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1.040/1.401Project Management
Spring 2006
Risk AnalysisDecision making under risk and uncertainty
Department of Civil and Environmental Engineering
Massachusetts Institute of Technology
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Preliminaries
Announcements
Remainder
email Sharon Lin the team info by midnight, tonight
Monday Feb 27 - Student Experience Presentation Wed March 1stAssignment 2 due
Today, recitation Joe Gifun, MIT facility
Next Friday, March 3rd, Tour PDSI construction site
1st group noon1:30 2nd group 1:303:00
Construction nightmares discussion
16 - Psi Creativity Center, Design and Bidding phases
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Project Management Phase
FEASIBILITY DESIGN
PLANNING
CLOSEOUTDEVELOPMENT OPERATIONS
Financing&Evaluation
Risk Analysis&Attitude
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Risk Management Phase
FEASIBILITY DESIGNPLANNING
CLOSEOUTDEVELOPMENT OPERATIONS
RISK MNG
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.
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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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Uncertainty and Risk
risk as uncertainty about a consequence
Preliminary questions
What sort of risks are there and who bears them inproject management?
What practical ways do people use to cope withthese 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 sufficient
tenants
Community opposition Infighting & acrimonious
relationships 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 is spentfocusing on risks
Many practices in construction are driven by risk 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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Risk Preference
People are not indifferent to uncertainty
Lack of indifference from uncertainty arises fromuneven 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 uncertaintybased on circumstances and preferences
Risk averse individuals will pay risk premiums
to avoid uncertainty
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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 dont mind losing
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)
The optimistic rule (maximax)
The risklover seeks to maximize the maximum gain
Compromise (the Hurwitz rule):
Max (min + (1- ) max) , 0 1
= 1 pessimistic
= 0.5 neutral
= 0 optimistic
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The bridge caseunknown probties
replace
repair
$ 1.09 million
Investment PV
$1.61 M
$0.55
$1.43
Pessimistic rulemin (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 caseknown probties
replace
repair
$ 1.09 million
Investment PV
$1.61 M
$0.55
$1.43
Expected monetary valueE = (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 casedecision
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 withthe highest probability
Expected value of Opportunity Loss
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To buy soon or to buy later
Buy soon
Current price = 100S1 = + 30%S2 = no price variationS3 = - 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 makechoices as is they are maximizing a given criterion: theexpected utility.
Expected utility is a measure of the individual's implicitpreference, for each policy in the risk environment.
It is represented by a numerical value associated witheach monetary gain or loss in order to indicate theutility 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) = -102.5Utility 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 contract price 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 commonwhat aresome 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
The risk averter buys a future contract that
allow to buy at $ 97.38
The trading company (risk lover) will takeadvantage/disadvantage of future benefit/loss
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Certainty Equivalent Example Consider a risk averse individual with
preference fnffaced with an investment cthat provides 50% chance of earning $20000
50% chance of earning $0
Average moneyfrom investment =
.5*$20,000+.5*$0=$10000 Average satisfactionwith the investment=
.5*f($20,000)+.5*f($0)=.25
This individual would be willing to trade for asureinvestment yielding satisfaction>.25instead Can get .25 satisfaction for a sure f-1(.25)=$5000
We call this the certainty equivalentto the investment
Therefore this person should be willing to tradethis investment for a sure amount of
money>$5000
.25
Mean valueOf investme
Mean satisfactionwithinvestment
Certainty equivaleof investment
$5000
.50
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Example Contd (Risk Premium)
The risk averse individual would be willing totrade the uncertain investment c for any certainreturn which is > $5000
Equivalently, the risk averse individual would bewilling to pay another party an amount rup to$5000 =$10000-$5000 for other less risk averseparty to guarantee $10,000
Assuming the other party is not risk averse, thatparty wins because gain ron 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 functionf
Note: E[X] is the mean (expected value) operator
The mean outcomeof uncertain investment c is E[c]
In example, this was .5*$20,000+.5*$0=$10,000
The mean satisfaction withthe 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 equivalentof 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 meanscan classify risk attitude by comparing thecertainty equivalent and expected value
For risk loving individuals, f-1(E[f(c)])>E[c]
They want Certainty equivalent > mean outcome
For risk neutralindividuals, f-1(E[f(c)])=E[c]
For risk averseindividuals, 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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Gamble or not to Gamble
EMV
(0.5)(-1) + (0.5)(1) = 0
Preference function f(-1)=0, f(1)=100Certainty 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 factorsbut still need to make differentattributes comparable
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The bridge case - Multiple tradeoffs
MTTF = mean time to failure
Computation of Pareto-Optimal SetFor decision D2
ReplaceMTTF 10.0000Cost 1.00
C3MTTF 6.6667Cost 0.30
C4MTTF 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 allattributes 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 Stellardue 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 students 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 choicesdo we have?
How does the chance of winning vary with ourbidding price?
How does our profit vary with our bidding priceif we win?
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Example Bidding Decision TreeTime
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Bidding Decision Tree with
Stochastic Costs, Competing Bids
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Selecting Desired Electrical Capacity
T
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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 ofreorder (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 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 byrepeatedly sampling values from the probability distributions
Computer software tools can perform as many trials (orscenarios) as you want and allow to select the optimal strategy
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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 Ri k P f f L
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With Risk Preferences for Large
Uncertainties at lower bid
With Ri k Pr f r n f r
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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 isproviding 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 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
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Adaptive Strategies
An adaptive strategy is one that changes thecourse of action based on what is observedi.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 valueof 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 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
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Considerations
Tradeoffs
Short-term speed and flexibility
Overlapping design & construction and different constructionactivities 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 attitudeStellar Readings section
Get prepared for next class:
You can manage construction risksStellar
On-line textbook, from 2.4 to 2.12
Recommended:
Meredith Textbook, Chapter 4 Prj Organization Risk management and insurancesStellar
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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!