1.040/1.401 Project Management Spring 2006 Risk Analysis Decision making under risk and uncertainty

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 – 1:30 • 2nd group 1:30 – 3:00 • Construction nightmares discussion • 16 - Psi Creativity Center, Design and Bidding phases

3. Financing&Evaluation Risk Analysis&Attitude Project Management Phase DESIGN PLANNING DEVELOPMENT OPERATIONS CLOSEOUT FEASIBILITY

4. 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. RISK MNG DESIGN PLANNING DEVELOPMENT OPERATIONS CLOSEOUT FEASIBILITY

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. 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 … Some Risks

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 don’t 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 (α min + (1- α) max) , 0 ≤ α ≤ 1 • α = 1 pessimistic • α = 0.5 neutral • α = 0 optimistic

18. The bridge case – unknown prob’ties $ 1.09 million replace 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 prob’ties $ 1.09 million replace 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 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 Buy later 0. 5 0.25 0.25

24. 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. The Utility Theory

25. Adding a Preference function 1.35 1 .7 125 65 100 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

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 = • .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 for a sure investment yielding satisfaction>.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 money>$5000 Mean satisfaction with investment .50 .25 Certainty equivalent of investment Mean value Of investment $5000

30. Example Cont’d (Risk Premium) • 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

31. 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

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(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)])<E[c]

33. Motivations for a Risk Premium • Consider • Risk averse individual A for whom f-1(E[f(c)])<E[c] • Less risk averse party B • 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

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(E[f(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 student’s 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. Bidding Decision Tree with Stochastic Costs, Competing Bids

45. Selecting Desired Electrical Capacity

46. 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)

47. Procurement Tree

48. 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

49. 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

50. Recall Competing Bid Tree