Project Risk Analysis and Management course MSc Industrial and Management Engineering Engineering and Management Department, Instituto Superior Técnico Academic Year 2007/2008 – 2nd Semester 1st test, 14/06/2008, 09:00 PROPOSAL FOR RESOLUTION Part I (6.5 values) 1. A Tornado graph provides information about: a) The impact on the outcome measure of varying the inputs in their range values simultaneously b) The level of variation in the input values that changes the decision to be taken c) The impact on the outcome measure of varying the inputs in their range values individually d) The space for the two way sensitivity analysis for two of the input variables e) None of the above 2. Which of the following activities might be included as an objective for risk management? a) The reduction of safety hazards b) The reduction of security lapses c) The increase in return of investment d) a) and b) e) a), b) and c) 3. Rank by decreasing order of changes of unlucky outcomes decisions based upon: a) Deterministic dominance, first order stochastic dominance, second order stochastic dominance, expected monetary value b) Deterministic dominance, second order stochastic dominance, first order stochastic dominance, expected monetary value c) Expected monetary value, deterministic dominance, first order stochastic dominance, second order stochastic dominance d) Expected monetary value, first order stochastic dominance, second order stochastic dominance, deterministic dominance e) None of the above 4. The following experiment was applied to ask for the probability of economic recession, by asking an individual which p value would make indifferent the choice between option 1 and option 2. The experiment represents: 1 a) A direct method to extract probability assessments using a betting strategy game b) An indirect method to extract probability assessments using a betting strategy game c) A direct method to extract probability assessments using a reference lottery game d) An indirect method to extract probability assessments using a reference lottery game e) None of the above 5. Which of the following statements is true with reference to the extended Pearson Tukey method: a) A continuous fan node is replaced by a three branch uncertainty node; there is an elicitation of the three outcomes to choose and a free choice of the three probabilities to assign to these outcomes; and the method should be used only for symmetric distributions b) A continuous fan node is replaced by a three branch uncertainty node; there is an elicitation of the three outcomes to choose and a free choice of the three probabilities to assign to these outcomes; and the method should be used only for asymmetric distributions c) A continuous fan node is replaced by a three branch uncertainty node; there is an elicitation of the three outcomes to choose and the method already defines the three probabilities assigned to these outcomes; and the method should be used only for symmetric distributions d) A continuous fan node is replaced by a three branch uncertainty node; there is an elicitation of the three outcomes to choose and the method already defines the three probabilities assigned to these outcomes; and the method should be used only for asymmetric distributions e) A continuous fan node is replaced by a four branch uncertainty node; there is an elicitation of the four outcomes to choose and the method already defines the four probabilities assigned to these outcomes; and the method should be used only for asymmetric distributions 2 6. You have a prior probability distribution for an uncertain event. Which of the following circumstances will apply to the posterior probability distribution? a) Bayes theorem is used as a mechanism for using the data to update the prior probability distribution in order to arrive at a posterior probability distribution b) The prior probability distribution uses additional data collected by the decision‐
maker in comparison to the posterior probability distribution c) The posterior probability distribution will need to follow the same probability distribution as the prior probability distribution, but will have different values for parameters d) a) and c) e) None of the above 7. Riskview is a program useful to: a)
b)
c)
d)
Represent decision trees Represent influence diagrams Represent and adjust probability distributions to data Simulate uncertain quantities that result from an interaction of several uncertain quantities modeled with probability distributions e) None of the above 8. Using a theoretical probability distribution to quantify uncertainty from a set of data is appropriate when: a) The distribution captures the characteristics of the system from which the uncertain event arises b) The characteristics of data correspond to the assumptions that give rise to a standard distribution c) The decision maker does not want to make subjective assessments of data d) a) and b) e) a), b) and c) 9. If you have the following influence diagram (with X1 and X4 having each two decisions, and X2 and X3 representing uncertainty nodes with two branches) and the corresponding dataset with historical information on values for X1, X2, X3 , X4 and Y (being Y the payoff variable), which will be the easiest way to model uncertainty of Y? 3 a) Computing through the use of an influence diagram because there will be a small number of possible outcomes b) Computing through the use of an influence diagram because there will be a large number of possible outcomes c) Estimating an econometric regression with Y as a dependent variable and X1 and X4 as explanatory/independent variables, so that the remaining variability in Y represents its probability distribution capturing uncertainty d) Estimating an econometric regression with Y as a dependent variable and X1, X2, X3 and X4 as explanatory/independent variables, so that the remaining variability in Y represents its probability distribution capturing uncertainty e) Estimating an econometric regression with Y as a dependent variable and X2 and X3 as explanatory/independent variables, so that the remaining variability in Y represents its probability distribution capturing uncertainty 10. Which of the following values increase the value of imperfect information: a) The highest the value of perfect information b) The highest the level of accuracy of an expert predicting outcomes c) The highest the expected value in the absence of additional information d) a) and b) e) a), b) and c) 11. Which of the following statements is true? a) The value of control is higher than the value of perfect information b) The value of perfect information is higher than the value of imperfect information c) The value of imperfect information is higher than the value of control d) a) and b) e) b) and c) 12. You have 500 euros to invest, and you might invest it in three different investment options, with the risk outcomes represented in the decision tree below (outcomes represented in terms of net earnings in euros). If the investor is risk averse and the utility of 25 is 100, which of the following statements apply? 4 a) The certainty equivalent of the high risk investment is above 100 b) The certainty equivalent of the low risk investment is above 100 c) The certainty equivalent of high risk investment is lower than the certainty equivalent of the low risk investment d) All of the above e) None of the above 13. The SHAMPU framework for projects risk management is: a)
