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
Preliminaries
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Announcements
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Remainder
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Today, recitation Joe Gifun, MIT facility
Next Friday, March 3rd, Tour PDSI construction site
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email Sharon Lin the team info by midnight, tonight
Monday Feb 27 - Student Experience Presentation
Wed March 1st – Assignment 2 due
1st group noon – 1:30
2nd group 1:30 – 3:00
Construction nightmares discussion
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16 - Psi Creativity Center, Design and Bidding phases
Project Management Phase
FEASIBILITY
DESIGN
PLANNING
DEVELOPMENT CLOSEOUT
Financing&Evaluation
Risk Analysis&Attitude
OPERATIONS
Risk Management Phase
FEASIBILITY
DESIGN
PLANNING
DEVELOPMENT CLOSEOUT
OPERATIONS
RISK MNG
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Risk management (guest seminar 1st wk April)
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Assessment, tracking and control
Tools:
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Risk Hierarchical modeling: Risk breakdown structures
Risk matrixes
Contingency plan: preventive measures, corrective actions, risk budget,
etc.
Decision Making Under Risk
Outline
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Risk and Uncertainty
Risk Preferences, Attitude and Premiums
Examples of simple decision trees
Decision trees for analysis
Flexibility and real options
Decision making
Uncertainty and Risk
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“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?
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Some Risks
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Weather changes
Different productivity
(Sub)contractors are
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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
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Community opposition
Infighting & acrimonious
relationships
Unrealistically low bid
Late-stage design changes
Unexpected subsurface
conditions
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Soil type
Groundwater
Unexpected Obstacles
Settlement of adjacent
structures
High lifecycle costs
Permitting problems
…
Importance of Risk
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Much time in construction management is spent
focusing on risks
Many practices in construction are driven by risk
Bonding requirements
 Insurance
 Licensing
 Contract structure
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General conditions
 Payment Terms
 Delivery Method
 Selection mechanism
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Outline
Risk and Uncertainty
 Risk Preferences, Attitude and Premiums
 Examples of simple decision trees
 Decision trees for analysis
 Flexibility and real options
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Decision making under risk
Available Techniques
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Decision modeling
Decision making under uncertainty
 Tool: Decision tree
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Strategic thinking and problem solving:
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Dynamic modeling (end of course)
Fault trees
Introduction to Decision Trees
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We will use decision trees both for
Illustrating decision making with uncertainty
 Quantitative reasoning
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Represent
Flow of time
 Decisions
 Uncertainties (via events)
 Consequences (deterministic or stochastic)
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Decision Tree Nodes
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Decision (choice) Node
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Chance (event) Node
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Terminal (consequence) node
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Outcome (cost or benefit)
Time
Risk Preference
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People are not indifferent to uncertainty
Lack of indifference from uncertainty arises from
uneven preferences for different outcomes
 E.g. someone may
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dislike losing $x far more than gaining $x
 value gaining $x far more than they disvalue losing $x.
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Individuals differ in comfort with uncertainty
based on circumstances and preferences
Risk averse individuals will pay “risk premiums”
to avoid uncertainty
Risk preference
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The preference depends on decision maker point of view
Categories of Risk Attitudes
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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
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Risk attitudes change over
Time
 Circumstance
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Decision Rules
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The pessimistic rule (maximin = minimax)
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The conservative decisionmaker seeks to:
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The optimistic rule (maximax)
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maximize the minimum gain (if outcome = payoff)
or minimize the maximum loss (if outcome = loss, risk)
The risklover seeks to maximize the maximum gain
Compromise (the Hurwitz rule):
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Max (α min + (1- α) max) , 0 ≤ α ≤ 1
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α = 1 pessimistic
α = 0.5 neutral
α = 0 optimistic
The bridge case – unknown prob’ties
$ 1.09 million
replace
$1.61 M
repair
$0.55
$1.43
•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!
Investment PV
The bridge case – known prob’ties
$ 1.09 million
replace
0.25
repair
0.5
$1.61 M
$0.55
Investment PV
0.25
$1.43
Expected monetary value
E = (0.25)(1.61) + (0.5)(0.55) + (0.25)(1.43) = $ 1.04 M
Data link
The bridge case – decision
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The pessimistic rule (maximin = minimax)
 Min
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(Ei) = Min (1.09 , 1.04) = $ 1.04 repair
In this case = optimistic rule (maximax)
 Awareness
attitude
of probabilities change risk
Other criteria
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Most likely value
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For each policy option we select the outcome with
the highest probability
Expected value of Opportunity Loss
To buy soon or to buy later
-100
Buy soon
Buy later
-100-30+5 = -125
-100+5 = -95
-100+5+30 = -65
Current price = 100
S1 = + 30%
S2 = no price variation
S3 = - 30%
Actualization = 5
To buy soon or to buy later
-100
Buy soon
Buy later
0. 5
0.25
-125
-95
0.25
-65
The Utility Theory
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When individuals are faced with uncertainty they make
choices as is they are maximizing a given criterion: the
expected utility.
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Expected utility is a measure of the individual's implicit
preference, for each policy in the risk environment.
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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.
Adding a Preference function
1.35
1
.7
125
100
65
Expected (mean) value
E = (0.5)(125) + (0.25)(95) + (0.25)(65) = -102.5
Utility value:
f(E) = ∑ Pa * f(a) = 0.5 f(125) + 0.25 f(95) + .25 f(65) =
= .5*0.7 + .25*1.05 + .25*1.35 = ~0.95
Certainty value = -102.5*0.975 = -97.38
Defining the Preference Function
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Suppose to be awarded a $100M contract price
Early estimated cost $70M
What is the preference function of cost?
