1. Civil Systems Planning Benefit/Cost Analysis
Paulina Jaramillo/Joe Marriott
12-706/ /
Lecture 10

2. 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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3. Structuring Decisions (2)
Can use:
Fundamental objective hierarchy.
Influence diagrams.
Decision Trees
Risk Profiles
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4. Fundamental Objectives Hierarchy
Increase Lifetime Earnings
Increase Current Salary
Marry Rich
Go to School
Undergrad
Grad School
Find New Job
Get a Raise
Update Resume
Network
Do a Better Job
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5. 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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6. Influence Diagram Marry Rich Undergrad Go to School Grad School
Lifetime
Earnings
Grad School
High Salary
Find a Better Job
Work
Get a Raise
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7. 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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8. 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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9. Texaco vs. Pennzoil 12-706 and 73-359 Settlement Amount ($ Billion)
Accept $2 Billion 2
Texaco Accept $5 Billion 5
(0.17)
(0.5)
(0.33)
(0.2)
(0.3)
Counteroffer
$5 Billion
Final Court
Decision
10.3 5
Texaco Refuses
Counteroffer
Texaco
Counteroffer
$3 Billion
Final Court
Decision
10.3 5
Refuse
Accept $3 Billion 3
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10. 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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11. 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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12. 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)
How many decision strategies are there in general for a tree? Count based on the number of decision nodes!
In this case, we have 2 nodes. Thus 3 strategy options.
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13. Texaco vs. Penzoil, Again
Risk profile for “Accept $2 Billion” is obvious - get $2B with 100% chance.
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14. Risk Profile Texaco Counteroffer, accept $3 billion
Below is just the part of original tree to consider when calculating the risk profile:
Counteroffer
$5 Billion
Texaco
$3 Billion
Texaco Accept $5 Billion 5
Texaco Refuses
Final Court
Decision
10.3
Accept $3 Billion 3
(0.17)
(0.5)
(0.33)
(0.2)
(0.3)
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15. Texaco vs. Pennzoil, continued
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16. Cumulative Risk Profiles
Graphs of cumulative distributions
Percent chance that “payoff is less than x”
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17. 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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18. Dominance Example
CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other.
If there is a value x such that the chance of the payoff being less than x is 100% in alternative B and the chance of payoff being less than x in alternative A is 0%, then B is dominated by A.
Graphically: Continue the the vertical line where alternative A laves 0%. If that vertical lines meets with 100% for Alternative B, then A dominates B.
and

19. Next Class Multi-Attribute Decision Making.
Multi-Objective Programming.
Value of Information.
Homework Due.
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