Capacity and Demand Management
MD254
Service Operations
Professor Joy Field
Strategic Role of Capacity Decisions in Services

A capacity expansion strategy can be used proactively to:
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Create demand through supply (e.g. JetBlue, Dunkin Donuts)
Lock out competitors, especially where the market is too small for
two competitors (e.g. WalMart)
Get down the learning curve to reduce costs (e.g. Southwest
Airlines)
Support fast delivery and flexibility (e.g. Mandarin Oriental)
A lack of short-term capacity can generate customers for the
competition (e.g. restaurant staffing)
Capacity decisions balance costs of lost sales if capacity is
inadequate against operating losses if demand does not
reach expectations.
Strategy of building ahead of demand is often taken to avoid
losing customers.
Capacity Planning Challenges in Services
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Inability to create a steady flow of demand to fully utilize
capacity
Enforced idle capacity if no customers are in the service
system
Customers are participants in the service and the level of
congestion impacts perceived quality.
Customer arrivals fluctuate and service demands also
vary.
Capacity is typically measured in terms of (bottleneck)
resources rather than outputs (e.g. number of airplane
seats available per day rather than number of
passengers flown per day).
Customer-Induced Demand
and Service Time Variability
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Arrival: customer arrivals are independent decisions not
evenly spaced.
Capability: the level of customer knowledge and skills
and their service needs vary
Request: uneven service times result from unique
demands.
Effort: level of commitment to coproduction or selfservice varies.
Subjective Preference: personal preferences introduce
unpredictability.
Modeling Service Delivery Systems
Using Queuing Models
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Customer population
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The service system
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The source of input to the service system
Whether the input source is finite or infinite
Whether the customers are patient or impatient
Number of lines - single vs. multiple lines
Arrangement of service facilities – servers, channels, and phases
Arrival and service patterns – e.g. for many service processes,
interarrival and service times are exponentially distributed (arrival and
service rates are Poisson distributed)
Priority rule (queue discipline)

Static
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First-come, first-served (FCFS) discipline
Dynamic
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Individual customer characteristics: e.g. earliest due date (EDD), shortest
processing time (SPT), priority, preemptive
Status of the queue, e.g. number of customers waiting, round robin
Queue Configurations
and Service Performance
Multiple Queue
Single queue
Take a Number
3
4
8
2
6
10
12
11
5
7
9
Enter
Arrangement of Service Facilities
Channels and Phases
Service facility
Server arrangement
Parking lot
Self-serve
Cafeteria
Servers in series
Toll booths
Servers in parallel
Supermarket
Self-serve, first stage; parallel servers, second stage
Hospital
Many service centers in parallel and series, not all used by each patient
Distribution of Patient Interarrival Times
for a Health Clinic
Relative frequency, %
Patient interarrival times approximate an exponential distribution.
40
30
20
10
0
1
3
5
7
9
11 13 15 17 19
Patient interarrival time, minutes
3.5
3
2.5
2
1.5
1
0.5
0
1 3 5 7 9 11 13 15 17 19 21 23
Percentage of average daily
physician visits
Average calls per hour
Temporal Variation in Arrival Rates
140
130
120
110
100
90
80
70
60
1
2
3
4
Hour of day
Day of w eek
Ambulance Calls
by Hour of Day
Physician Arrivals
by Day of Week
5
Queue Discipline
Queue
discipline
Static
(FCFS rule)
Dynamic
Selection based
on individual
customer
attributes
Selection
based on status
of queue
Number of
customers
waiting
Round robin
Priority
Preemptive
Processing time
of customers
(SPT or cµ rule)
Single-Server, Exponential Interarrival
and Service Times (M/M/1) Model
Assumptions:
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Number of servers = 1
Number of phases = 1
Input source: infinite, no balking or reneging
Arrivals: mean arrival rate =  ; mean interarrival time = 1 / 
Service: mean service rate =  ; mean service time = 1 / 
Waiting line: single line; unlimited length
Priority discipline: FCFS
Single-Server Operating Characteristics


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Average utilization:  
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Probability that n customers are in the system: Pn  (1  )n
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Probability of less than n customers in the
system:
Pn  1  n
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Average number of customers in the system: Ls 
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Average number of customers in line: Lq  Ls
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Average time spent in the system: Ws 
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Average time spent in line: Wq  Ws
1



Multiple-Server (M/M/c) Model
Assumptions:
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Number of servers = M
Number of phases = 1
Input source: infinite, no balking or reneging
Arrivals: mean arrival rate =  ; mean interarrival time = 1 / 
Service: mean service rate =  ; mean service time = 1 / 
Waiting line: single line; unlimited length
Priority discipline: FCFS
Multiple-Server Operating Characteristics
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Average utilization:  

M
M 1 ( / ) n
Probability that zero customers are in the system: P0  [ 
n 0
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Probability that n customers are in the system:

( / ) n
( /  ) n
P0 for 0  n  M,
P for n  M
n M 0
n!
M!M
P0 ( / ) M 
Average number of customers in line: Lq 
M!(1  ) 2
L
1
Average time spent in line/system: Wq  q , Ws  Wq 


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n!
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Average number of customers in the system: Ls  Ws
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Average waiting time for an arrival not immediately served: Wa 
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Prob. that an arrival will have to wait for service: Pw 
Wq
Wa
( / ) M 1

