Department of Civil and Environmental Engineering Massachusetts Institute of Technology

1.040/1.4011.040/1.401Project ManagementProject Management

Spring 2006Spring 2006

Risk AnalysisRisk AnalysisDecision making under risk and Decision making under risk and

uncertaintyuncertainty

Department of Civil and Environmental Department of Civil and Environmental EngineeringEngineeringMassachusetts Institute of Technology Massachusetts Institute of Technology

PreliminariesPreliminaries

AnnouncementsAnnouncements RemainderRemainder

email Sharon Lin the team info by midnight, tonightemail Sharon Lin the team info by midnight, tonight Monday Feb 27 - Student Experience PresentationMonday Feb 27 - Student Experience Presentation Wed March 1st – Assignment 2 dueWed March 1st – Assignment 2 due

Today, recitation Joe Gifun, MIT facilityToday, recitation Joe Gifun, MIT facility Next Friday, March 3rd, Tour PDSI construction siteNext Friday, March 3rd, Tour PDSI construction site

1st group noon – 1:301st group noon – 1:30 2nd group 1:30 – 3:002nd group 1:30 – 3:00

Construction nightmares discussionConstruction nightmares discussion 16 - Psi Creativity Center, Design and Bidding 16 - Psi Creativity Center, Design and Bidding

phasesphases

Project Management PhaseProject Management Phase

FEASIBILITY

DESIGNPLANNING

CLOSEOUTDEVELOPMENT OPERATIONS

Financing&EvaluationRisk Analysis&Attitude

Risk Management PhaseRisk Management Phase

FEASIBILITY

DESIGNPLANNING

CLOSEOUTDEVELOPMENT OPERATIONS

RISK MNGRISK MNG

Risk management (guest seminar 1st wk April)Risk management (guest seminar 1st wk April) Assessment, tracking and controlAssessment, tracking and control Tools:Tools:

Risk Hierarchical modeling: Risk breakdown structuresRisk Hierarchical modeling: Risk breakdown structures Risk matrixesRisk matrixes Contingency plan: preventive measures, corrective actions, Contingency plan: preventive measures, corrective actions,

risk budget, etc.risk budget, etc.

Decision Making Under Decision Making Under Risk OutlineRisk Outline

Risk and UncertaintyRisk and Uncertainty Risk Preferences, Attitude and Risk Preferences, Attitude and

PremiumsPremiums Examples of simple decision treesExamples of simple decision trees Decision trees for analysisDecision trees for analysis Flexibility and real optionsFlexibility and real options

Decision makingDecision making

Uncertainty and RiskUncertainty and Risk

““risk” as risk” as uncertainty about a uncertainty about a consequenceconsequence

Preliminary questionsPreliminary questions What sort of risks are there and who What sort of risks are there and who

bears them in project management?bears them in project management? What practical ways do people use to What practical ways do people use to

cope with these risks?cope with these risks? Why is it that some people are willing to Why is it that some people are willing to

take on risks that others shun?take on risks that others shun?

Some RisksSome Risks Weather changesWeather changes Different productivityDifferent productivity (Sub)contractors are(Sub)contractors are

UnreliableUnreliable Lack capacity to do Lack capacity to do

workwork Lack availability to do Lack availability to do

workwork UnscrupulousUnscrupulous Financially unstableFinancially unstable

Late materials deliveryLate materials delivery LawsuitsLawsuits Labor difficultiesLabor difficulties Unexpected Unexpected

manufacturing costsmanufacturing costs Failure to find Failure to find

sufficient tenantssufficient tenants

Community oppositionCommunity opposition Infighting & Infighting &

acrimonious acrimonious relationshipsrelationships

Unrealistically low bidUnrealistically low bid Late-stage design Late-stage design

changes changes Unexpected Unexpected

subsurface conditionssubsurface conditions Soil typeSoil type GroundwaterGroundwater Unexpected ObstaclesUnexpected Obstacles

