Chapter 3: Strategic Capacity
Management
We will discuss …
 What is capacity?
 The concept of process capacity
 Capacity utilization
 Economies and diseconomies of scale
 Capacity balance
 Little's law
 Relating inventory, flow time, and flow rate
 Batch sizes and capacity
 Decision Trees
Strategic Capacity Planning
 Capacity
 the ability to hold, receive, store, or accommodate.
 measures can (as opposed to does)
 Strategic capacity planning
 approach for determining the overall capacity level
of capital intensive resources, including facilities,
equipment, and overall labor force size.
Examples??
Two Ways to Improve a Process
Reduce excess capacity at some step in the
process
Lower the cost for the same output
 Use the capacity at an underutilized process
step to increase the capacity at a bottleneck
Increase the output at the same cost
A bottleneck is the weakest link
Process capacity = minimum {Res 1 capacity,. Res 2 capacity, …)
Capacity Utilization
Capacity utilization rate =
Capacity used / Best operating level
 Capacity used
 rate of output actually achieved
 Best operating level
 capacity for which the process was designed
Avg
unit cost
of output
Underutilization
Overutilization
Best Operating
Level
Volume
Example of Capacity Utilization
 During one week of production, a plant produced 83
units of a product. Its historic highest or best
utilization recorded was 120 units per week. What is
this plant’s capacity utilization rate?

Answer:
Capacity utilization rate =
Capacity used .
Best operating level
= 83/120
=0.69 or 69%
Economies & Diseconomies of Scale
Economies of Scale and the Experience Curve
working
Average
unit cost
of output
100-unit
plant
200-unit
plant
300-unit
plant
400-unit
plant
Diseconomies of Scale start working
Volume
Other Issues
Capacity Focus
 The concept of the
focused factory holds
that production
facilities work best
when they focus on a
fairly limited set of
production objectives
Plants Within Plants
(PWP)
 Extend focus concept to
operating level
Capacity Flexibility
 Flexible processes
 Flexible workers
 Flexible plants
Capacity Planning: Balance
Unbalanced stages of production
Units
per
month
Stage 1
6,000
Stage 2
7,000
Stage 3
5,000
Maintaining System Balance: Output of one stage is the exact
input requirements for the next stage
Balanced stages of production
Units
per
month
Stage 1
Stage 2
6,000
6,000
Stage 3
6,000
Little’s Law
What it is:
Inventory (I) = Flow Rate (R) * Flow Time (T)
Implications:
• Out of the three performance measures (I,R,T), two can be chosen by
management, the other is GIVEN by nature
• Hold throughput (flow rate) constant: Reducing inventory = reducing flow time
Patients
11
Cumulative
Inflow
10
9
Cumulative
Outflow
8
7
Flow Time
6
Inventory
5
4
3
2
Inventory=Cumulative Inflow – Cumulative Outflow
1
0 7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
Time
16:00
17:00
Can be used in analyzing capacity issues!
18:00
Examples
 Suppose that from 12 to 1 p.m. 200
students per hour enter the GQ and  Airline check-in data indicate from 9
each student is in the system for an
to 10 a.m. 255 passengers checked
average of 45 minutes. What is the
in. Moreover, based on the number
average number of students in the
waiting in line, airport management
GQ?
found that on average, 35 people
 Inventory = Flow Rate * Flow Time
 = 200 per hour * 45 minutes (= 0.75
were waiting to check in. How long
hours)
did the average passenger have to
 = 150 students
wait?
 If ten students on average are
waiting in line for sandwiches and
each is in line for five minutes, on
average, how many students are
arrive each hour for sandwiches?
 Flow Rate = Inventory / Flow Time =
10 Students / 5 minutes = 0.083 hour
 = 120 students per hour
 Flow Time = Inventory / Flow Rate =
35 passengers / 255 passengers per
hour = 0.137 hours

= 8.24 minutes
The Impact of Batch Size on Capacity
Production cycle
Batch of 12
Production cycle
Batch of 60
Batch of 120
Batch of 300
60
120
180
240
300
Time [minutes]
Produce Part B (1 box corresponds to 12 units = 12 scooters)
Set-up from Part A to Part B
Produce Part A (1 box corresponds to 24 units = 12 scooters)
Set-up from Part B to Part A
Number Produced in 720 Min
Batch Size
Part A
Part B
12
60
60
60
180
180
120
240
240
300
300
300
Capacity Analysis with Batching
• Capacity calculation:
Capacity given Batch Size=
(in units/time)
Batch Size
Set-up time + Batch-size*Time per unit
• Note: Capacity increases with batch size:
0.5
1/p
Capacity 0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
• Note further: … and so does inventory
650
610
570
530
490
450
410
370
330
290
250
210
170
130
90
10
0
50
0.05
Batch Size
Process 1
Assembly process
Set-up time, S
120 minutes
Per unit time, p
2 minutes/unit
3 minutes/unit
Capacity (B=12)
0.0833 units/min
0.33 units/minute
Capacity (B=300)
0.4166 units/min
0.33 units/minute
-
Data about set-up times and batching
Batch size = 12
Setup
Batch size
Per unit
Capacity (per min)
Capacity (per hour)
Batch size = 300
120
0
120
0
12
12
300
300
2
3
2
3
0.083
0.333
0.417
0.333
5
20
25
20
Process Capacity
(per hour)
5
20
Capacity
0.5
1/p
0.45
0.4
0.35
Capacity of slowest
step other than the one
requiring set-up
0.3
0.25
0.2
0.15
0.1
0.05
Batch size is too small,
process capacity could be
increased (set-up step is
at the bottleneck)
650
610
570
530
490
450
410
370
330
290
250
210
170
90
130
50
10
0
Batch Size
Batch size is too large, could be
reduced with no negative impact
on process capacity (set-up is
not at the bottleneck)
Figure : Choosing a “good” batch size
B/[S+B*p] = k implies that B = S*k / (1 – p*k)
Problem
STEP 1
1
20
Act Time in min/part
Setup Time in min
STEP 2
2
0
STEP 3
1.5
0
Part a: What is the capacity for a batch size = 50?
