Garnet, Mandelbaum and Reiman (2002) (M/M/S+M)
• Srinivasan, Talim and Wang (2002) (Call center with an IVR)
Customer interaction with a call center
with an IVR
Customer
joining
the system
Waiting in queue
…
IVR
End of Service
Schematic model
“IVR”
“Agents”
N servers
S servers
1
1
N-S
2
λ
3
θ
.
.
.
p
…
2
.
.
.
1-p
N
S
μ
Model description
•
•
•
•
•
•
•
N – number of trunk lines
Poisson(λ) - arrival process
exp(θ) - IVR service time
p – probability to request agent’s service
S – number of agents
exp(μ) - agent’s service time
No abandonment
Closed Jackson network
N servers
S servers
p
1
…
2
exp(μ)
exp(θ)
1-p
1 server
3
exp(λ)
…
Stationary probabilities
• Stationary distribution of closed Jackson network (product form)



• Stationary probabilities of having i calls at the IVR and j calls at the
agents pool
where
Probability to find the system busy
Srinivasan, Talim and Wang (2002)
Probability(busy signal)=
P (N call in the system(PASTA))=
waiting time
Srinivasan, Talim and Wang (2002)
• Probability that the system is in state (i,j), when a call is about to
finish its IVR process:
• Distribution function of the waiting time
• Expected waiting time
Other performance measures
• Expected queue length
• Agents’ utilization
• Offered load
Operational regimes
• Quality - Driven
• Few busy signal
• Short waiting time for agents
• Agents over IVR
• Efficiency - Driven
• High utilization of agents
• IVR over Agents
• Quality&Efficiency – Driven (QED)
• Careful balance between service quality and resources efficiency
The domain for asymptotic analysis: QED
• M/M/S/N queue (Massey A.W. and Wallace B.R.)
• Our system (intuition)
The domain for asymptotic analysis: QED
(continuation)
Theorem. Let λ, S and N tend to
simultaneously. Then the conditions
are equivalent to the conditions
QED
where
Approximation of P(W>0)
Theorem. Let λ, S and N tend to
simultaneously and satisfy the
QED conditions, where μ, p, θ are fixed. Then
 0
where
 0
Exact formula for P(W>0)
• Exact
• Approximate
Illustration of the P(W>0) approximation
1.2
A smal-size call center
1.2
1
1
0.8
0.8
A mid-size call center
0.6
0.6
exact
exact
approx
0.4
approx
0.4
0.2
0.2
0
0
S, agents
S, agents
1.2
1.2
A mid-size call center
1
1
0.8
0.8
0.6
0.6
exact
approx
0.4
approx
0.4
0.2
0.2
S, agents
100
98
96
94
92
90
88
86
84
82
80
78
76
74
72
70
68
66
64
62
0
60
0
A large call center-
S, agents
Approximation of P(busy)
Theorem. Let λ, S and N tend to
 0
where
 0
where
simultaneously and satisfy the
QED conditions, where μ, p, θ are fixed. Then
Approximation of E[W]
Theorem. Let λ, S and N tend to
simultaneously and satisfy the
QED conditions, where μ, p, θ are fixed. Then
 0
where
 0
Approximation of waiting time density
Theorem. Let λ, S and N tend to
simultaneously and satisfy the
QED conditions, where μ, p, θ are fixed. Then
 0
where
 0
Illustration of the waiting time density
1
 t 
fW |W 0 
  g (t , ,  )
S
 S
1.1
1
0.9
0.8
g(t,10,-1)
0.6
g(t,10,0)
0.5
g(t,10,1)
0.4
0.3
0.2
0.1
t, time
14
13.3
12.6
11.9
11.2
10.5
9.8
9.1
8.4
7.7
7
6.3
5.6
4.9
4.2
3.5
2.8
2.1
1.4
0.7
0
0
density
0.7
QED Performance
•
:characterization
•
:Quality - Driven
•
:Efficiency - Driven
Special cases
M/G/N/N loss system (Jagerman)
Special cases
M/M/S system
(Halfin and Whitt)
Special cases (M/M/S/N system)
Theorem. Let λ, S and N tend to
where
is fixed. Then
simultaneously and satisfy the following conditions:
Costs of call center
•
•
•
•
•
•
Salaries – 63%
Hiring and training costs – 6%
Costs for office space – 5%
Trunk costs – 5%
IT and telecommunication equipment – 10%
Others – 11%
Costs of call center
•
•
•
•
•
•
Salaries – 63%
Hiring and training costs – 6%
Costs for office space – 5%
Trunk costs – 5%
IT and telecommunication equipment – 10%
Others – 11%
Optimization problem
•
•
•
•
•
- cost of an agent per time unit
- telephone cost per trunk and time unit
- number of staffed agents
- number of telephone trunks
- expected trunk utilization
IVR vs. Agents
IVR vs. Agents
Possible future research
• Add abandonment and retrials to the model
• Mixed customer population
• Dimensioning: finding the parameters  and
for given cost of an agent and cost of
customer’s delay
