### Decision

```Chapter 10 - Objectives
 Structure uncertain decisions – tree format
 Symmetric
 Asymmetric
 Sequential decisions and Information seeking
 Analyze uncertain decisions
 Solve a decision tree – Maximize (or Minimize) the expected value
 Risk Profile
 Simple tree
 Sequential decisions
 Asymmetric tree
 Sensitivity Analysis – Robustness – easy to do with Precision Tree
Chapter 10
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Analyze uncertain decisions
 Create Tree
Structure
 Symmetric Tree
 Asymmetric Tree
 Input
data on probabilities and values
 Construct mathematical equation of objective function
 Solve a decision tree – Maximize (or Minimize) the
expected value
 Risk Profile
 Sensitivity analysis of parameters
 Excel
spreadsheet structure  facilitate sensitivity
analysis of key parameters
Chapter 10
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Users of Decision Trees
 Oil
(Energy) – Shell, Chevron, Exxon, Conoco, Texaco,
 Pharmaceuticals (Medical) – Eli Lilly, Abbot Labs, Merck,
Pfizer, Bristol Myers, Baxter
 Chemical – Monsanto, DuPont
 Consulting groups – Strategic Decisions, Innovative
Decisions
 Individual companies
 AT&T
 GM, Kodak (Decision analysis not a substitute for good product
development strategy and implementation)
Chapter 10
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Investment in Automation
Boss Controls (BC) is gearing up to manufacture an option to be made
available on 1 million new cars world-wide. Initial estimates are that the
take rate for the option could be as low as 30% or as high as 50%. Assume
the 50% take rate has a 0.6 probability of occurring. The plan calls for BC to
deliver the option to the OEM’s at a price of \$60. Timothy O’Leary,VP for
imaginative products, is considering two alternatives that differ significantly
in the level of investment in automation and the related variable cost of
production.
Low Investment = \$8M
Variable Cost = \$27 per option
=======================================================================
High Investment = \$13M Variable Cost = \$14 per option
Chapter 10
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Schematic of Boss Controls
Without data & symmetric
rectangle  decision
circle  random event
Automation
Investment
Decision
Chapter 10
Demand
Uncertainty
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Information Content in Decision Tree
 Tree
Construction – Layout -- Information regarding
relationships (& sequence) between decisions and
uncertainty.
 Probabilities - Information regarding uncertainty
 Assigned to branches of random events
 Value
- Information regarding cost or profits or parameters
 Associated with all branches: events and decisions
 Formula
captures how the values interrelate.
Specific Goal: Maximize or Minimize Expected Value
Implied Real Goal: Update Intuition
Chapter 10
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Figure 10.1: A basic decision tree with one
decision node and one random node
Chapter 10
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Figure 10-2: Influence diagram for capacity
planning example
Sales
Competitor
Actions
How Much
Capacity
Total
Revenue
Actual
Yield
Total
Profit
Total Cost
Star Electronic, a cellular phone manufacturer, is exploring optimum production capacity for a new phone.
The new product requires a new production line and there is uncertainty regarding its yield. Management
is focusing on three capacity options. Their competitor’s new product may have either marginal or
significant impact on the demand for Star’s new product, which could be high, medium, or low.
Chapter 10
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Figure 10.3: Schematic tree for capacity
planning example
How Much
Capacity
Chapter 10
Yield
Competitor Sales
Actions
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Figure 10.4 Design change asymmetric tree
Solves
Problem
Yes
Yes
No
Make Design
Change
No
Manufacturing
Savings
Warranty
Costs
Manufacturing
Savings
Warranty
Costs
It is only 6 months before the vehicle launch of the MX36. A sound emanating from the instrument panel
has been detected on some test drives. However, engineers are not able to reproduce the sound in a
controlled environment. They are fairly certain the problem is from a series of three assembled parts.
They have a new single modular design that can be implemented quickly and should solve the problem.
There is a potential added benefit from the modular design: reduced manufacturing and assembly cost.
