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Title: Lecture 4 Risk Analysis


1
1.040/1.401Project ManagementSpring 2006Risk
AnalysisDecision making under risk and
uncertainty

Department of Civil and Environmental
Engineering Massachusetts Institute of Technology
2
Preliminaries
  • Announcements
  • Remainder
  • email 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 130
  • 2nd group 130 300
  • Construction nightmares discussion
  • 16 - Psi Creativity Center, Design and Bidding
    phases

3
Project Management Phase
DESIGN PLANNING
DEVELOPMENT
OPERATIONS
FEASIBILITY
CLOSEOUT
4
Risk Management Phase
RISK MNG
DESIGN PLANNING
DEVELOPMENT
OPERATIONS
FEASIBILITY
CLOSEOUT
  • 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
  • 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 riskAvailable 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
Time
  • Decision (choice) Node
  • Chance (event) Node
  • Terminal (consequence) node
  • Outcome (cost or benefit)

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

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 dont 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 (a min (1- a) max) , 0 a 1
  • a 1 pessimistic
  • a 0.5 neutral
  • a 0 optimistic

18
The bridge case unknown probties
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 probties
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
  • 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
-100-305 -125
-1005 -95
-100530 -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
100
125
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) .50.7 .251.05
.251.35 0.95 Certainty value -102.50.975
-97.38
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
  • .520,000.5010000
  • Average satisfaction with the investment
  • .5f(20,000).5f(0).25
  • This individual would be willing to trade for a
    sure investment yielding satisfactiongt.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 moneygt5000

Mean satisfaction with investment
.50
.25
Certainty equivalent of investment
Mean value Of investment
5000
30
Example Contd (Risk Premium)
  • The risk averse individual would be willing to
    trade the uncertain investment c for any certain
    return which is gt 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

31
Certainty Equivalent
  • More generally, consider situation in which have
  • Uncertainty with respect to consequence c
  • Non-linear preference function f
  • Note EX is the mean (expected value) operator
  • The mean outcome of uncertain investment c is
    Ec
  • In example, this was .520,000.5010,000
  • The mean satisfaction with the investment is
    Ef(c)
  • In example, this was .5f(20,000).5f(0).25
  • We call f-1(Ef(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(.520,000.50)5,00
    0

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(Ef(c))gtEc
  • They want Certainty equivalent gt mean outcome
  • For risk neutral individuals, f-1(Ef(c))Ec
  • For risk averse individuals, f-1(Ef(c))ltEc

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

34
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(Ef(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 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
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

38
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

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 objectiveThe students 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
54
Monetary Value of 7M Bid
55
With Risk Preferences 6.75M
56
With Risk Preferences 7M
57
Larger Uncertainties in Cost(Monetary Value)
58
Large Uncertainties II(Monetary Values)
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
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
75
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 off w/greater flexibility!
  • Frequently retrofitting gt 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
  • 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!
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