Settlement of adjacent Settlement of adjacent structuresstructures

High lifecycle costsHigh lifecycle costs Permitting problemsPermitting problems ……

Importance of RiskImportance of Risk Much time in construction Much time in construction

management is spent focusing on risksmanagement is spent focusing on risks Many practices in construction are Many practices in construction are

driven by riskdriven by risk Bonding requirementsBonding requirements Insurance Insurance LicensingLicensing Contract structureContract structure

General conditionsGeneral conditions Payment TermsPayment Terms Delivery MethodDelivery Method Selection mechanismSelection mechanism

OutlineOutline



Decision making under riskDecision making under riskAvailable TechniquesAvailable Techniques

Decision modelingDecision modeling Decision making under uncertaintyDecision making under uncertainty Tool: Tool: Decision treeDecision tree

Strategic thinking and problem Strategic thinking and problem solving:solving: Dynamic modeling (end of course)Dynamic modeling (end of course)

Fault treesFault trees

Introduction to Decision Introduction to Decision TreesTrees

We will use decision trees both forWe will use decision trees both for Illustrating decision making with Illustrating decision making with

uncertaintyuncertainty Quantitative reasoningQuantitative reasoning

RepresentRepresent Flow of timeFlow of time DecisionsDecisions Uncertainties (via events)Uncertainties (via events) Consequences (deterministic or stochastic)Consequences (deterministic or stochastic)

Decision Tree NodesDecision Tree Nodes

Decision (choice) NodeDecision (choice) Node

Chance (event) NodeChance (event) Node

Terminal (consequence) nodeTerminal (consequence) node Outcome (cost or benefit)Outcome (cost or benefit)

Time

Risk PreferenceRisk Preference

People are not indifferent to uncertaintyPeople are not indifferent to uncertainty Lack of indifference from uncertainty arises Lack of indifference from uncertainty arises

from uneven preferences for different from uneven preferences for different outcomesoutcomes

E.g. someone may E.g. someone may dislike losing $x far more than gaining $xdislike losing $x far more than gaining $x value gaining $x far more than they disvalue value gaining $x far more than they disvalue

losing $x.losing $x.

Individuals differ in comfort with Individuals differ in comfort with uncertainty based on circumstances and uncertainty based on circumstances and preferencespreferences

Risk averse individuals will pay “risk Risk averse individuals will pay “risk premiums” to avoid uncertaintypremiums” to avoid uncertainty

Risk preferenceRisk preference

The preference depends on decision maker The preference depends on decision maker point of viewpoint of view

Categories of Risk Categories of Risk AttitudesAttitudes

Risk attitude is a general way of Risk attitude is a general way of classifying risk preferencesclassifying risk preferences

ClassificationsClassifications Risk averse fear loss and seek surenessRisk averse fear loss and seek sureness Risk neutral are indifferent to Risk neutral are indifferent to

uncertaintyuncertainty Risk lovers hope to “win big” and don’t Risk lovers hope to “win big” and don’t

mind losing as muchmind losing as much Risk attitudes change over Risk attitudes change over

TimeTime CircumstanceCircumstance

Decision RulesDecision Rules

The pessimistic rule (maximin = minimax)The pessimistic rule (maximin = minimax) The conservative decisionmaker seeks to:The conservative decisionmaker seeks to:

maximize the minimum gain (if outcome = payoff)maximize the minimum gain (if outcome = payoff) or minimize the maximum loss (if outcome = loss, risk)or minimize the maximum loss (if outcome = loss, risk)

The optimistic rule (maximax)The optimistic rule (maximax) The risklover seeks to maximize the maximum The risklover seeks to maximize the maximum

gaingain Compromise (the Hurwitz rule):Compromise (the Hurwitz rule):

Max (Max (αα min + (1- min + (1- αα) max) , 0 ) max) , 0 ≤ α ≤ ≤ α ≤ 11 αα = 1 pessimistic = 1 pessimistic αα = 0.5 neutral = 0.5 neutral αα = 0 optimistic = 0 optimistic

The bridge case – unknown The bridge case – unknown prob’tiesprob’ties

replace

repair

$ 1.09 million

Investment PV

$1.61 M

$0.55

$1.43

•Pessimistic rulePessimistic rule• min (1, 1.61) = 1 replace the bridgemin (1, 1.61) = 1 replace the bridge

•The optimistic rule (maximax)The optimistic rule (maximax)• max (1, 0.55) = 0.55 repair … and hope it max (1, 0.55) = 0.55 repair … and hope it works!works!

