Todays Goals

1
Todays Goals

• Structuring Decisions
• Determine attributes for a hierarchy
• Calculate NPV
• Structure an Influence Diagram
• Homework 1 (due Tuesday September 16)
• Value of Patience
• Early Bird Inc.
• SS Kuniang
• Read Influence Diagrams by Ron Howard and James
  Matheson

2
Value Hierarchy

• A value hierarchy is intended to help decision
  makers clearly think about their values, and thus
  be able to state their objectives.
• How do we compare financial costs with, say,
  trees?

3
Structuring ObjectivesKR 2 CR p44-51 K 2

• A value or evaluation consideration are the
  things we care about, the things that should be
  taken into account when evaluating alternatives.
• Costs
• profits
• Health
• An objective indicates a direction in which we
  strive to do better.
• minimize costs
• maximize profits
• minimize traffic deaths
• An attribute is how you measure an objective
• costs and profits may be measured in discounted
  dollars (with a particular discount rate)
• Traffic deaths is the attribute for the third
  objective.
• A goal is something that we either achieve or
  not.
• reduce costs to below 1M/year
• No more than 100 traffic deaths per year.

4
Developing Attributes
5
Checklist for attributes

• Complete
• Have we included all areas of concern?
• Operational
• Meaningful to decision maker
• Facilitate communication
• Non-redundancy
• Avoid double counting
• Minimum size
• Decomposable
• Useful if some of the attributes are independent
  from one another it eases the assessment of
  preferences.

6
Prescribed Fire

• As a class, lets develop attributes for the
  controlled burning case study.

7
Prescribed Fire
8
Time Preference

• 100 a year from now is not worth as much as 100
  today. Why?

9
Time Preference

• 100 a year from now is not worth as much as 100
  today. Why?
• Impatience
• Uncertainty
• Real returns
• The market reflects this through interest
• Also called the time value of money
• Market interest rate vs personal discount rate

Example Seed
10
Interest

• What will be the value in the future of money
  invested today?
• Compound Interest
• money invested grows by (1r) each year.
• If you invest x, then in 2 years you will have
  x(1r)(1r) x(1r)2
• After n years you will have x(1r)n

11
Present Value

• What is the value today of money you will receive
  in the future?
• How much would you need to invest today, at 10
  interest, in order to have 110 in a year?
• The present value of 110 to be received in a
  year, when interest rate is 10 is 100.

12
Present value

• In general, in order to have x a year from now,
  how much do you need to invest (given an interest
  rate r)?
• y(1r) x
• Invest y x/(1r)
• You multiply by a discount factor d 1/(1r)
• The PV of x to be paid in a year is
• dx x/(1r)

13
Present Value of a cash flow stream

• What is the value of the cash flow stream
  (x0,x1,x2,,xn)? Assume interest is compounded
  each period.
• the PV of x1 is x1/(1r)
• the PV of x2 is x2/(1r)2
• the PV of xn is xn/(1r)n
• The PV of the stream is
• x0 x1/(1r) x2/(1r)2 xn/(1r)n

14
Present value of a cash flow stream

• Example What is value of (-2,1,1,1) at 10?

15
Net Present Value

• The Net Present Value of a project is the Present
  Value of the returns minus the initial cost. NPV

16
Developing Alternatives

• Use creativity to develop more alternatives for a
  problem.
• The value hierarchy can be very helpful here.
• When uncertainty is involved you may want to
  consider alternatives that are not interesting in
  a deterministic case
• Hedging
• Options

17
Influence Diagrams

• IDs are a way of structuring a decision problem.
• They can be used at an abstract level to
  understand
• What information will be known when decisions are
  made and
• Which chance events are relevant to each other
• They can also be used with details to solve the
  decision problem.

