1. 1.040/1.401 Project Management Spring 2006 Risk Analysis Decision making under risk and uncertainty
Department of Civil and Environmental Engineering
Massachusetts Institute of Technology

2. Preliminaries Announcements Construction nightmares discussion
Remainder
Sharon Lin the team info by midnight, tonight
Monday Feb 27 - Student Experience Presentation
Wed March 1st – Assignment 2 due
Today, recitation Joe Gifun, MIT facility
Next Friday, March 3rd, Tour PDSI construction site
1st group noon – 1:30
2nd group 1:30 – 3:00
Construction nightmares discussion
16 - Psi Creativity Center, Design and Bidding phases

3. Project Management Phase
DESIGN
PLANNING
FEASIBILITY
DEVELOPMENT
CLOSEOUT
OPERATIONS
Financing&Evaluation
Risk Analysis&Attitude

4. Risk Management Phase Risk management (guest seminar 1st wk April)
RISK MNG
DESIGN
PLANNING
FEASIBILITY
DEVELOPMENT
CLOSEOUT
OPERATIONS
Risk management (guest seminar 1st wk April)
Assessment, tracking and control
Tools:
Risk Hierarchical modeling: Risk breakdown structures
Risk matrixes
Contingency plan: preventive measures, corrective actions, risk budget, etc.

5. Decision Making Under Risk Outline
Risk and Uncertainty
Risk Preferences, Attitude and Premiums
Examples of simple decision trees
Decision trees for analysis
Flexibility and real options

6. Decision making

7. Uncertainty and Risk “risk” as uncertainty about a consequence
Preliminary questions
What sort of risks are there and who bears them in project management?
What practical ways do people use to cope with these risks?
Why is it that some people are willing to take on risks that others shun?

8. Some Risks Weather changes Community opposition Different productivity
(Sub)contractors are
Unreliable
Lack capacity to do work
Lack availability to do work
Unscrupulous
Financially unstable
Late materials delivery
Lawsuits
Labor difficulties
Unexpected manufacturing costs
Failure to find sufficient tenants
Community opposition
Infighting & acrimonious relationships
Unrealistically low bid
Late-stage design changes
Unexpected subsurface conditions
Soil type
Groundwater
Unexpected Obstacles
Settlement of adjacent structures
High lifecycle costs
Permitting problems …

9. Importance of Risk
Much time in construction management is spent focusing on risks
Many practices in construction are driven by risk
Bonding requirements
Insurance
Licensing
Contract structure
General conditions
Payment Terms
Delivery Method
Selection mechanism

10. Outline Risk and Uncertainty Risk Preferences, Attitude and Premiums
Examples of simple decision trees
Decision trees for analysis
Flexibility and real options

11. Decision making under risk Available Techniques
Decision modeling
Decision making under uncertainty
Tool: Decision tree
Strategic thinking and problem solving:
Dynamic modeling (end of course)
Fault trees

12. Introduction to Decision Trees
We will use decision trees both for
Illustrating decision making with uncertainty
Quantitative reasoning
Represent
Flow of time
Decisions
Uncertainties (via events)
Consequences (deterministic or stochastic)

13. Decision Tree Nodes Decision (choice) Node Chance (event) Node
Time
Decision (choice) Node
Chance (event) Node
Terminal (consequence) node
Outcome (cost or benefit)
Note probabilities associated with events
Note consequences associated with terminal nodes

14. Risk Preference People are not indifferent to uncertainty
Lack of indifference from uncertainty arises from uneven preferences for different outcomes
E.g. someone may
dislike losing $x far more than gaining $x
value gaining $x far more than they disvalue losing $x.
Individuals differ in comfort with uncertainty based on circumstances and preferences
Risk averse individuals will pay “risk premiums” to avoid uncertainty
Stress that Risk Applies to other concepts than money

15. Risk preference
The preference depends on decision maker point of view

16. Categories of Risk Attitudes
Risk attitude is a general way of classifying risk preferences
Classifications
Risk averse fear loss and seek sureness
Risk neutral are indifferent to uncertainty
Risk lovers hope to “win big” and don’t mind losing as much
Risk attitudes change over
Time
Circumstance

17. Decision Rules The pessimistic rule (maximin = minimax)
The conservative decisionmaker seeks to:
maximize the minimum gain (if outcome = payoff)
or minimize the maximum loss (if outcome = loss, risk)
The optimistic rule (maximax)
The risklover seeks to maximize the maximum gain
Compromise (the Hurwitz rule):
Max (α min + (1- α) max) , 0 ≤ α ≤ 1
α = 1 pessimistic
α = 0.5 neutral
α = 0 optimistic

18. The bridge case – unknown prob’ties
$ 1.09 million
replace
$1.61 M
$0.55
$1.43
repair
Investment PV
Pessimistic rule
min (1, 1.61) = 1 replace the bridge
The optimistic rule (maximax)
max (1, 0.55) = 0.55 repair … and hope it works!