The bridge case – known The bridge case – known prob’tiesprob’ties

replace

repair

$ 1.09 million

Investment PV

$1.61 M

$0.55

$1.43

Expected monetary valueExpected monetary valueE = (0.25)(1.61) + (0.5)(0.55) + (0.25)(1.43) = E = (0.25)(1.61) + (0.5)(0.55) + (0.25)(1.43) =

$ 1.04 M$ 1.04 M

0.25

0.5

0.25

Data link

The bridge case – The bridge case – decisiondecision

The pessimistic rule (maximin = The pessimistic rule (maximin = minimax)minimax) Min (Ei) = Min (1.09 , 1.04) = $ Min (Ei) = Min (1.09 , 1.04) = $

1.04 repair1.04 repair In this case = optimistic rule In this case = optimistic rule

(maximax)(maximax) Awareness of probabilities change Awareness of probabilities change

risk attituderisk attitude

Other criteriaOther criteria

Most likely valueMost likely value For each policy option we select the For each policy option we select the

outcome with the highest probabilityoutcome with the highest probability Expected value of Opportunity LossExpected value of Opportunity Loss

To buy soon or to buy laterTo 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

To buy soon or to buy laterTo buy soon or to buy later

Buy soon

-125

-95

-65

Buy later

-100

0. 5

0.25

0.25

The Utility TheoryThe Utility Theory

When individuals are faced with uncertainty When individuals are faced with uncertainty they make choices as is they are maximizing a they make choices as is they are maximizing a given criterion: the given criterion: the expected utilityexpected utility..

Expected utility is a measure of the individual's Expected utility is a measure of the individual's implicit preference, for each policy in the risk implicit preference, for each policy in the risk environment.environment.

It is represented by a numerical value It is represented by a numerical value associated with each monetary gain or loss in associated with each monetary gain or loss in order to indicate the utility of these monetary order to indicate the utility of these monetary values to the decision-maker.values to the decision-maker.

Adding a Preference Adding a Preference functionfunction

Expected (mean) valueExpected (mean) valueE = (0.5)(125) + (0.25)(95) + (0.25)(65) = -E = (0.5)(125) + (0.25)(95) + (0.25)(65) = -

102.5102.5Utility value:Utility value:

f(E) = ∑ Pf(E) = ∑ Paa * f(a) = 0.5 f(125) + 0.25 f(95) * f(a) = 0.5 f(125) + 0.25 f(95) + .25 f(65) =+ .25 f(65) =

= .5*0.7 + .25*1.05 + .25*1.35 = ~0.95= .5*0.7 + .25*1.05 + .25*1.35 = ~0.95Certainty value = -102.5*0.975 = -97.38Certainty value = -102.5*0.975 = -97.38

100125 65

1.7

1.35

Defining the Preference Defining the Preference FunctionFunction

Suppose to be awarded a $100M Suppose to be awarded a $100M contract pricecontract price

Early estimated cost $70MEarly estimated cost $70M What is the preference function of What is the preference function of

cost?cost? Preference means utility or satisfactionPreference means utility or satisfaction

$

utility

70

Notion of a Risk Notion of a Risk PremiumPremium

A risk premium is the amount paid by a A risk premium is the amount paid by a (risk averse) individual to avoid risk(risk averse) individual to avoid risk