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Figure 10.5: Influence diagram for machine planning for
capacity example: sequential decisions
Machine type  number of machines
Competitor’s
Actions
Total
Demand
Initial
Yield
Annual
Production
Learning
Curve
Machine
Type
Chapter 10
How Many
Machines
Total Cost
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Total
Revenue
Net
Profit
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Figure 10.6: Schematic tree for machine
planning for capacity example
Type of
Machine
Chapter 10
How Many
Machines
Yield
Learning
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Competitor Total
Demand
Actions
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Controlled Forest Fire Case
A fire set under controlled conditions is an important tool in managing
the national forests of the United States. These fires are used to clear
away forest residue that might otherwise turn a minor fire into a major
conflagration. A prescribed burn might be used to clear an area as small
as 15 acres in the Tahoe National Forest in Nevada or as large 2000 acres
in the Prescott National Forest in Arizona. They are also utilized to
enhance wildlife habitat and prepare a site for seedlings. However,
planning and executing a controlled fire is a complex and risky process.
The spread of a fire is affected by uncertainty surrounding the
environmental conditions and the fire's behavior once it is started.
Decision makers must decide under what conditions to start a fire and
the level of resources to made available on-site as the controlled fire is
initiated. The final outcome is also uncertain as to its effects on vegetation,
soil, timber, hazards, and wildlife. Once a fire plan has been established,
decision makers still must make a careful assessment of current and
forecasted weather conditions before going ahead.
Chapter 10
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Figure 10.7: Controlled forest fire (Cohan et al.
1984) – Information  delay 2nd decision
Random Event
Commit
Resources?
Test Burn
Outcome
- Preferred
- Acceptable
- Unacceptable
Chapter 10
Decision Node
Initiate
Full Burn?
Environmental
Conditions
- Wind
- Temp
- Humidity
- Stability
Fire
Behavior
- Intensity
- Rate
- Spotting
- Smoke
- Flame Length
Chelst & Canbolat
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Real-Time
Burn Decisions
- Continue
- Modify
- Stop
- Escape
Fire
Effects
- Vegetation
- Soil
- Timber
- Hazards
- Wildlife
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Sequential and Conditional Decisions
 Sequential Decisions
 Two or more decisions in sequence followed by one ore more
random events
 Schematic tree
 Conditional Decisions
 A decision followed by a random event followed by another
decision followed by more random events
 Optimal second decision depends on the first decision and the
outcome of the first random event.
 Schematic tree
Chapter 10
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Activity: Conditional Decisions
A
sequence of decisions with random events in between
 A random event corresponds to gaining information
before the next decision
 Describe your own example of a sequence of decisions
and random events interspersed.
 _________________
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Probability Decision Tree Basics
Making Choices Through Analysis
 Decisions = Square Nodes
 Branches = Alternatives
 Random Events = Circle Nodes
 Branches = Set of Outcomes
 Probabilities  attached to every branch from a random (circle) node
 Values
(Intermediate)  Numbers stored on some branches
 Values of each decision alternative and sequence of
probabilistic outcomes
 Final Numbers just appear at end of tree branches.
 Specific
math formula  used to calculate the Final Values
 Value Storage in SOFTWARE varies by software package
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Basic Analytic steps
 Tree
Construction - generally straightforward
 Asymmetric trees can be complex
 Calculation
of End Point Values
 Textbook Trivial
 Real-world decisions can involve complicated formulae or even
complex spreadsheets
 Minimize
(or Maximize) Expected Value - Tree
Rollback - Trivial calculation of Expected Value
E(X) =  X P(X)
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Results “Analysis”
 Compare
Expected Values
 Compare Risk Profiles
 Magnitude of downside risk
 Probability of worst case scenario
 Robustness of optimal strategy
 Probabilities
 Values and other parameters
Chapter 10
with regard to
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Advanced Tree Analysis
 Value
& Risk Management
 Max improvement – Expected Value of Perfect Control (EVPC)
 Change Probability or Value of a negative (or positive) outcome and
calculate its impact on the expected value of the optimal strategy.
 Attitude
towards risk - utility theory
 Integrate
risk and multiple objectives
 Sequentially – Risk profile input into multiple objectives
 Precision Tree Software does NOT allow you to track on the tree
multiple values/objectives (e.g. cost & time) of the same decision
while optimizing one specific objective function.