18
Influence Diagrams

• Decisions and Alternatives
• Uncertain events and outcomes
• Consequences (how outcomes effect the decision
  maker)

19
Influence Diagrams

• Decisions and Alternatives
• Uncertain events and outcomes
• Consequences (how outcomes effect the decision
  maker)
• Probabilistic relevance (which chance events are
  relevant to each other)
• Information available (what will be known when
  decisions are made)

20
Influence Diagramsnodes

• Squares represent Decisions/Actions (alternatives
  that can be chosen, such as particular missions,
  or investment in new technology).
  
• Ovals represent chance events, (uncertainties,
  states of nature that will be determined later)
• Rounded squares represent an intermediate
  calculation or consequence
• Diamonds represent final consequences or payoff

21
Arcs in Influence Diagrams
B
Decision A effects the probabilities of event B
The probability distribution over B is
conditional on decision A.
A
B
The outcome of A effects the probabilities of
event B The probability distribution over B is
conditional on the outcome of A.
A
A
B
Decision A is made prior to Decision B
The outcome of A is known prior to of Decision B
A
B
22
Arcs in Influence Diagrams
Relevance
B
Decision A effects the probabilities of event B
The probability distribution over B is
conditional on decision A.
A
B
The outcome of A effects the probabilities of
event B The probability distribution over B is
conditional on the outcome of A.
A
A
B
Decision A is made prior to Decision B
The outcome of A is known prior to of Decision B
A
B
23
Arcs in Influence Diagrams
Relevance
B
Decision A effects the probabilities of event B
The probability distribution over B is
conditional on decision A.
A
B
The outcome of A effects the probabilities of
event B The probability distribution over B is
conditional on the outcome of A.
A
The lack of an arrow is a strong statement. An
arrow indicates weak relevance
24
Arcs in Influence Diagrams
B
Decision A effects the probabilities of event B
The probability distribution over B is
conditional on decision A.
A
B
The outcome of A effects the probabilities of
event B The probability distribution over B is
conditional on the outcome of A.
A
Sequence/Information
A
B
Decision A is made prior to Decision B
The outcome of A is known prior to of Decision B
A
B
25

• This means that the outcome of chance event A
  will be know when decision B is taken.
• It DOES NOT mean that the chance event A simply
  influences, or is important to the decision B

26
Influence Diagram Example
You can bet on a coin flip. If you bet 1 on
heads, you get 2 if the coin lands heads-up 0
otherwise.
27
Influence Diagram Example
You can bet on a coin flip. If you bet 1 on
heads, you get 2 if the coin lands heads-up 0
otherwise.
What would this arrow mean?
28
Influence Diagram Example
You can bet on a coin flip. If you bet 1 on
heads, you get 2 if the coin lands heads-up 0
otherwise.
What would this arrow mean?
29
Influence Diagram Example
You can bet on a coin flip. If you bet 1 on
heads, you get 2 if the coin lands heads-up 0
otherwise.
What other situations can be represented by this
same ID?
30
Example RD Investment
TECHNICAL SUCCESS
RD FUNDING
Value
MARKETVALUE GIVEN SUCCESS
31
Climate change RD Decision

• A sequential problem

TECHNICAL SUCCESS
ABATEMENT Cost CURVE
SOCIETAL COST
RD FUNDING
DAMAGE CURVE
ABATEMENT LEVEL
32
Case Study

• Structure an Influence Diagram for ODA case

33
Decision Trees

• Decision Trees also have square nodes for
  decisions and oval nodes for uncertainties.
• There is one branch for each alternative at a
  decision node.
• There is one branch for each outcome at a
  uncertainty node.