Risk premiums are very common – what Risk premiums are very common – what are some examples?are some examples? Insurance premiumsInsurance premiums Higher fees paid by owner to reputable Higher fees paid by owner to reputable

contractorscontractors Higher charges by contractor for risky workHigher charges by contractor for risky work Lower returns from less risky investmentsLower returns from less risky investments Money paid to ensure flexibility as guard Money paid to ensure flexibility as guard

against riskagainst risk

Conclusion: To buy or Conclusion: To buy or not to buynot to buy

The risk averter buys a “future” The risk averter buys a “future” contract that allow to buy at $ 97.38contract that allow to buy at $ 97.38

The trading company (risk lover) will The trading company (risk lover) will take advantage/disadvantage of take advantage/disadvantage of future benefit/loss future benefit/loss

Certainty Equivalent Certainty Equivalent ExampleExample Consider a risk averse individual with Consider a risk averse individual with

preference fn preference fn ff faced with an faced with an investment c that providesinvestment c that provides 50% chance of earning $2000050% chance of earning $20000 50% chance of earning $050% chance of earning $0

Average Average moneymoney from investment = from investment = .5*$20,000+.5*$0=$10000.5*$20,000+.5*$0=$10000

Average Average satisfactionsatisfaction with the with the investment=investment= .5*f($20,000)+.5*f($0)=.25.5*f($20,000)+.5*f($0)=.25

This individual would be willing to This individual would be willing to trade for a trade for a suresure investment yielding investment yielding satisfaction>.25 insteadsatisfaction>.25 instead Can get .25 satisfaction for a sure fCan get .25 satisfaction for a sure f--

11(.25)=$5000(.25)=$5000 We call this the We call this the certainty equivalentcertainty equivalent to the to the

investmentinvestment Therefore this person should be willing to Therefore this person should be willing to

trade this investment for a sure amount of trade this investment for a sure amount of money>$5000money>$5000

.25

Mean valueOf investment

Mean satisfaction withinvestment

Certainty equivalentof investment

$50

00

.50

Example Cont’d (Risk Example Cont’d (Risk Premium)Premium) The risk averse individual would be willing The risk averse individual would be willing

to trade the uncertain investment c for any to trade the uncertain investment c for any certain return which is > $5000certain return which is > $5000

Equivalently, the risk averse individual Equivalently, the risk averse individual would be willing to pay another party an would be willing to pay another party an amount amount rr up to $5000 =$10000-$5000 for up to $5000 =$10000-$5000 for other less risk averse party to guarantee other less risk averse party to guarantee $10,000$10,000 Assuming the other party is not risk averse, Assuming the other party is not risk averse,

that party wins because gain that party wins because gain rr on average on average The risk averse individual wins b/c more The risk averse individual wins b/c more

satisfiedsatisfied

Certainty EquivalentCertainty Equivalent More generally, consider situation in which haveMore generally, consider situation in which have

Uncertainty with respect to consequence Uncertainty with respect to consequence cc Non-linear preference function Non-linear preference function ff

Note: E[X] is the mean (expected value) operatorNote: E[X] is the mean (expected value) operator The mean The mean outcomeoutcome of uncertain investment c is of uncertain investment c is

E[c]E[c] In example, this was .5*$In example, this was .5*$20,000+.5*$0=$10,00020,000+.5*$0=$10,000

The mean The mean satisfaction withsatisfaction with the investment is the investment is E[f(c)]E[f(c)] In example, this was .5*f($20,000)+.5*f($0)=.25In example, this was .5*f($20,000)+.5*f($0)=.25

We call fWe call f-1-1(E[f(c)]) the (E[f(c)]) the certainty equivalentcertainty equivalent of c of c Size of Size of sure sure return that would give the same satisfaction return that would give the same satisfaction

as as cc In example, was fIn example, was f-1-1(.25)=f(.25)=f-1-1(.5*20,000+.5*0)=$5,000 (.5*20,000+.5*0)=$5,000