 Create parallel trees.
 Input single MAUT formula
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Investment in Automation
Construct and Solve Probability Decision Tree
Boss Controls (BC) is gearing up to manufacture an option to be made
available on 1 million new cars world-wide. Initial estimates are that the
take rate for the option could be as low as 30% or as high as 50%. Assume
the 50% take rate has a 0.6 probability of occurring. The plan calls for BC to
deliver the option to the OEM’s at a price of \$60. Timothy O’Leary,VP for
imaginative products, is considering two alternatives that differ significantly
in the level of investment in automation and the related variable cost of
production.
Low Investment = \$8M
Variable Cost = \$27 per option
=======================================================================
High Investment = \$13M Variable Cost = \$14 per option
Chapter 10
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Investment in Automation
Structure Decision Tree
30% Take
Low
50% Take
Automation
Investment
30% Take
High
50% Take
Names of branches
Chapter 10
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Investment in Automation
Input Data and Solve Probability Decision Tree
 Input the fixed costs along the appropriate branches
 Calculate the total variable cost of production at each branch
 At End value node: Travel along each path from the root node
until the end node adding and subtracting costs along the way.
Record the values at the end of each branch-path.
 At Random event node: Roll back the tree – Calculate
expected values at every random event node.
 At the Decision node: Compare the expected values and
select the better value.
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Figure 10.1: A basic decision tree with one
decision node and one random node
Calculated
Expected Value
Probability
Calculated
End Values
Values
Optimal: Minimize
Expected Value
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Formula to calculate value on Take_Rate branch
 Total
Revenue = Volume*Take_rate*(Price – Variable Cost)
 Calculate
for Low Investment and Low Take_rate =
 Calculate
for High Investment and High Take_rate =
OEM’s price of \$60.
Take_rate is 30% or 50%
Variable Cost with low investment = \$27 per option
Variable Cost with high investment = \$14 per option
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Figure 10.8: - Automation investment: Calculate
revenue and end values – sum values along path
Calculated
Revenue
Calculated
End Values
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Rollback Tree
Random event  Calculate expected value
Decision node  Choose better value
Calculated
Expected Value
High
50%
TRUE
-13
Automation Investment
Choose smallest
Expected Value
Decision
6.32 (MAX{6.32, 5.86})
Low
-8
Chapter 10
23
0.6
10.0
Take Rate
6.32 (=10*0.6 + 0.8*0.4)
40.0%
0.4
30%
0.8
13.8
50%
FALSE
60.0%
60.0%
16.5
Optimal
prob.
0
8.5
Non- Optimal.
path
Take Rate
5.86 (=8.5*0.6 + 1.9*0.4)
40.0%
0
30%
1.9
9.9
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Risk Profile
Do NOT expect the Expected Value!
\$6.32 million WHY?
 Expected
value is a weighted sum - Multiply the
probabilities along the path by the endpoint value
 Profile
– Group equal values and sum their associated
probabilities
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Figure 10.10: Automation Investment - Risk profile
0.6
0.5
Probability
0.4
50%
30%
0.3
0.2
0.1
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10
9
8
7
6
5
4
3
2
1
0
0
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Figure 10.11: Automation Investment Cumulative risk profile
Cumulative Probability
1
0.8
0.6
50%
30%
0.4
0.2
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10
9
8
7
6
5
4
3
2
1
0
0
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Maximum value of risk management
Expected Value of Perfect Control (EVPC) of
random event
 Goal: Determine
the value of eliminating Uncertainty
or Risk
 This provides an upper bound on the value of risk
management with regard to that uncertainty.
 Process:
 Assign probability of “1” to the best outcome of an
uncertain event.
 Recalculate the overall expected value.
 The NET Improvement in expected value is the EVPC.
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Expected Value of Perfect Control: Automation Investment
Assign probability of “1” to best outcome
Net Change: \$10 – 6.32 = \$3.68 million
100%
50%
High
Automation Investment
TRUE
-13
Decision
10 (MAX(10, 8.5))
Take Rate
10 =10*1 + 0.8*0)
0%
30%
13.8
50%
Low
FALSE
-8
Chapter 10
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100%
16.5
1.0
10.0
0
0.8
0
8.5
Take Rate
8.5=8.5*1.0 + 1.9*0)
0%
0
30%
1.9
9.9
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Investment in Automation
Robustness of Optimal Solution?
