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1.040/1.401Project Management
Spring 2006
Risk AnalysisDecision making under risk and uncertainty
Department of Civil and Environmental EngineeringMassachusetts Institute of Technology
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Project Management Phase
FEASIBILITY DESIGN
PLANNING
CLOSEOUT DEVELOPMENT OPERATIONS
Financing&Evaluation
Risk Analysis&Attitude
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Risk Management Phase
• 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.
FEASIBILITY DESIGNPLANNING
CLOSEOUT DEVELOPMENT OPERATIONS
RISK MNG
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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
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Decision making
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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 onrisks that others shun?
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Some Risks• Weather changes
• 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 sufficienttenants
• Community opposition
• Infighting & acrimoniousrelationships
• Unrealistically low bid
• Late-stage design changes
• Unexpected subsurfaceconditions – Soil type
– Groundwater
– Unexpected Obstacles
• Settlement of adjacentstructures
• High lifecycle costs
• Permitting problems
• …
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Importance of Risk•
Much time in construction management isspent focusing on risks
• Many practices in construction are driven byrisk
– Bonding requirements – Insurance
– Licensing
– Contract structure
• 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
• Decision modeling
– Decision making under uncertainty
– Tool: Decision tree
• Strategic thinking and problem solving:
– Dynamic modeling (end of course)
• Fault trees
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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)
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Decision Tree Nodes
• Decision (choice) Node
• Chance (event) Node
• Terminal (consequence) node – Outcome (cost or benefit)
Time
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Risk Preference
• People are not indifferent to uncertainty
– Lack of indifference from uncertainty arises fromuneven preferences for different outcomes
( Sự giảm của Sự không khác biệt từ sự không chắc chắn bắt nguồn từ sự ưu thích không bằng nhau về các kết quả khác nhau)
– 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 uncertaintybased on circumstances and preferences
• Risk averse individuals will pay “risk premiums” to
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Risk preference
• The preference depends on decision maker point of
view
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Categories of Risk Attitudes
• Risk attitude is a general way of classifying riskpreferences
• Classifications
– Risk averse fear loss and seek sureness – Risk neutral are indifferent to uncertainty
– Risk lovers hope to “win big” and don’t mindlosing as much
• Risk attitudes change over
– Time
– Circumstance
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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)
• A{( 0.4,100) (0.2, 50) (0.3,-100) (0.1, -50)}• B{( 0.4,80) (0.2, 60) (0.3,-80) (0.1, -50)}
• 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
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The bridge case – unknown prob’ties
$1.61 M
$0.55
$1.43
replace
repair
$ 1.09 million
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!
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The bridge case – known prob’ties
$1.61 M
$0.55
$1.43
replace
repair
$ 1.09 million
Investment PV
Expected monetary value
E = (0.25)(1.61) + (0.5)(0.55) + (0.25)(1.43) = $ 1.04 M
0.25
0.5
0.25
Data link
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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
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Other criteria
• Most likely value
– For each policy option we select the outcome with
the highest probability
• Expected value of Opportunity Loss
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To buy soon or to buy later
Buy soon
Current price = 100
S1 = + 30%
S2 = no price variation
S3 = - 30%
Actualization = 5
-100-30+5 = -125
-100+5 = -95
-100+5+30 = -65
Buy later
-100
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To buy soon or to buy later
Buy soon
-125
-95
-65
Buy later
-100
0. 5
0.25
0.25
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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 witheach monetary gain or loss in order to indicate the utility
of these monetary values to the decision-maker.
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Adding a Preference function
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
100125 65
1
.7
1.35
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Defining the Preference Function
• Suppose to be awarded a $100M contractprice
• Early estimated cost $70M
• What is the preference function of cost? – Preference means utility or satisfaction
$
utility
70
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Notion of a Risk Premium
• A risk premium is the amount paid by a (riskaverse) individual to avoid risk
• Risk premiums are very common – what are
some examples? – Insurance premiums
– Higher fees paid by owner to reputablecontractors
– 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
• 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
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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 fora sure investment yielding satisfaction>.25instead
– 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 tradethis investment for a sure amount ofmoney>$5000
.25
Mean value
Of investme
Mean satisfaction with
investment
Certainty equivale
of investment
$ 5 0 0 0
.50
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Example Cont’d (Risk Premium)
• The risk averse individual would be willing totrade the uncertain investment c for any
certain return which is > $5000
•Equivalently, the risk averse individual wouldbe 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
• 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
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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)])
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Motivations for a Risk Premium
• Consider
– Risk averse individual A for whom f -1(E[f(c)]) f -1(E[f(c)])
– B gets average monetary gain of r
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.25
Mean value
Of investment
Mean satisfaction with
investment
Certainty equivalent
of investment
$ 5 0 0 0
.50
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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 !!!!!
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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 differentattributes comparable
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The bridge case - Multiple tradeoffs
MTTF = mean time to failure
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
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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
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03/06/06 - Preliminaries
• Announcements – 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
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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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Multiple objective
The student’s dilemma
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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
• 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?
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Example Bidding Decision Tree Time
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Bidding Decision Tree with
Stochastic Costs, Competing Bids
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Selecting Desired Electrical Capacity
l
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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)
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Procurement Tree
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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
• 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
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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 valuesbut an uncertain value for any particular time or event.
• For each uncertain variable, you define the possible valueswith a probability distribution.
• Distribution types include:
• A simulation calculates multiple scenarios of a model byrepeatedly sampling values from the probability distributions
• Computer software tools can perform as many trials (orscenarios) as you want and allow to select the optimalstrategy
…
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Monetary Value of $6.75M Bid
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Monetary Value of $7M Bid
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With Risk Preferences: 6.75M
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With Risk Preferences: 7M
L U t i ti i C t
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Larger Uncertainties in Cost
(Monetary Value)
L U t i ti II
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Large Uncertainties II
(Monetary Values)
With Risk Preferences for Large
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With Risk Preferences for Large
Uncertainties at lower bid
With Risk Preferences for
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With Risk Preferences for
Higher Bid
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Optimal Strategy
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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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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
Ways to Ensure of Flexibility
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Ways to Ensure of Flexibility
in Construction
• Alternative Delivery
• Clear spanning (to allowmovable 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
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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, explicitlyplan to adapt as events unfold
– Typically we delay a decision into the future
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Real Options
• Real Options theory provides a means ofestimating financial value of flexibility
– E.g. option to abandon a plant, expand bldg
• Key insight: NPV does not work well withuncertain costs/revenues
– E.g. difficult to model option of abandoninginvest.
• 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
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Considerations
• Tradeoffs
– 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 offw/greater flexibility!
• Frequently retrofitting $ > up-front $
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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•
Required – 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
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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 : aconstructively simple approach to decision making
• Bedford, Probabilistic risk analysis: foundations and methods
• … and a lot more!
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