Risk Attitude ReduxRisk Attitude Redux

The shapes of the preference functions The shapes of the preference functions means can classify risk attitude by means can classify risk attitude by comparing the certainty equivalent and comparing the certainty equivalent and expected valueexpected value For risk For risk loving loving individuals, individuals, ff-1-1(E[f(c)])(E[f(c)])>E[c]>E[c]

They want Certainty equivalent > mean outcomeThey want Certainty equivalent > mean outcome For risk For risk neutralneutral individuals, individuals, ff-1-1(E[f(c)])(E[f(c)])=E[c]=E[c] For risk For risk averseaverse individuals, individuals, ff-1-1(E[f(c)])(E[f(c)])<E[c]<E[c]

Motivations for a Risk Motivations for a Risk PremiumPremium

Consider Consider Risk averse individual A for whom Risk averse individual A for whom ff--

11(E[f(c)])(E[f(c)])<E[c]<E[c] Less risk averse party BLess risk averse party B

A can lessen the effects of risk by paying a A can lessen the effects of risk by paying a risk premium risk premium rr of up to E[c]- of up to E[c]-ff-1-1(E[f(c)]) to B (E[f(c)]) to B in return for a in return for a guarantee guarantee of of E[c] incomeE[c] income The risk premium shifts the risk to BThe risk premium shifts the risk to B The net investment gain for A is E[c]-r, but A is The net investment gain for A is E[c]-r, but A is

more satisfied because E[c] – r > fmore satisfied because E[c] – r > f-1-1(E[f(c)])(E[f(c)]) B gets average monetary gain of B gets average monetary gain of rr

Gamble or not to GambleGamble 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)]) = 0No help from risk analysis !!!!!

Multiple Attribute Multiple Attribute DecisionsDecisions

Frequently we care about multiple Frequently we care about multiple attributesattributes CostCost TimeTime QualityQuality Relationship with ownerRelationship with owner

Terminal nodes on decision trees can Terminal nodes on decision trees can capture these factors – but still need to capture these factors – but still need to make different attributes comparablemake different attributes comparable

The bridge case - Multiple The bridge case - Multiple tradeoffstradeoffs

MTTF = mean time to failure

Computation of Pareto-Optimal SetFor 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

Pareto OptimalityPareto Optimality

Even if we cannot directly weigh one attribute Even if we cannot directly weigh one attribute vs. another, we can rank some consequencesvs. another, we can rank some consequences

Can rule out decisions giving consequences Can rule out decisions giving consequences that are inferior with respect to that are inferior with respect to allall attributes attributes We say that these decisions are “dominated by” We say that these decisions are “dominated by”

other decisionsother decisions Key concept here: May not be able to identify Key concept here: May not be able to identify

best decisionsbest decisions, but we can rule out obviously , but we can rule out obviously badbad

A decision is “Pareto optimal” (or efficient A decision is “Pareto optimal” (or efficient solution) if it is not dominated by any other solution) if it is not dominated by any other decisiondecision

03/06/06 - Preliminaries03/06/06 - Preliminaries AnnouncementsAnnouncements

Due dates Stellar Schedule and not SyllabusDue dates Stellar Schedule and not Syllabus Term projectTerm project

Phase 2 due March 17thPhase 2 due March 17th Phase 3 detailed description posted on Stellar, due May Phase 3 detailed description posted on Stellar, due May

1111 Assignment PS3 posted on Stellar – due date Assignment PS3 posted on Stellar – due date

March 24March 24 Decision making under uncertaintyDecision making under uncertainty

Reading questions/comments?Reading questions/comments? Utility and risk attitudeUtility and risk attitude You can manage construction risksYou can manage construction risks Risk management and insurances - RecommendedRisk management and insurances - Recommended

Decision Making Under Decision Making Under RiskRisk



Multiple objectiveMultiple objectiveThe student’s dilemmaThe student’s dilemma

BiddingBidding

What What choiceschoices do we have? do we have? How does the chance of winning How does the chance of winning

vary with our bidding price?vary with our bidding price? How does our profit vary with our How does our profit vary with our

bidding price if we win?bidding price if we win?