 The “High”
investment alternative involves a new
technology.
 Management is concerned that the capital equipment estimate
could be off by + 7%.
 There is even more concern regarding the variable cost estimate
that could be off by + 10%
 The
Low investment alternative is well tested and there is
hope that continuous improvement could reduce the
variable cost by 5%.
 Because they did not know, they set the take rate
probabilities at 0.6 and 0.4 respectively. However, there is a
lot of uncertainty regarding this probability.
Chapter 10
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Investment in Automation
Robustness of Optimal Solution
 Magnitude
of Difference = (\$6.32M-\$5.86M) = \$460,000
 Investment(s)
 How much increase in HIGH Investment fixed cost results in
change in best decision?
 Variable
Cost(s)
 How much would the variable cost for Low Investment have to
decline to make it preferred?
 Probability
of 30% take rate: Increases? Decreases?
 What else might change and why?
Chapter 10
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Precision Tree Sensitivity Analysis
Output – Separate Worksheets

Sensitivity – one parameter at a time
 Multiple lines – Objective function for each decision. Crossing
lines  change in optimal decision
 One line –Objective function for optimal strategy: A change in
optimal decision is usually bend in line
Chapter 10
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Figure 10.23: Sensitivity analysis automation
investment – fixed cost of high investment
Expected Value
7.5
7
6.5
High
Low
6
5.5
-\$12.0
-\$12.2
-\$12.4
-\$12.6
-\$12.8
-\$13.0
-\$13.2
-\$13.4
-\$13.6
-\$13.8
-\$14.0
5
High Investment
Chapter 10
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Figure 10.24: Expected value of the optimal decision for
each value of the fixed cost of high investment.
7.5
Expected Value
7
6.5
6
5.5
Chapter 10
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Value Added Decision Making
-\$12.0
-\$12.2
-\$12.4
High Investment
-\$12.6
-\$12.8
-\$13.0
-\$13.2
-\$13.4
-\$13.6
-\$13.8
-\$14.0
5
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Figure 10.25: Sensitivity analysis automation investment –
low take rate probability
8.5
8
Expected Value
7.5
7
6.5
6
High
5.5
Low
5
4.5
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
4
Low Probability
Chapter 10
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Figure 10.26: Sensitivity analysis automation investment –
variable cost of high investment
7.5
Expected Value
7
6.5
High
Low
6
\$16.0
\$15.5
\$15.0
\$14.5
\$14.0
\$13.5
\$13.0
\$12.5
\$12.0
\$11.5
5.5
Variable Cost - High Investment
Chapter 10
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Figure 10.27: Sensitivity analysis automation investment –
variable cost of low investment
Expected Value
6.4
6.2
High
6
Low
5.8
\$27.2
\$27.0
\$26.8
\$26.6
\$26.4
\$26.2
\$26.0
\$25.8
\$25.6
5.6
Variable Cost – Low Investment
Chapter 10
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Figure 10.28:
Strategy region
graph for two-way
sensitivity analysis
Chapter 10
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Make or Buy Decision
 Decision
Context: Manufacture a component yourself or
contract with a supplier to manufacture it.
There is a design for a component but you are not sure when it
comes time to manufacture, that the design will be feasible as is. If
not, there will need to be a quick major redesign of the component. If
you manufacture it, you expect that with the redesign it will cost 8%
more than the original estimate. The decision to make or buy must
be made now before you have time to fully check out the design. The
demand for the product is also uncertain. If you sign a contract with
the supplier for a specific piece price, if the current design turns out
to be infeasible, you know the supplier will use the design change as
an excuse to increase the price 15%.