19. The bridge case – known prob’ties
$ 1.09 million
replace
$1.61 M
$0.55
$1.43
0.25
repair
0.5
Investment PV
0.25
Expected monetary value
E = (0.25)(1.61) + (0.5)(0.55) + (0.25)(1.43) = $ 1.04 M
Data link

20. The bridge case – decision
The pessimistic rule (maximin = minimax)
Min (Ei) = Min (1.09 , 1.04) = $ 1.04 repair
In this case = optimistic rule (maximax)
Awareness of probabilities change risk attitude

21. Other criteria Most likely value Expected value of Opportunity Loss
For each policy option we select the outcome with the highest probability
Expected value of Opportunity Loss

22. To buy soon or to buy later
-100
Buy soon
= -125
= -95
= -65
Buy later
Current price = 100
S1 = + 30%
S2 = no price variation
S3 = - 30%
Actualization = 5

23. To buy soon or to buy later
-100
Buy soon
-125
-95
-65
Buy later
0. 5
0.25
0.25

24. The Utility Theory
When individuals are faced with uncertainty they make choices as is they are maximizing a given criterion: the expected utility.
Expected utility is a measure of the individual's implicit preference, for each policy in the risk environment.
It is represented by a numerical value associated with each monetary gain or loss in order to indicate the utility of these monetary values to the decision-maker.

25. Adding a Preference function
1.35 1 .7
125
100 65
Expected (mean) value
E = (0.5)(125) + (0.25)(95) + (0.25)(65) =
Utility value:
f(E) = ∑ Pa * f(a) = 0.5 f(125) f(95) f(65) =
= .5* * *1.35 = ~0.95
Certainty value = *0.975 =
If 2 strategies have the same EMV, one can take decision only by preference multiplying factor

26. Defining the Preference Function
Suppose to be awarded a $100M contract price
Early estimated cost $70M
What is the preference function of cost?
Preference means utility or satisfaction
utility 70 $

27. Notion of a Risk Premium
A risk premium is the amount paid by a (risk averse) individual to avoid risk
Risk premiums are very common – what are some examples?
Insurance premiums
Higher fees paid by owner to reputable contractors
Higher charges by contractor for risky work
Lower returns from less risky investments
Money paid to ensure flexibility as guard against risk

28. Conclusion: To buy or not to buy
The risk averter buys a “future” contract that allow to buy at $ 97.38
The trading company (risk lover) will take advantage/disadvantage of future benefit/loss

29. Certainty Equivalent Example
Consider a risk averse individual with preference fn f faced with an investment c that provides
50% chance of earning $20000
50% chance of earning $0
Average money from investment =
.5*$20,000+.5*$0=$10000
Average satisfaction with the investment=
.5*f($20,000)+.5*f($0)=.25
This individual would be willing to trade for a sure investment yielding satisfaction>.25 instead
Can get .25 satisfaction for a sure f-1(.25)=$5000
We call this the certainty equivalent to the investment
Therefore this person should be willing to trade this investment for a sure amount of money>$5000
Mean satisfaction with
investment
.50
.25
Certainty equivalent
of investment
Mean value
Of investment
Risk averse individual
.25 only corresponded to SURE return of $5000
Should be willing to trade this investment for a SURE investment that returns anything more than 5,000
this would be a gain for the this party, because would be HAPPIER with it than with the unsure investment shown here
this could be a gain for another party who is less risk averse, because get MORE MONEY for the trade
$5000

30. Example Cont’d (Risk Premium)
The risk averse individual would be willing to trade the uncertain investment c for any certain return which is > $5000
Equivalently, the risk averse individual would be willing to pay another party an amount r up to $5000 =$10000-$5000 for other less risk averse party to guarantee $10,000
Assuming the other party is not risk averse, that party wins because gain r on average
The risk averse individual wins b/c more satisfied
Stress that the reason for willingness to trade is that thee satisfaction resulting from a certain return >$5000 is > .25
Guarantor
is given $2K automatically
if $20000 comes in, gives $10000 to risk averse party: make $10K+2K= 12K
if 0 comes in , give $10K to risk averse party; make -10K+2K = -8K
therefore on average, make (12K-8K)/2= 2K