]
M!(1  )
1
M  
Capacity Utilization and Capacity Squeeze
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A capacity squeeze is the breakdown in the ability of the operating
system to serve customers in a timely manner as the capacity utilization
approaches 100%. As the variability in arrival and service rates
increases, a capacity squeeze occurs at a lower capacity utilization.
100
System line
length


With:

Then:
Ls 

1 
10

8
0
0.2
0.5
0.8
0.9
0.99
6
4
2
0
0
Capacity utilization
1.0
Ls
0
0.25
1
4
9
99
Service System Cost Tradeoff
Total Cost of Service
Let: Cw = Hourly cost of waiting customer
Cs = Hourly cost per server
C = Number of servers
Total cost/hour = Hourly service cost + Hourly customer waiting
cost
Total cost/hour = Cs C + Cw Ls
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The total cost of service reflects both the firm’s capacity cost
as well as the customers’ cost of waiting. Service processes
should be designed to minimize the sum of these two costs.
How can the economic cost of customer waiting be
determined?
Queuing Model Takeaways
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Variability in arrivals and service times contribute equally to
congestion as measured by Lq.
Even though servers will be idle some of the time, there will be
customer lines and waits, on average. These lines/waits will get
very long very quickly as capacity utilization approaches 100%.
 Given the potential for a capacity squeeze as capacity utilization
approaches 100%, service firms typically design their processes
with a capacity cushion (i.e., the amount of capacity above the
average expected demand). The greater the variability in
arrival/service rates, the larger the capacity cushion needed for a
given service level.
To improve system performance (waits and line lengths):
 A single queue vs. multiple queues with multiple channels.
 More servers can be added (reducing capacity utilization but at a
higher operating cost).
 A fast single server is preferred to multiple-servers with the same
overall service rate.
Managing Waiting Lines
In a lifetime, the average person will spend:
SIX MONTHS Waiting at stoplights
EIGHT MONTHS
Opening junk mail
ONE YEAR Looking for misplaced objects
TWO YEARS
Reading E-mail
FOUR YEARS Doing housework
FIVE YEARS Waiting in line
SIX YEARS Eating
The Psychology of Waiting
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People dislike “empty” time – Fill this time in a
positive way.
Service-related diversions convey a sense that the
service has started (e.g. handing out menus).
Waiting can induce anxiety in some customers –
Reduce anxiety by providing information to the
customer (e.g. expected wait times).
Customers want to be treated “fairly” while waiting –
First-come-first-served (FCFS) queuing discipline or
logical prioritization process (e.g. triage)
Managing the Customer Waiting Experience
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Conceal the queue from the customer.
Engage the customer in co-production tasks during
the wait.
Provide diversions during the wait.
Serve priority customers or customers who are
willing to plan ahead faster.
Automate standard services to enable self-service.
Manage waiting time perceptions – under promise,
over deliver.
Managing Demand and Capacity
to Reduce Lines and Waiting Times
MANAGING
DEMAND
Developing
complementary
services
Reservation
systems and
overbooking
MANAGING
CAPACITY
Segmenting
demand
Sharing
capacity
Offering
price
incentives
Crosstraining
employees
Promoting
off-peak
demand
Using
part-time
employees
Yield
management
Increasing
customer
participation
Scheduling
work shifts
Creating
adjustable
capacity
Managing Demand
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Segmenting demand (e.g. random vs. scheduled
arrivals)
Offering price incentives (e.g. lower matinee pricing
at movie theaters)
Promoting off-peak demand (e.g. use of a resort
hotel during the off-season for business or
professional groups)
Developing complementary services (e.g. HVAC)
Reservation systems and overbooking (tradeoff
between opportunity cost of unused capacity and
costs of not honoring an overbooked reservation)
Managing Capacity
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Increasing customer participation (e.g. e-commerce)
Scheduling work shifts (based on historical demand
patterns and desired service level)
Creating adjustable capacity (e.g. Tesco online
grocery fulfillment)
Using part-time employees (e.g. during tax season)
Cross-training employees (to increase workforce
flexibility and leverage capacity to provide additional
value-added services)
Sharing capacity (e.g. gate-sharing arrangements)
Flow Management
Three stage service process, average service rates:
Customers
40/hour
20/hour
40/hour
Customers
(highly variable arrival
rate, average=20/hour)
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Flow management focuses on relieving bottlenecks so
that customers can move more smoothly and quickly
through the service process.
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How can the flow of this service process be improved?
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Resource-side
Demand-side
Maximizing Utilization vs. Flow Management
Customers
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40/hour
20/hour
40/hour
Customers
Compare and contrast the process performance with a
maximizing utilization vs. flow management approach.
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Why does flow management usually improve capacity
utilization, but maximizing utilization often results in poor
flow?
Yield Management
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Yield management attempts to dynamically allocate
fixed capacity to match the potential demand in
various market segments to maximize revenues and
profits.
Although airlines were the first to develop yieldmanagement, other capacity-constrained service
industries (e.g. hotels, car rental firms, cruises) also
use yield management.
Possible ethical issues associated with yield
management?
(http://en.wikipedia.org/wiki/Yield_management)
Ideal Characteristics for Yield Management
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Relatively fixed capacity
Ability to segment markets (i.e., discount
allocation)
Perishable inventory (i.e., potential for
“spoilage”)
Product sold in advance
Fluctuating demand
Low marginal fulfillment costs and high
marginal capacity change costs