Continued…
Chapter 10
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Make or Buy Data
Random Events
1. Design Feasibility (Prob.)
Current Design will Work
Need a Major Redesign
0.4
0.6
2. Demand (Volume & Prob.)
Low
1.0 million
0.3
Medium 1.25 million
0.5
High
1.5 million
0.2
Chapter 10
Costs: Make In-House
Facility investment fixed Cost -\$55M
Variable Cost/ per part
If current design works - \$100/part
If new Design is needed - \$108/part
Costs: Buy from Supplier
Facility investment fixed Cost - \$0
Variable Cost/ per part
If current design works - \$140/part
If new Design is needed - \$161/part
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Activity: Construct Schematic Tree
Make or Buy Decision
Chapter 10
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Activity: Make or Buy
Construct & Analyze Tree
 Lay out Tree without numbers.
 Insert Probabilities.
 Write BELOW a formula to calculate Total
Cost.
 Total Cost =
__________________________
Chapter 10
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Figure 10.12: Make/Buy structure
a) Influence diagram
Chapter 10
b) Schematic tree
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Activity: Formula & Construct Tree

Use the formula to determine TWO end values
 Make  Design works  Low Demand
= \$\$_____________
 Buy  Design Does Not Work  High Demand
= \$\$_____________
Fill in Tree on slide – Roll it back.
Chapter 10
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Low
Design Feasibility
Prob
Make Costs
1
Works
Buy Costs
Works
0.4
100
140
Does NOT
0.6
108
161
8%
15%
Premium
30.0%
40.0%
100
Demand
\$\$_______
Medium
50.0%
1.25
Current Design
Make
TRUE
55
High
20.0%
1.5
\$\$________
Low
30.0%
1
Demand
1
1.25
1.5
Prob.
0.3
0.5
0.2
Fixed Costs
Make
55
Buy
0
Does NOT work 60.0%
108
\$_______
0.2
180
0.08
205
0.18
163
Demand
187.3
Medium
50.0%
High
20.0%
1.25
Decision
0.12
1.5
0.3
190
0.12
217
Make or Buy
\$\$__________
Low
30.0%
1
Works
40.0%
Demand
140
171.5
Medium
50.0%
High
20.0%
1.25
Make or Buy
Current Design
Buy
FALSE
0
Low
0
210
30.0%
0
161
1
Notice the values that are stored
on each branch. A formula is used
to calculate the end values.
Chelst & Canbolat
Value Added Decision Making
Demand
\$\$_______
Medium
50.0%
High
20.0%
1.25
1.5
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0
175
1.5
\$\$__________
Does NOT work 60.0%
161
0
140
0
201.25
0
\$_______
Expected value
Design Feasibility
Prob
Works
0.4
Does NOT
0.6
Premium
Make Costs
100
108
8%
Low
Buy Costs
1
Works
140
40.0%
161
177.5
Medium
50.0%
High
20.0%
1.25
15%
TRUE
55
Prob.
0.3
0.5
0.2
1.5
Current Design
183.38
Low
30.0%
1
Does NOT work 60.0%
108
Decision
0.2
180
0.08
205
0.18
163
Demand
187.3
Medium
50.0%
High
20.0%
1.25
Fixed Costs
Make
55
Buy
0
0.12
155
Demand
100
Make
Demand
1
1.25
1.5
30.0%
1.5
0.3
190
0.12
217
Make or Buy
183.38
Low
30.0%
1
Works
40.0%
Demand
171.5
140
Medium
50.0%
1.25
High
Make or Buy
Buy
FALSE
0
20.0%
1.5
Current Design
186.935
Low
30.0%
1
Does NOT work 60.0%
161
Expected value
0
175
0
210
0
161
Demand
197.225
Medium
50.0%
High
20.0%
1.25
1.5
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0
140
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0
201.25
0
241.5
Figure 10.13: Complete
Make/Buy decision tree
Modify picture
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Figure 10.14 Partial decision tree Make/Buy
Chapter 10
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Make or Buy: Interpret Answer
Chapter 10

\$183.4 Million (Make) vs. \$186.9 Million (Buy)

Is the \$3.55 Million Difference significant to you?

If it were hundreds of millions would it matter more?

Don’t Expect the Expected Value!!!
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Make or Buy: Interpret Answer
 What is \$9 Billion worth of purchases divided
by \$180 Million per decision? 50
 How can you use this number to justify the
use of Expected Values?