Example Bidding Example Bidding Decision TreeDecision TreeTime

Bidding Decision Tree with Bidding Decision Tree with Stochastic Costs, Stochastic Costs, Competing BidsCompeting Bids

Selecting Desired Electrical Selecting Desired Electrical CapacityCapacity

Decision Tree Example: Decision Tree Example: Procurement TimingProcurement Timing

DecisionsDecisions Choice of order time (Order early, Choice of order time (Order early,

Order late)Order late) EventsEvents

Arrival time (On time, early, late)Arrival time (On time, early, late) Theft or damage (only if arrive early)Theft or damage (only if arrive early)

Consequences: CostConsequences: Cost Components: Delay cost, storage cost, Components: Delay cost, storage cost,

cost of reorder (including delay)cost of reorder (including delay)

Procurement TreeProcurement Tree



PremiumsPremiums Decision trees for representing Decision trees for representing

uncertaintyuncertainty Decision trees for analysisDecision trees for analysis Flexibility and real optionsFlexibility and real options

Analysis Using Decision Analysis Using Decision TreesTrees

Decision trees are a powerful Decision trees are a powerful analysis toolanalysis tool

Example analytic techniquesExample analytic techniques Strategy selection (Monte Carlo Strategy selection (Monte Carlo

simulation)simulation) One-way and multi-way sensitivity One-way and multi-way sensitivity

analysesanalyses Value of informationValue of information

Recall Competing Bid TreeRecall Competing Bid Tree

Monte Carlo simulationMonte Carlo simulation Monte Carlo simulation randomly generates values for Monte Carlo simulation randomly generates values for

uncertain variables over and over to simulate a model.uncertain variables over and over to simulate a model. It's used with the variables that have a known range It's used with the variables that have a known range

of values but an uncertain value for any particular of values but an uncertain value for any particular time or event. time or event.

For each uncertain variable, you define the possible For each uncertain variable, you define the possible values with a probability distribution.values with a probability distribution.

Distribution types include:Distribution types include:

A simulation calculates multiple scenarios of a model A simulation calculates multiple scenarios of a model by repeatedly sampling values from the probability by repeatedly sampling values from the probability distributionsdistributions

Computer software tools can perform as many trials Computer software tools can perform as many trials (or scenarios) as you want and allow to select the (or scenarios) as you want and allow to select the optimal strategyoptimal strategy

…

Monetary Value of Monetary Value of $6.75M Bid$6.75M Bid

Monetary Value of $7M Monetary Value of $7M BidBid

With Risk Preferences: With Risk Preferences: 6.75M6.75M

With Risk Preferences: With Risk Preferences: 7M7M

Larger Uncertainties in Larger Uncertainties in CostCost

(Monetary Value)(Monetary Value)

Large Uncertainties IILarge Uncertainties II(Monetary Values)(Monetary Values)

With Risk Preferences for With Risk Preferences for Large Uncertainties at Large Uncertainties at

lower bidlower bid

With Risk Preferences for With Risk Preferences for Higher BidHigher Bid

Optimal StrategyOptimal Strategy




uncertaintyuncertainty Examples of simple decision treesExamples of simple decision trees Decision trees for analysisDecision trees for analysis Flexibility and real optionsFlexibility and real options

Flexibility and Real Flexibility and Real OptionsOptions

Flexibility isFlexibility is providing additional providing additional choiceschoices

Flexibility typically has Flexibility typically has Value by acting as a way to lessen the Value by acting as a way to lessen the

negative impacts of uncertaintynegative impacts of uncertainty Cost Cost

Delaying decisionDelaying decision Extra timeExtra time Cost to pay for extra “fat” to allow for Cost to pay for extra “fat” to allow for

flexibilityflexibility

Ways to Ensure of Ways to Ensure of Flexibility Flexibility

in Constructionin Construction Alternative Delivery Alternative Delivery Clear spanning (to Clear spanning (to

allow movable walls) allow movable walls) Extra utility Extra utility

conduits (electricity, conduits (electricity, phone,…)phone,…)

