1. Chapter 3: Strategic Capacity Management

2. 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

3. Strategic Capacity Planning
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?? 3

4. 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, …)

5. 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
Underutilization
Best Operating
Level
Avg
unit cost
of output
Volume
Overutilization 5

6. 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% 6

7. Economies & Diseconomies of Scale
100-unit
plant
200-unit
300-unit
400-unit
Volume
Average
unit cost
of output
Economies of Scale and the Experience Curve working
Diseconomies of Scale start working

8. 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 10

9. Capacity Planning: Balance
Unbalanced stages of production
Units
per
month
Stage 1
Stage 2
Stage 3
6,000
7,000
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
Stage 3
6,000
6,000
6,000 12

10. Little’s Law Can be used in analyzing capacity issues!
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
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00 11 10 9 8 7 6 5 4 3 2 1
Flow Time
Inventory
Inventory=Cumulative Inflow – Cumulative Outflow
Cumulative
Inflow
Outflow
Time
Patients
Can be used in analyzing capacity issues!

11. Examples
Suppose that from 12 to 1 p.m. 200 students per hour enter the GQ and each student is in the system for an average of 45 minutes. What is the average number of students in the GQ?
Inventory = Flow Rate * Flow Time
= 200 per hour * 45 minutes (= 0.75 hours)
= 150 students
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 = hour
= 120 students per hour
Airline check-in data indicate from 9 to 10 a.m. 255 passengers checked in. Moreover, based on the number waiting in line, airport management found that on average, 35 people were waiting to check in. How long did the average passenger have to wait?
Flow Time = Inventory / Flow Rate = 35 passengers / 255 passengers per hour = hours
= 8.24 minutes

12. 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

13. Capacity Analysis with Batching
Capacity calculation:
Note: Capacity increases with batch size:
Note further: … and so does inventory
Batch Size
Set-up time + Batch-size*Time per unit
Capacity given Batch Size=
(in units/time)
Capacity
1/p
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5 10 50 90
130
170
210
250
290
330
370
410
450
490
530
570
610
650
Batch Size

14. Data about set-up times and batching
Process 1
Assembly process
120 minutes -
Per unit time, p
2 minutes/unit
3 minutes/unit
Capacity (B=12)
units/min
0.33 units/minute
Capacity (B=300)
units/min

15. B/[S+B*p] = k implies that B = S*k / (1 – p*k)
Figure : Choosing a “good” batch size
Batch size is too small, process capacity could be increased (set-up step is at the bottleneck)
Batch size is too large, could be reduced with no negative impact on process capacity (set-up is not at the bottleneck)
Capacity
1/p
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5 10 50 90
130
170
210
250
290
330
370
410
450
490
530
570
610
650
Batch Size
Capacity of slowest
step other than the one
requiring set-up
B/[S+B*p] = k implies that B = S*k / (1 – p*k)

16. Problem Part a: What is the capacity for a batch size = 50?
Part b: For a batch size of 10, what is the bottleneck
What batch size should be chosen to smooth the flow?

17. 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 ??

18. 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

19. 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. 20

20. 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:
0.1
0.5
0.4
Low
Medium
High A 10 50 90 B
-120 25
200 C 20 40 60 21

21. Example of a Decision Tree Problem (Continued): Step 1
Example of a Decision Tree Problem (Continued): Step 1. We start by drawing the three decisions A B C 22

22. $90k $50k $10k A $200k $25k B -$120k C $60k $40k $20k
Example of Decision Tree Problem (Continued): Step 2. Add our possible states of nature, probabilities, and payoffs A B C
High demand (0.4)
Medium demand (0.5)
Low demand (0.1)
$90k
$50k
$10k
$200k
$25k
-$120k
$60k
$40k
$20k 23

23. Example of Decision Tree Problem (Continued): Step 3
Example of Decision Tree Problem (Continued): Step 3. Determine the expected value of each decision
$90k
High demand (0.4)
Medium demand (0.5)
Low demand (0.1)
$50k
$62k
$10k A
EVA=0.4(90)+0.5(50)+0.1(10)=$62k 24

24. Example of Decision Tree Problem (Continued): Step 4. Make decision
High demand (0.4)
Medium demand (0.5)
Low demand (0.1) A B C
$90k
$50k
$10k
$200k
$25k
-$120k
$60k
$40k
$20k
$62k
$80.5k
$46k
Alternative B generates the greatest expected profit, so our choice is B or to construct a new facility 25

25. 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 $4000
Small:
Larger $9000
After 3 years small systems can
be traded in for a larger $7500
$4000
Future demand is
Likelihood of needing larger system later is 0.80
What system should he buy?

26. Problem 2 L: .8 9,000 S: .2 10,000 Large Exp Need large Trade-in
13,500
6,000
9,200
Small
11,500
4,000