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Preference means utility or satisfaction
utility
70
$
Notion of a Risk Premium
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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
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Conclusion: To buy or not to buy
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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
Certainty Equivalent Example
Consider a risk averse individual with
preference fn f faced with an investment c
that provides
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.25
Certainty equivalen
of investment
.5*$20,000+.5*$0=$10000
Average satisfaction with the investment=
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.50
Average money from investment =
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50% chance of earning $20000
50% chance of earning $0
Mean satisfaction with
investment
.5*f($20,000)+.5*f($0)=.25
This individual would be willing to trade for a
sure investment yielding satisfaction>.25
instead
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Can get .25 satisfaction for a sure f-1(.25)=$5000
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Mean value
Of investme
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
$5000
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Example Cont’d (Risk Premium)
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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
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Certainty Equivalent
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More generally, consider situation in which have
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Note: E[X] is the mean (expected value) operator
The mean outcome of uncertain investment c is E[c]
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In example, this was .5*$20,000+.5*$0=$10,000
The mean satisfaction with the investment is E[f(c)]
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Uncertainty with respect to consequence c
Non-linear preference function f
In example, this was .5*f($20,000)+.5*f($0)=.25
We call f-1(E[f(c)]) the certainty equivalent of c
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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
Risk Attitude Redux
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The shapes of the preference functions means
can classify risk attitude by comparing the
certainty equivalent and expected value
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For risk loving individuals, f-1(E[f(c)])>E[c]
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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]
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Motivations for a Risk Premium
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Consider
Risk averse individual A for whom f-1(E[f(c)])<E[c]
 Less risk averse party B
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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
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Gamble or not to Gamble
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 !!!!!
Multiple Attribute Decisions
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Frequently we care about multiple attributes
Cost
 Time
 Quality
 Relationship with owner
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Terminal nodes on decision trees can capture
these factors – but still need to make different
attributes comparable
The bridge case - Multiple tradeoffs
Computation of Pareto-Optimal Set
For decision D2
Replace
MTTF 10.0000
Cost 1.00
C3
MTTF 6.6667
Cost 0.30
C4
MTTF 5.7738
Cost 0.00
Aim: maximizing bridge duration, minimizing cost
MTTF = mean time to failure
Pareto Optimality
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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
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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
03/06/06 - Preliminaries
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Announcements
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Due dates Stellar Schedule and not Syllabus
Term project
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Assignment PS3 posted on Stellar – due date March 24
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Phase 2 due March 17th
Phase 3 detailed description posted on Stellar, due May 11
Decision making under uncertainty
Reading questions/comments?
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Utility and risk attitude
You can manage construction risks
Risk management and insurances - Recommended
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

Multiple objective
The student’s dilemma
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
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Bidding
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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?
Example Bidding Decision Tree
Time
Bidding Decision Tree with
Stochastic Costs, Competing Bids
Selecting Desired Electrical Capacity
Decision Tree Example:
Procurement Timing
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Decisions
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Choice of order time (Order early, Order late)
Events
Arrival time (On time, early, late)
 Theft or damage (only if arrive early)
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Consequences: Cost
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Components: Delay cost, storage cost, cost of
reorder (including delay)
Procurement Tree
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
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Analysis Using Decision Trees
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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
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Recall Competing Bid Tree
Monte Carlo simulation
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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:
…
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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
Monetary Value of $6.75M Bid
Monetary Value of $7M Bid
With Risk Preferences: 6.75M
With Risk Preferences: 7M
Larger Uncertainties in Cost
(Monetary Value)
Large Uncertainties II
(Monetary Values)
With Risk Preferences for Large
Uncertainties at lower bid
With Risk Preferences for
Higher Bid
Optimal Strategy
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

Flexibility and Real Options
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Flexibility is providing additional choices
Flexibility typically has
Value by acting as a way to lessen the negative
impacts of uncertainty
 Cost
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Delaying decision
 Extra time
 Cost to pay for extra “fat” to allow for flexibility
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Ways to Ensure of Flexibility
in Construction
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Alternative Delivery
Clear spanning (to allow
movable walls)
Extra utility conduits
(electricity, phone,…)
Larger footings &
columns
Broader foundation
Alternative
heating/electrical
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Contingent plans for
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Value engineering
Geotechnical conditions
Procurement strategy
Additional elevator
Larger electrical panels
Property for expansion
Sequential construction
Wiring to rooms
Adaptive Strategies
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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
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Real Options
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Real Options theory provides a means of
estimating financial value of flexibility
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Key insight: NPV does not work well with
uncertain costs/revenues
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E.g. option to abandon a plant, expand bldg
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
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Example: Structural Form
Flexibility
Considerations
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Tradeoffs
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Short-term speed and flexibility
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Short-term cost and flexibility
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Overlapping design & construction and different construction
activities limits changes
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 $
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
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Readings
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Required
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More information:
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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
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Recommended:
Meredith Textbook, Chapter 4 Prj Organization
 Risk management and insurances – Stellar
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Risk - MIT libraries
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Haimes, Risk modeling, assessment, and management
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Mun, Applied risk analysis : moving beyond uncertainty
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Flyvbjerg, Mega-projects and risk
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Chapman, Managing project risk and uncertainty : a
constructively simple approach to decision making
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Bedford, Probabilistic risk analysis: foundations and methods
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… and a lot more!