31. Certainty Equivalent More generally, consider situation in which have
Uncertainty with respect to consequence c
Non-linear preference function f
Note: E[X] is the mean (expected value) operator
The mean outcome of uncertain investment c is E[c]
In example, this was .5*$20,000+.5*$0=$10,000
The mean satisfaction with the investment is E[f(c)]
In example, this was .5*f($20,000)+.5*f($0)=.25
We call f-1(E[f(c)]) the certainty equivalent of c
Size of sure return that would give the same satisfaction as c
In example, was f-1(.25)=f-1(.5*20,000+.5*0)=$5,000
Use term “mean” rather than expected value

32. Risk Attitude Redux
The shapes of the preference functions means can classify risk attitude by comparing the certainty equivalent and expected value
For risk loving individuals, f-1(E[f(c)])>E[c]
They want Certainty equivalent > mean outcome
For risk neutral individuals, f-1(E[f(c)])=E[c]
For risk averse individuals, f-1(E[f(c)])<E[c]

33. Motivations for a Risk Premium
Consider
Risk averse individual A for whom f-1(E[f(c)])<E[c]
Less risk averse party B
A can lessen the effects of risk by paying a risk premium r of up to E[c]-f-1(E[f(c)]) to B in return for a guarantee of E[c] income
The risk premium shifts the risk to B
The net investment gain for A is E[c]-r, but A is more satisfied because E[c] – r > f-1(E[f(c)])
B gets average monetary gain of r

34. Gamble or not to Gamble Preference function f(-1)=0, f(1)=100
EMV
(0.5)(-1) + (0.5)(1) = 0
Preference function f(-1)=0, f(1)=100
Certainty eq. f-1(E[f(c)]) = 0
No help from risk analysis !!!!!

35. Multiple Attribute Decisions
Frequently we care about multiple attributes
Cost
Time
Quality
Relationship with owner
Terminal nodes on decision trees can capture these factors – but still need to make different attributes comparable

36. The bridge case - Multiple tradeoffs
Computation of Pareto-Optimal Set
For decision D2
Replace
MTTF
Cost 1.00 C3
MTTF
Cost 0.30 C4
MTTF
Cost 0.00
Aim: maximizing bridge duration, minimizing cost
MTTF = mean time to failure

37. Pareto Optimality
Even if we cannot directly weigh one attribute vs. another, we can rank some consequences
Can rule out decisions giving consequences that are inferior with respect to all attributes
We say that these decisions are “dominated by” other decisions
Key concept here: May not be able to identify best decisions, but we can rule out obviously bad
A decision is “Pareto optimal” (or efficient solution) if it is not dominated by any other decision
Mention one decision low in cost, high in time
One decision high in cost, low in time
Point is that in decision analysis, only consider pareto optimal

38. 03/06/06 - Preliminaries Announcements Reading questions/comments?
Due dates Stellar Schedule and not Syllabus
Term project
Phase 2 due March 17th
Phase 3 detailed description posted on Stellar, due May 11
Assignment PS3 posted on Stellar – due date March 24
Decision making under uncertainty
Reading questions/comments?
Utility and risk attitude
You can manage construction risks
Risk management and insurances - Recommended

39. Decision Making Under Risk
Risk and Uncertainty
Risk Preferences, Attitude and Premiums
Examples of simple decision trees
Decision trees for analysis
Flexibility and real options

40. Multiple objective The student’s dilemma

41. Decision Making Under Risk
Risk and Uncertainty
Risk Preferences, Attitude and Premiums
Examples of simple decision trees
Decision trees for analysis
Flexibility and real options

42. Bidding What choices do we have?
How does the chance of winning vary with our bidding price?
How does our profit vary with our bidding price if we win?