part a
Batch is:
Capacity of Resource
(parts/min)
parts/hour
(minutes/part)
50
0.714
0.500
0.667
42.9
30.0
40.0
1.4
2
1.5
Capacity is 0.5 parts/min or 30 parts/hour
Part b: For a batch size of 10, what is the bottleneck
part b
Batch is:
Capacity of Resource
(parts/min)
10
0.333
0.500
0.667
Step 1 is bottleneck
What batch size should be chosen to smooth the flow?
Process Utilization and Capacity Utilization
 Process Utilization = Flow Rate / Process Capacity
 Example: Tom can process 100 forms per day and he actually
processes 70 forms.
 Process utilization = ??
 Utilization of resource = Flow rate / Capacity of resource
 Process 400 items per hour
 Capacities of resources (items/hour):
 Resource 1: 500 implies utilization of 80%
 Resource 2: 450 implies utilization of 89%
 Resource 3: 600 implies utilization of 67%
 Bottleneck is the resource with the lowest capacity and the highest
utilization
 Bottleneck is ??
Decision Trees
 Used to structure complex
decision problems
 Use expected return
criteria
 Consider probabilities of
occurrence of events
 Use:
 chance nodes (denoted by
circles )
 decision (or choice) nodes
(denoted by squares)
 Use a concept of “folding
back” to arrive at the best
policy
Example of a Decision Tree Problem
A glass factory specializing in crystal is experiencing a
substantial backlog, and the firm's management is
considering three courses of action:
A) Arrange for subcontracting
B) Construct new facilities
C) Do nothing (no change)
The correct choice depends largely upon demand, which may
be low, medium, or high. By consensus, management
estimates the respective demand probabilities as 0.1, 0.5,
and 0.4.
Example of a Decision Tree Problem (Continued):
The Payoff Table
The management also estimates the profits when choosing from the
three alternatives (A, B, and C) under the differing probable levels
of demand. These profits, in thousands of dollars are presented in
the table below:
A
B
C
0.1
Low
10
-120
20
0.5
Medium
50
25
40
0.4
High
90
200
60
Example of a Decision Tree Problem (Continued):
Step 1. We start by drawing the three decisions
A
B
C
Example of Decision Tree Problem (Continued): Step 2. Add our
possible states of nature, probabilities, and payoffs
High demand (0.4)
Medium demand (0.5)
Low demand (0.1)
A
High demand (0.4)
B
C
Medium demand (0.5)
Low demand (0.1)
High demand (0.4)
Medium demand (0.5)
Low demand (0.1)
$90k
$50k
$10k
$200k
$25k
-$120k
$60k
$40k
$20k
Example of Decision Tree Problem (Continued):
Step 3. Determine the expected value of each
decision
High demand (0.4)
Medium demand (0.5)
$62k
Low demand (0.1)
$90k
$50k
$10k
A
EVA=0.4(90)+0.5(50)+0.1(10)=$62k
Example of Decision Tree Problem
(Continued): Step 4. Make decision
High demand (0.4)
$62k
A
B
$80.5k
Medium demand (0.5)
Low demand (0.1)
High demand (0.4)
Medium demand (0.5)
Low demand (0.1)
C
High demand (0.4)
$46k
Medium demand (0.5)
Low demand (0.1)
$90k
$50k
$10k
$200k
$25k
-$120k
$60k
$40k
$20k
Alternative B generates the greatest expected profit, so
our choice is B or to construct a new facility
Problem 2
 Owner of a small firm
wants to purchase a PC for
billing, payroll, client
records
 Need small systems now -larger maybe later
 Alternatives:
 Small: No expansion
capabilities @ $4000
 Small: expansion @6000
 Larger system @ $9000
 After 3 years small
systems can
 be traded in for a larger
one @ $7500
 Expanded @ $4000
 Future demand is
 Likelihood of needing larger
system later is 0.80
 What system should he
buy?
Problem 2
L: .8
S: .2
9,000
9,000
9,000
10,000
Large
10,000
Need large
9,000
Exp
Exp
Trade-in
L: .8
S: .2
13,500
6,000
9,200
Small
11,500
Trade-in
Need large
L: .8
S: .2
10,000
4,000
11,500