 Is a net \$177.5 Million difference significant?
50 x \$3.55 M
Chapter 10
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02/26/12
Risk Profile- Sort Ordered: Class Exercise
Buy
Make
Value
Value
Probability
Probability
1.
________
______
1.
________
______
2.
________
______
2.
________
______
3.
________
______
3.
________
______
4.
________
______
4.
________
______
5.
________
______
5.
________
______
6.
________
______
6.
________
______
What do you notice?
Chapter 10
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Statistics & Risk Profile – Precision Tree Output
S T A T IS T IC S
M a ke
D e c is io n
M ean
1 8 3 .3 8
M in im u m
1 5 5 .0 0
M a xim u m
2 1 7 .0 0
M ode
1 9 0 .0 0
S td D e v
1 8 .9 7
Chapter 10
P R O F IL E :
Buy
1 8 6 .9 4
1 4 0 .0 0
2 4 1 .5 0
2 0 1 .2 5
2 9 .5 8
Chelst & Canbolat
Value Added Decision Making
M ake
#
X
Buy
P
X
P
1 155
0 .1 2
140
0 .1 2
2 163
0 .1 8
161
0 .1 8
3 180
0 .2 0
175
0 .2 0
4 190
0 .3 0
201
0 .3 0
5 205
0 .0 8
210
0 .0 8
6 217
0 .1 2
242
0 .1 2
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55
Figure 10.15: Risk profile for Make/Buy
Chapter 10
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C u m u la tiv e P r o b .
Cumulative Risk Profile: Precision Tree Output
1 .2
1 : M ake
1
2 : Buy
0 .8
0 .6
0 .4
0 .2
0
120
140
160 180
200
220
240 260
280
V a lue
MAKE
BUY
Chapter 10
P(X < 180) = ___,
P(X < 180) = ___,
P(X<190) = ____, P(X<220) = ____
P(X<190) = ____, P(X<220) = ____
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Figure 10.16: Cumulative risk profile for
Make/Buy
Chapter 10
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Cumulative Risk Profile:
What do you observe?
P(X < 180) =
 P(X < 190) =
 P(X < 220) =
 Which is better: graph further to the left or to the right
when minimizing?
 IF Stochastic Dominance – no crossing of lines  Strategy
is preferred irrespective of risk attitude
 What would the answer be if the problem Maximized Profit
instead of Minimizing Cost?

Chapter 10
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Value Added Decision Making
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02/26/12
Statistics & Risk Profile – Precision Tree Output
Stochastic Dominance of New Alternative “B”
Make
Supplier A
Supplier B
Design Works (\$/ Part)
100
140
147
Premium (If Design does
NOT Work)
8%
15%
10%
P R O F IL E :
M ake
S T A T IS T IC S
M a k e S u p p lie r A
S u p p lie r B
S u p p lie r A
S u p p lie r B
#
X
P
X
P
X
P
M ean
1 8 3 .4
1 8 6 .9
1 9 0 .9
1
155
0 .1 2
140
0 .1 2
147
0 .1 2
M in
1 5 5 .0
1 4 0 .0
147
2
163
0 .1 8
161
0 .1 8
162
0 .1 8
M ax
2 1 7 .0
2 4 1 .5
2 4 2 .5
3
180
0 .2 0
175
0 .2 0
184
0 .2 0
M ode
1 9 0 .0
2 0 1 .3
2 0 2 .1
4
190
0 .3 0
201
0 .3 0
202
0 .3 0
1 9 .0
2 9 .6
2 8 .7
5
205
0 .0 8
210
0 .0 8
221
0 .0 8
6
217
0 .1 2
242
0 .1 2
243
0 .1 2
S td D e v
Chapter 10
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Figure 10.18: Cumulative profile showing
dominance of Supplier A over Supplier B
Cumulative Probability
1
0.8
Make
0.6
Suuplier A
Supplier B
0.4
0.2
Chapter 10
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Value Added Decision Making
280
260
240
220
200
180
160
140
120
0
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61
Asymmetric Decision Tree
 It
is only six months before vehicle launch. On some
occasions on test drives, individuals have noticed a
sound emanating from the instrument panel. However,
engineers are not able to reproduce the sound in a
controlled environment. They are pretty sure the
problem is from a series of three assembled parts. They
have a new single modular design that can be
implemented quickly and that should solve the problem.