43. Example Bidding Decision Tree
Time

44. Choosing Elevator Count

45. Bidding Decision Tree with Stochastic Costs, Competing Bids

46. Selecting Desired Electrical Capacity

47. Decision Tree Example: Procurement Timing
Decisions
Choice of order time (Order early, Order late)
Events
Arrival time (On time, early, late)
Theft or damage (only if arrive early)
Consequences: Cost
Components: Delay cost, storage cost, cost of reorder (including delay)

48. Procurement Tree

49. Decision Making Under Risk
Risk and Uncertainty
Risk Preferences, Attitude and Premiums
Decision trees for representing uncertainty
Decision trees for analysis
Flexibility and real options

50. Analysis Using Decision Trees
Decision trees are a powerful analysis tool
Example analytic techniques
Strategy selection (Monte Carlo simulation)
One-way and multi-way sensitivity analyses
Value of information

51. Recall Competing Bid Tree

52. Monte Carlo simulation
Monte Carlo simulation randomly generates values for uncertain variables over and over to simulate a model.
It's used with the variables that have a known range of values but an uncertain value for any particular time or event.
For each uncertain variable, you define the possible values with a probability distribution.
Distribution types include:
A simulation calculates multiple scenarios of a model by repeatedly sampling values from the probability distributions
Computer software tools can perform as many trials (or scenarios) as you want and allow to select the optimal strategy …

53. Monetary Value of $6.75M Bid
This is histogram
Streess that lumpsum amount
Very few negative

54. Monetary Value of $7M Bid
Try to change scale

55. With Risk Preferences: 6.75M

56. With Risk Preferences: 7M

57. Larger Uncertainties in Cost (Monetary Value)

58. Large Uncertainties II (Monetary Values)
Ask what expect to see before showing this

59. With Risk Preferences for Large Uncertainties at lower bid

60. With Risk Preferences for Higher Bid

61. Optimal Strategy

62. Sensitivity Analysis I

63. Sensitivity Analysis II
Explain that regions at which different decisions are desirable

64. Decision Making Under Risk
Risk and Uncertainty
Risk Preferences, Attitude and Premiums
Decision trees for representing uncertainty
Examples of simple decision trees
Decision trees for analysis
Flexibility and real options

65. Flexibility and Real Options
Flexibility is providing additional choices
Flexibility typically has
Value by acting as a way to lessen the negative impacts of uncertainty
Cost
Delaying decision
Extra time
Cost to pay for extra “fat” to allow for flexibility

66. Ways to Ensure of Flexibility in Construction
Alternative Delivery
Clear spanning (to allow movable walls)
Extra utility conduits (electricity, phone,…)
Larger footings & columns
Broader foundation
Alternative heating/electrical
Contingent plans for
Value engineering
Geotechnical conditions
Procurement strategy
Additional elevator
Larger electrical panels
Property for expansion
Sequential construction
Wiring to rooms

67. Illustration of Flexibility

68. Illustration of Flexibility: Selection of Elevator Count
More sophisticated model taking into account
Initial costs
Repair costs
Loss due to lost conveyance

69. Sensitivity Analysis

70. Outcome

71. Strategy Selection

72. Adaptive Strategies
An adaptive strategy is one that changes the course of action based on what is observed – i.e. one that has flexibility
Rather than planning statically up front, explicitly plan to adapt as events unfold
Typically we delay a decision into the future

73. Real Options
Real Options theory provides a means of estimating financial value of flexibility
E.g. option to abandon a plant, expand bldg
Key insight: NPV does not work well with uncertain costs/revenues
E.g. difficult to model option of abandoning invest.
Model events using stochastic diff. equations
Numerical or analytic solutions
Can derive from decision-tree based framework

74. Example: Structural Form Flexibility
Hotel initially aimed at the low-end

75. Considerations Tradeoffs Frequently retrofitting $ > up-front $
Short-term speed and flexibility
Overlapping design & construction and different construction activities limits changes
Short-term cost and flexibility
E.g. value engineering away flexibility
Selection of low bidder
Late decisions can mean greater costs
NB: both budget & schedule may ultimately be better off w/greater flexibility!
Frequently retrofitting $ > up-front $

76. Decision Making Under Risk
Risk and Uncertainty
Risk Preferences, Attitude and Premiums
Decision trees for representing uncertainty
Examples of simple decision trees
Decision trees for analysis
Flexibility and real options

77. Readings Required Recommended: More information:
Utility and risk attitude – Stellar Readings section
Get prepared for next class:
You can manage construction risks – Stellar
On-line textbook, from 2.4 to 2.12
Recommended:
Meredith Textbook, Chapter 4 Prj Organization
Risk management and insurances – Stellar

78. Risk - MIT libraries Haimes, Risk modeling, assessment, and management
Mun, Applied risk analysis : moving beyond uncertainty
Flyvbjerg, Mega-projects and risk
Chapman, Managing project risk and uncertainty : a constructively simple approach to decision making
Bedford, Probabilistic risk analysis: foundations and methods
… and a lot more!