Civil Systems Planning
Benefit/Cost Analysis
Paulina Jaramillo/Joe Marriott
12-706/19-702 / 73-359
Lecture 10
1
Structuring Decisions
All about the objectives (what you want to
achieve)
Decision context: setting for the decision
Decision: choice between options (there is
always an option, including status quo)
Waiting for more information also an option
Uncertainty: as we’ve seen, always exists
Outcomes: possible results of uncertain events
Many uncertain events lead to complexity
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Structuring Decisions (2)
Can use:
Fundamental objective hierarchy.
Influence diagrams.
Decision Trees
Risk Profiles
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Fundamental Objectives
Hierarchy
Increase Lifetime Earnings
Increase Current Salary
Find New Job
Update Resume
Marry Rich
Undergrad
Get a Raise
Network
Go to School
Grad School
Do a Better Job
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Influence Diagram/Decision
Trees
Probably cause confusion. If one
confuses you, do the other.
Important parts:
Decisions
Calculation/constant
Chance Events
Consequence/payoff
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Influence Diagram
Marry Rich
Undergrad
Go to School
Grad School
High Salary
Lifetime
Earnings
Find a Better Job
Work
Get a Raise
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Other Notes
Chance node branches need to be mutually
exclusive/exhaustive
Only one can happen, all covered
“One and only one can occur”
Timing of decisions along the way influences
how trees are drawn (left to right)
As with NPV, sensitivity analysis, etc, should be
able to do these by hand before resorting to
software tools.
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Solving Decision Trees
We read/write them left to right, but “solve” them
right to left.
Because we need to know expected values of
options before choosing.
Calculate values for chance nodes
Picking best option at decision nodes
We typically make trees with “expected value” or
NPV or profit as our consequence
Thus, as with BCA, we choose highest value.
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Texaco vs. Pennzoil
Settlement Amount ($ Billion)
Accept $2 Billion
2
Texaco Accept $5 Billion
5
(0.17)
(0.2)
Counteroffer
$5 Billion
Texaco Refuses
Final Court
Counteroffer
(0.5)
Decision
(0.5)
(0.3)
10.3
5
0
Texaco
(0.2)
Counteroffer
$3 Billion
Final Court
(0.33)
Decision
Refuse
Accept $3 Billion
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(0.5)
(0.3)
10.3
5
0
3
9
To Solve the Tree
Solve from right to left:
At chance node multiply monetary value to
probability and add them.
At choice node choose highest value.
EMV for Simple Texaco vs. Pennzoil Tree:
$4.63 Billion
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Risk Profiles
 Risk profile shows a distribution of possible payoffs
associated with particular strategies.
 A strategy is what you plan to do going in to the
decision. Holds your plans constant, allows chances to
occur
Only eliminate things YOU wouldn’t do, not things “they” might
not do.
 Its not just finding the NPV of a branch.
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Risk Profiles (cont.)
Let’s think about the “subset” of the Texaco decision
tree where we are only curious about the
uncertainty/risk profile associated with various
strategies to consider.
These represent the riskiness of each option
There are only 3 “decision strategies” in the base
Texaco case:
Accept the $2 billion offer (topmost branch of 1st dec. node)
Counteroffer $5 Billion, but plan to refuse counteroffer (lower
branch of 1st node, upper branch of second)
Counteroffer $5B, but plan to accept counteroffer (lower
branch of both decision nodes)
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Texaco vs. Penzoil, Again
Risk profile for “Accept $2 Billion” is obvious - get
$2B with 100% chance.
Risk Profile for "Accept to $2 Billion"
Chance that Settlement Equals X
120%
100%
100%
80%
60%
40%
20%
0%
0%
0
1
2
0%
0%
3
4
0%
0%
0%
0%
0%
0%
0%
5
6
7
8
9
10
11
x ($ Billion)
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Risk Profile Texaco Counteroffer, accept
$3 billion
 Below is just the part of original tree to consider when calculating
the risk profile:
Texaco Accept $5 Billion
5
(0.17)
(0.2)
Counteroffer
$5 Billion
Texaco Refuses
Final Court
Counteroffer
(0.5)
Decision
(0.5)
(0.3)
10.3
5
0
Texaco
Counteroffer
$3 Billion
(0.33)
Accept $3 Billion
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Texaco vs. Pennzoil, continued
Risk Profile for "Counteroffer $5 Billion, Accept Texaco's $3
Billion Counteroffer"
42%
40%
33%
35%
30%
25%
20%
15%
15%
10%
10%
Risk Profile for "Counteroffer $5 Billion, Reject Texaco's $3
Billion Counteroffer"
5%
0%
0%
0
1
2
0%
3
4
5
0%
0%
0%
0%
6
7
8
9
x ($ Billion)
0%
10
70%
11
Chance that Settlement Equals x
Chance that Settlement Equals x
45%
59%
60%
50%
40%
30%
25%
20%
17%
10%
0%
0
0%
0%
0%
0%
1
2
3
4
5
0%
0%
0%
0%
6
7
8
9
0%
10
11
x ($ Billion)
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Cumulative Risk Profiles
Graphs of cumulative distributions
Percent chance that “payoff is less than x”
Chance that payoff is less or equal to
x
Cumulative Risk Profile for 3 Options in Texaco Case
120%
100%
80%
60%
Counteroffer $5 Billion, Accept Texaco's
$3 Billion Counteroffer
Accept $2 Billion
40%
Counteroffer $5 Billion, Refuse Texaco's
$3 Billion Counteroffeer
20%
0%
0
2
4
6
8
10
12
x ($billion)
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Dominance
To pick between strategies, it is useful to
have rules by which to eliminate options
Let’s construct an example - assume
minimum “court award” expected is $2.5B
(instead of $0). Now there are no “zero
endpoints” in the decision tree.
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Dominance Example
Chance that payoff is less or equal to x
CRP below for 2 strategies shows “Accept
$2 Billion” is dominated by the other.
120%
100%
80%
60%
40%
20%
0%
0
2
4
6
8
10
12
x ($billion)
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Next Class
Multi-Attribute Decision Making.
Multi-Objective Programming.
Value of Information.
Homework Due.
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