34
Example
H
Decision
T
dont bet
(0)
35
Example
You believe that the coin doesnt like you.
H
Decision
T
dont bet
(0)
36
Example
Draw the tree for this ID
37
Example ISRU choice on moon
Find water on moon?
Water extraction on moon successful?
Try to extract water on Moon
ISRU choice on moon
Search for water on Moon
Value
38
First decision node
39
Uncertainty node
40
Decision node try to extract
41
This is the whole tree so far
42
Extraction uncertainty
43
Final ISRU choice
44
This is the final tree. 19 end nodes.
45
Evacuation Decision

• Draw a decision tree

Forecast
hurricane hits
Evacuate Immediately
Evacuate after forecast
Welfare
cost of evacuation
Safety
46
Example

• You are offered a game. You can choose to not
  play to take coin toss A or to continue.
• If you take coin toss A you get 2 if it comes up
  heads -1 if it comes up tails.
• If you continue, then you toss a coin.
• If it comes up heads you can choose to pay 1 and
  stop or take coin toss B.
• If you take coin toss B you get 5 if it comes
  up heads -6 if its tails.
• If it comes up tails, you can stop or take coin
  toss C.
• If you take coin toss C you get 8 if it comes up
  heads -2 if its tails.
• Draw the ID and the decision tree of this problem.

47
Solving Decision Trees

• We can calculated the expected value of a
  decision tree.
• Work backwards
• At an uncertainty node, take the expected value
• At a decision node, choose the alternative with
  highest expected value.

48
p.5
A Decision Tree
plan 1a
close, p .2
plan 1b
Data Mining
p.4
not close,
p.3
D1
p.6
water found, p .2
plan 3
p.3
plan 4a
Bowling Balls
p.5
not found
plan 4b
49
25
p.5
Find expected value of end nodes
plan 1a
close, p .2
-10
plan 1b
Data Mining
p.4
30
-25
not close,
p..3
30
p.6
water found, p .2
plan 3
p.3
31
plan 4a
Bowling Balls
40
p.5
not found
plan 4b
50
25
p.5
Choose best decision in each case
plan 1a
25
close, p .2
-10
plan 1b
Data Mining
p.4
30
30
-25
not close,
p..3
30
p.6
water found, p .2
plan 3
p.3
31
plan 4a
Bowling Balls
40
p.5
not found
plan 4b
40
51
25
p.5
calculate expected value of next uncertainty node
plan 1a
25
close, p .2
-10
plan 1b
Data Mining
29
p.4
30
30
-25
not close,
p..3
30
p.6
water found, p .2
plan 3
38
p.3
31
plan 4a
Bowling Balls
40
p.5
not found
plan 4b
40
52
25
p.5
Choose best decision
plan 1a
25
close, p .2
-10
plan 1b
Data Mining
29
p.4
30
30
-25
not close,
p..3
30
p.6
water found, p .2
plan 3
38
p.3
31
plan 4a
Bowling Balls
40
p.5
not found
plan 4b
40
53
25
p.5
You now have a strategy
plan 1a
25
close, p .2
-10
plan 1b
Data Mining
29
p.4
30
30
-25
not close,
p..3
30
p.6
water found, p .2
plan 3
38
p.3
31
plan 4a
Bowling Balls
40
p.5
not found
plan 4b
40
54
Example

• A pharmaceutical company is deciding whether to
  invest in RD for a new product or not. First
  they must decide whether to perform the first
  test. Once they have the results of the first
  test they can then decide whether to perform the
  second test. The first test has a cost of
  250,000, and a probability of success of 0.1. If
  the first test is not successful, the drug will
  fail for sure. The second test costs 1M, and has
  probability 50 of being successful. If the drug
  is successful it will earn 10M. If it is not
  successful, it will earn 0.
• Draw the decision tree for this problem, and roll
  it back to determine optimal strategy.

55
Decision Tree
10-.25-1 8.75M
Continue
P.1
-1-.25 -1.25M
Invest in first stage
-.25M
Stop
Continue
-1-.25M
1-P.9
-.25M
Stop
0
Dont Invest in first stage
56
Decision Tree
10-.25-1 8.75M
3.75
Continue
3.75
P.1
-1-.25 -1.25M
Invest in first stage
.15
-.25M
Stop
Continue
-1-.25M
1-P.9
-.25M
-.25
Stop
0
Dont Invest in first stage