b)
c)
d)
A specific process for managing risk Has been used since the 1970s as a risk management process Used by most companies nowadays A tool that focuses specifically on the risk factors which have a negative impact on a project e) None of the above Part II (13.5 values) Exercise 1 (2 values) Using the following information and the influence diagram below, draw the decision tree for the machine replacement decision. A manufacturer plant manager who faces a string of defective products must decide what action to take. A maintenance engineer has been dispatched to do a preliminary inspection on machine 3, which is suspected to be the source of the problem. The preliminary check will provide some indication as to whether Machine 3 truly is the culprit, but only a through and expensive series of tests (not possible at the moment) will reveal the truth. The manager has two alternatives. First, a replacement for machine 3 is available and could be brought in at a certain cost; if machine 3 is the problem, then work can proceed and the production schedule will not fall behind; if machine 3 is not the source of the defects, the problem will still exist, and the workers will have to change to another product while the problem is tracked down. 5 Second, the workers could be changed immediately to the other product. This action would certainly cause the production schedule for the current product to fall behind but would avoid the risk (and cost) of unnecessarily replacing machine 3. 6 Exercise 2 (3.5 values) Solve the decision tree for the Figure below which contains a profit maximization problem. Create risk profiles and cumulative risk profiles for all possible strategies in the Figure below. Is one strategy stochastically dominant? Explain. 7 The risk profiles could be computed both as calculating A vs B, or A,A1 vs. A,A2 vs. B. The solution for the case of comparing A and B is: 8 There is no first order stochastic dominance. Exercise 3 (2 values) Julie Myers, a graduating senior in accounting, is preparing for an interview with a Big Eight accounting firm. Before the interview, she sets her chances of eventually getting an offer of 50%. Then, on thinking about her friends who have interviewed and gotten offers from this firm, she realizes that of the people that received offers, 95% had good interviews. On the other hand, of those who did not receive offers, 75% said they had good interviews. If Julie Myers has a good interview, what are her chances of receiving an offer? Explain how to answer to this, but you do not need to compute the values. P(offer)=0.5 P(good interview|offer)=0.95 P(good interview|no offer)=0.75 P(offer|good interview)=P(offer|good) =[P(good|offer)*P(offer)]/[ P(good|offer)*P(offer)+ P(good|no offer)*P(no offer)] =0.95*0.5/(0.95*0.5+0.75*0.5)=0.5588 Exercise 4 (2 values) A friend of yours, who lives in Reno, has life insurance, homeowner’s insurance, and automobile insurance and also regularly plays the quarter slot machines in casinos. What kind of a utility function might explain this kind of behavior? How else might you explain such behavior? Insurance suggests risk aversion; applying money in slot machines suggests risk propensity. One possibility is that the decision‐maker could have a S‐shaped utility function, indicating that he is risk‐seeking for very small amounts but risk averse for large ones. Alternatively, he could just get a lot of entertainment value from playing the slot machines. If this is the case, this could perhaps be modeled with another dimension in his utility function. Another explanation is that he might be 9 prone to risk if insurance is compulsory. Exercise 5 (1.5 values) Someone argues that cigarette smoking is not unhealthy because his grandfather smoked three packs of cigarettes a day and lived to be 100. The grandfather's health could simply be an unusual case that does not speak to the health of smokers in general. Explain briefly which heuristic is playing in this situation and which are the consequences of this heuristic for decision and risk analysis. The availability heuristic is at place (people base their prediction of the frequency of an event or the proportion within a population based on how easily an example can be brought to mind). Example of consequence: The estimates produced using faulty methods that do not account for heuristics implies errors in the basis for action. In this case, the information is not representative of the risk of a normal population. Exercise 6 (2.5 values) Discuss the importance of distinguishing between targets, expected values and commitments in risk management processes. Provide examples on how target, expected values and commitments should be set and used in a risk management process. ‘Targets’ are values that people can aspire to in a project. Targets are set at a level lower than expected cost, with provisions accounting for the difference; need to be realistic to be credible; might be set at a level that has less than a 20% chance of being achieved; need to reflect the opportunity aspect of uncertainty and the need for goals that stretch people. ‘Expected values’ are unbiased predictors of outcomes from a project. ‘Commitments’ need to be distinguished in terms of and are based upon expected costs and contingency values; commitments are set at levels that have an 80% to 90% chance of not being exceeded is common. Distinguishing between targets, expected values and commitments is central for risk management processes. Organizations which do not quantify uncertainty have no real basis for distinguishing targets, expected values and commitments. In these cases, single value performance levels are employed to serve all three purposes, often with disastrous results –the cost estimate, the completion date and the promised performance become less and less plausible! Example applied to cost, time or other relevant measure of performance might be presented. 10