Operations Management:
Capacity Management in Services Module

Why do queues build up?

Process attributes and Performance measures of queuing processes

Safety Capacity
» Its effect on customer service
» Pooling of capacity

Queuing Processes with Limited Buffer
» Optimal investment


Specialists versus generalists
Managing Customer Service
» SofOptics
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Telemarketing at L.L.Bean




During some half hours, 80% of calls dialed received a busy
signal.
Customers getting through had to wait on average 10 minutes
for an available agent. Extra telephone expense per day for
waiting was $25,000.
For calls abandoned because of long delays, L.L.Bean still paid
for the queue time connect charges.
In 1988, L.L.Bean conservatively estimated that it lost $10
million of profit because of sub-optimal allocation of
telemarketing resources.
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Queuing Systems to model Service
Processes: A Simple Process
Order Queue
“buffer” size K
Incoming calls
Calls
on Hold
Sales Reps
processing
calls
Answered Calls
MBPF Inc. Call Center
Blocked Calls
(Busy signal)
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Abandoned Calls
(Tired of waiting)
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Performance Measures

Revenue Related
– Throughput R
– Abandonment Ra
– Probability of blocking Rb

Cost Related
– Server utilization r
– Inventory/WIP : # in queue Ii /system I

Customer Service related
– Waiting/Flow Time: time spent in queue Ti /system T
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Why do Queues Build?
 Variability

Capacity utilization
– Safety Capacity = capacity carried in excess of expected
demand to cover for system variability
» it provides a safety net against higher than expected arrivals or
services and reduces waiting time
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What to manage in such a process?
 Inputs
– Inter arrival times/distribution
– Service times/distribution

System structure
– Number of servers
– Number of queues
– Maximum queue length/buffer size

Operating control policies
– Queue discipline, priorities
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Queuing Theory:
Variability + Utilization = Waiting

A ctual
A verage
C ycle
T im e, W
Throughput-Delay curve:
V ariab ility
T heo retical
C ycle T im e
m

Queue Length Formula:
100%
U tilizatio n r
– Prob{waiting time in queue < t } = 1 - exp(-t / Ti ) where:
Ii 
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ρ
2(c  1)
1 ρ
Ci  C p
2
2
2
utilization variability
x
effect
effect
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Levers to reduce waiting and increase QoS:
 variability reduction + safety capacity
 How
to reduce system variability?
 How to manage safety capacity?
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Example 1: Call Center with one server,
unlimited buffer



A call center has a customer service representative (CSR)
taking calls. When the CSR is busy, the caller is put on hold.
The calls are taken in the order received.
Assume that calls arrive exponentially at the rate of one every
3 minutes. The CSR takes on average 2.5 minutes to complete
the reservation. The time for service is also assumed to be
exponentially distributed.
The CSR is paid $20 per hour. It has been estimated that each
minute that a customer spends in queue costs $2 due to
customer dissatisfaction and loss of future business.
– Safety capacity =
– Customer waiting cost =
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Example 2: Call Center with limited
buffer size


In reality only a limited number of people can be put on hold
(this depends on the phone system in place) after which a
caller receives busy signal. Assume that at most 5 people can
be put on hold. Any caller receiving a busy signal simply calls
a competitor resulting in a loss of $100 in revenue.
– # of servers c =
– buffer size K =
What is the hourly loss because of callers not being able to get
through?
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Example 3: Call Center with Resource
Pooling

2 phone numbers
– The call center hires a second CSR
who is assigned a new telephone
number. Customers are now free to
call either of the two numbers.
Once they are put on hold
customers tend to stay on line since
the other may be worse..

50%
Queue Server
50%
Queue Server
1 phone number: pooling
– both CSRs share the same
telephone number and the
customers on hold are in a single
queue
Queue
Servers
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Example 4: Call Center Staffing
 Assume
that the call center has a total of 6 lines.
With all other data as in Example 2, what is the
optimal number of CSRs that MBPF should staff the
call center with?
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Levers for Reducing Flow Time

“is to decrease the work content of (only ?) critical activities”,
and/or move it to non critical activities.

Reduce waiting time:
– reduce variability
» arrivals & service requests
» synchronize flows within the process
– increase safety capacity
» lower utilization
» Pooling
– Match resource availability with flows in and out of process
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Sof-Optics, Inc. = Managing the operations
of a customer service department
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Call Centers
 In
U.S.: $10B, > 70,000 centers, > 3M people (>3%
of workforce)
 Most cost-effective channel to serve customers
 Strategic Alignment
–
–
–
–

accounting: 90% are cost centers, 10% are revenue centers
role: 60% are viewed as cost, 40% as revenue generators
staffing: 60% are generalists, 40% specialists
Trend: more towards profit centers & revenue generators
Trade-off: low cost (service) vs. high revenue (sales)
Source: O. Zeynep Aksin 1997
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E.g.: Analysis of Service Systems



Divide day into blocks based on arrival rates
For each block evaluate performance measures given current staffing
Quantify financial impact of each action
– Workforce training: reduces mean and variability of service time
– Work flexibility from workforce: pools available capacity
– Time flexibility from workforce: better synchronization
S
– Improved Scheduling: better synchronization
– Retain experienced employees: increased safety capacity
– Additional workforce: Increases safety capacity
– Incentives to affect arrival patterns: better synchronization
– Decrease product variety: reduces variability of service time
D
– Increase maximum queue capacity
– Consignment program, fax, e-mail, web orders etc.
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Process Structure & Resource Capabilities:
Specialization Vs. Flexibility

Aggregation
– single server averaging 10 minutes
for service. Poisson arrivals with
a mean of 5/hr.

Specialization
– Service divided into two segments
(one server at each segment), each
averaging 5 minutes

Queue Server
Queue Server
Queue Server
Flexibility
– Second server added, with each
server performing entire service
Queue
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Servers
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Waiting Lines and Lean Operations
 The
role of limited buffer sizes
 The relationship between variability and maximum
buffer sizes
 The supervisor as buffer capacity
 Tradeoff between inventory and capacity
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Learning objectives:
General Service Process Management

Queues build up due to variability.

Reducing variability improves performance.

If service cannot be provided from stock, safety capacity must be provided
to cover for variability.
– Tradeoff is between cost of waiting, lost sales, and cost of capacity.

Improving Performance
– Reduce variability
– Increase safety capacity
» Pooling servers/capacity
– Increase synchronization between demand (arrivals) and service
» Manage demand
» Synchronize supply: resource availability
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