Which of the following is true? a)The maximin criterion is an approach in Optimization under uncertainty which finds a solution that has the best possible payoff. b)The maximin criterion is an approach in Optimization under uncertainty which finds a solution with the best worst possible payoff. c)A risk profile represents the probability distribution of uncertain inputs. d)Decision tree is a method to solve any optimization problem when the outcomes are subject to uncertainty.

Which of the following is true? a)The maximin criterion is an approach in Optimization under uncertainty which finds a solution that has the best possible payoff. b)The maximin criterion is an approach in Optimization under uncertainty which finds a solution with the best worst possible payoff. c)A risk profile represents the probability distribution of uncertain inputs. d)Decision tree is a method to solve any optimization problem when the outcomes are subject to uncertainty.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section9.2: Elements Of Decision Analysis

Problem 3P

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Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks: (1) it allows negative values, even though they may be extremely improbable, and (2) it is a symmetric distribution. Many situations are modelled better with a distribution that allows only positive values and is skewed to the right. Two of these that have been used in many real applications are the gamma and lognormal distributions. @RISK enables you to generate observations from each of these distributions. The @RISK function for the gamma distribution is RISKGAMMA, and it takes two arguments, as in =RISKGAMMA(3,10). The first argument, which must be positive, determines the shape. The smaller it is, the more skewed the distribution is to the right; the larger it is, the more symmetric the distribution is. The second argument determines the scale, in the sense that the product of it and the first argument equals the mean of the distribution. (The mean in this example is 30.) Also, the product of the second argument and the square root of the first argument is the standard deviation of the distribution. (In this example, it is 3(10=17.32.) The @RISK function for the lognormal distribution is RISKLOGNORM. It has two arguments, as in =RISKLOGNORM(40,10). These arguments are the mean and standard deviation of the distribution. Rework Example 10.2 for the following demand distributions. Do the simulated outputs have any different qualitative properties with these skewed distributions than with the triangular distribution used in the example? a. Gamma distribution with parameters 2 and 85 b. Gamma distribution with parameters 5 and 35 c. Lognormal distribution with mean 170 and standard deviation 60
The model in Example 9.3 has only two market outcomes, good and bad, and two corresponding predictions, good and bad. Modify the decision tree by allowing three outcomes and three predictions: good, fair, and bad. You can change the inputs to the model (monetary values and probabilities) in any reasonable way you like. Then you will also have to modify the Bayes rule calculations. You can decide whether it is easier to modify the existing tree or start from scratch with a new tree.
Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)
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In Example 11.1, the possible profits vary from negative to positive for each of the 10 possible bids examined. a. For each of these, use @RISKs RISKTARGET function to find the probability that Millers profit is positive. Do you believe these results should have any bearing on Millers choice of bid? b. Use @RISKs RISKPERCENTILE function to find the 10th percentile for each of these bids. Can you explain why the percentiles have the values you obtain?
Software development is an inherently risky and uncertain process. For example, there are many examples of software that couldnt be finished by the scheduled release datebugs still remained and features werent ready. (Many people believe this was the case with Office 2007.) How might you simulate the development of a software product? What random inputs would be required? Which outputs would be of interest? Which measures of the probability distributions of these outputs would be most important?