There is a potential added benefit from the modular
design: reduced manufacturing and assembly cost.
Chapter 10
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02/26/12
A Design Change Decision
Specific Case
 Volumes 100,000 vehicles
 One year’s production is relevant
Current
Customers Notice
0% warranty p = .50
1% warranty p = .30
5% warranty p = .20
Cost/warranty = \$50
Chapter 10
Proposed
Solves Problem p = .8
Fixed Costs \$150,000
Manufacturing Savings
\$0
p = .30
\$ 2.50 p = .70
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Design Change - Schematic Tree & Formula
Warranty Cost
Solves Problem
Design Changes
Total
Cost
Mnfg. Savings
 End Value
 Current Design: Warranty Claim * Warranty Cost * Volume
 New Design: Fixed Cost + (Warranty Claim * Warranty Cost * Volume)
+ (Manufacturing Savings * Volume)
Chapter 10
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Asymmetric Schematic Probability Decision
Tree – Design Change
Solves
Problem
Yes
No
Make Design
Change
Chapter 10
Manufacturing
Savings
Warranty
Costs
Manufacturing
Savings
Warranty
Costs
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Figure 10.19: Decision
tree for design change
example
Chapter 10
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Figure 10.20: Design change – Risk profile
Chapter 10
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Design Change – Risk Profile
Cumulative Probability
Cumulative Probability For Change Design of Change Design
1.2
1
0.8
1 : Yes
0.6
2 : No
0.4
0.2
0
-500000 -400000 -300000 -200000 -100000
0
100000
200000
Value
Chapter 10
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Interpret Risk Profile &
Motivate Next Lecture
 Describe Worst
 What
Case Scenario for preferred strategy
is its probability?
 Describe
a Bad Scenario with a substantial probability of
occurrence.
 What
Chapter 10
is its probability?
Chelst & Canbolat
Value Added Decision Making
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02/26/12
None
Warranty Claims
Prob.
Percent
0.5
0
0.3
0.01
0.2
0.05
Volumes
100000
Warranty \$
50
Fixed Costs
150000
Yes
80.0%
0
Manuf. Savings
25000
70.0%
250000
2.50
Yes
TRUE
-150000
30.0%
0
Solves Problem
12000
50.0%
None
0
Manuf. Savings
Prob.
Amount
0.3
0
0.7
2.5
Solves Problem
Yes
0.8
No
0.2
0.24
-150000
0.56
100000
None
Manuf. Savings
25000
2.50
No
20.0%
0
Warranty Claims
-40000
None
30.0%
-50000
Low
20.0%
-250000
Decision
12000
None
No
FALSE
0
0
0
Warranty Claims
-65000
0
Low
High
Chapter 10
50.0%
0
30.0%
-50000
20.0%
-250000
-50000
0
-250000
Chelst & Canbolat
Value Added Decision Making
30.0%
0
0.018
-200000
70.0%
250000
30.0%
0
0.042
50000
0.012
Manuf. Savings -400000
-225000
2.50
Change Design
0.07
100000
-25000
None
0.03
-150000
70.0%
250000
Manuf. Savings
2.50
High
30.0%
0
70.0%
250000
0.028
-150000
Answers to
Design Change
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Chapter 10 additional Figures
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Figure 10.21: Decision
tree for capacity
expansion case
Chapter 10
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Figure 10.22: Risk profile for capacity
expansion case
1
Cumulative Probability
0.8
0.6
Old Tech.
New Tech.
Productivity
0.4
0.2
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40
38
36
34
32
30
0
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Figure 10.29: Schematic tree of postal
automation
Chapter 10
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Figure 10.30: Schematic decision tree for the transmission
line problem
Chapter 10
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Figure 10.31: Decision
tree for drug
development strategy
Chapter 10
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Figure 10.32: Peak and expected peak sales for
drug development strategy case
Chapter 10
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