Larger footings & Larger footings & columns columns

Broader foundationBroader foundation Alternative Alternative

heating/electrical heating/electrical

Contingent plans forContingent plans for Value engineeringValue engineering Geotechnical conditionsGeotechnical conditions Procurement strategyProcurement strategy

Additional elevatorAdditional elevator Larger electrical Larger electrical

panelspanels Property for expansionProperty for expansion Sequential Sequential

constructionconstruction Wiring to roomsWiring to rooms

Adaptive StrategiesAdaptive Strategies

An adaptive strategy is one that An adaptive strategy is one that changes the course of action based changes the course of action based on what is observed – i.e. one that on what is observed – i.e. one that has flexibilityhas flexibility Rather than planning statically up front, Rather than planning statically up front,

explicitly plan to adapt as events unfoldexplicitly plan to adapt as events unfold Typically we delay a decision into the Typically we delay a decision into the

futurefuture

Real OptionsReal Options Real Options theory provides a means of Real Options theory provides a means of

estimating financial estimating financial valuevalue of flexibility of flexibility E.g. option to abandon a plant, expand bldgE.g. option to abandon a plant, expand bldg

Key insight: NPV does not work well with Key insight: NPV does not work well with uncertain costs/revenuesuncertain costs/revenues E.g. difficult to model option of abandoning E.g. difficult to model option of abandoning

invest.invest. Model events using stochastic diff. Model events using stochastic diff.

equationsequations Numerical or analytic solutionsNumerical or analytic solutions Can derive from decision-tree based frameworkCan derive from decision-tree based framework

Example: Structural Form Example: Structural Form FlexibilityFlexibility

ConsiderationsConsiderations

TradeoffsTradeoffs Short-term speed and flexibilityShort-term speed and flexibility

Overlapping design & construction and different Overlapping design & construction and different construction activities limits changesconstruction activities limits changes

Short-term cost and flexibilityShort-term cost and flexibility E.g. value engineering away flexibilityE.g. value engineering away flexibility Selection of low bidderSelection of low bidder Late decisions can mean greater costsLate decisions can mean greater costs

NB: both budget & schedule may ultimately be NB: both budget & schedule may ultimately be better off w/greater flexibility!better off w/greater flexibility!

Frequently retrofitting $ > up-front $Frequently retrofitting $ > up-front $




uncertaintyuncertainty Examples of simple decision treesExamples of simple decision trees Decision trees for analysisDecision trees for analysis Flexibility and real optionsFlexibility and real options

ReadingsReadings RequiredRequired

More information:More information: Utility and risk attitude – Stellar Readings Utility and risk attitude – Stellar Readings

sectionsection Get prepared for next class:Get prepared for next class:

You can manage construction risks – StellarYou can manage construction risks – Stellar On-line textbook, from 2.4 to 2.12On-line textbook, from 2.4 to 2.12

Recommended:Recommended: Meredith Textbook, Chapter 4 Prj Meredith Textbook, Chapter 4 Prj

OrganizationOrganization Risk management and insurances – Risk management and insurances –

StellarStellar

Risk - MIT librariesRisk - MIT libraries Haimes, Risk modeling, assessment, and managementHaimes, Risk modeling, assessment, and management

Mun, Mun, Applied risk analysis : moving beyond Applied risk analysis : moving beyond uncertaintyuncertainty

Flyvbjerg, Mega-projects and riskFlyvbjerg, Mega-projects and risk

Chapman, Managing project risk and uncertainty : a Chapman, Managing project risk and uncertainty : a constructively simple approach to decision makingconstructively simple approach to decision making

Bedford, Probabilistic risk analysis: foundations and Bedford, Probabilistic risk analysis: foundations and methodsmethods

… … and a lot more!and a lot more!

Department of Civil and Environmental Engineering Massachusetts Institute of Technology

Documents

Transcript of Department of Civil and Environmental Engineering Massachusetts Institute of Technology