Referring to the payoff table below answer the questions given below: State of Nature Decision Alternatives S1 S2 S2 S3 D1 7 4.5 5 2.5 D2 6 5 8 7 D3 4.5 5 5 5.5 D4 4 5 5.5 6.5 Construct decision tree for this problem Under the condition of uncertainty, what would be the recommended decision using the optimistic and pessimistic approaches?

Referring to the payoff table below answer the questions given below: State of Nature Decision Alternatives S1 S2 S2 S3 D1 7 4.5 5 2.5 D2 6 5 8 7 D3 4.5 5 5 5.5 D4 4 5 5.5 6.5 Construct decision tree for this problem Under the condition of uncertainty, what would be the recommended decision using the optimistic and pessimistic approaches?

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 1P

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Play Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters 15, 17, and 20. The current selling price is 45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters 5 million, 7.5 million, and 12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t 1) are determined as follows. Suppose that at the end of year t 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISKs output to find an interval such that you are 95% certain that the companys actual NPV will be within this interval.
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.)
7. Consider the following decision table, which Joe Blackburn has developed for Vanderbilt Enterprises: States of Nature Decision Alternatives Probability: 0.35 0.25 0.40 Low Medium High A $35 $80 $65 B $85 $50 $70 C $55 $70 $75 D $70 $85 $65 E $70 $75 $85 Part 2 The alternative that provides Blackburn the greatest expected monetary value (EMV LOADING... ) is ▼ D E A B C The EMV for this decision is $_______(enter your answer as a whole number).
A decision maker is looking to minimising costs through three alternative decisions a1 , b2 and c3 under two states of nature/events S1 and S2 with S2 having a probability of 30% . For a1 payoffs for s1 K100 million and s2 K540 million For a2 payoff for s1 K150 million and s2 –K50 million For a3 payoff for s1 K350 million and s2 K320 million Find EMV and recommend the course of action Find the EMV under certainty Use the EVC to find the EVPI Determine the opportunity loss table Find the course of action that minimises EOL Compare the minimum EOL with the EVPI.
A landlord can either lease for one or two years or sell offices outrightly for K100 million with payoffs as follows: Lease -100 50 150 Sell 100 100 100 The probability of rejecting is 30%, leasing for one year is 50% and for two years 20%. Required: What is the optimal decision strategy if perfect information were available? What is the expected value of perfect information? A decision maker is looking to minimising costs through three alternative decisions a1 , b2 and c3 under two states of nature/events S1 and S2 with S1 having a probability of 30% . For a1 payoffs for s1 K100 million and s2 K540 million For a2 payoff for s1 K150 million and s2 –K50 million For a3 payoff for s1 K350 million and s2 K320 million Required: Find EMV and recommend the course of action Find the…
9. A decision-maker has two alternative courses of action, A1 and A2. There are three possible states of nature, S1, S2, and S3. The table of conditional profits, as well as the probabilities for the states of nature, appear below. Based on this decision table, which decision alternative produces the higher EMV? States of Nature Alternatives S1 S2 S3 A1 10,000 20,000 6,000 A2 5,000 30,000 15,000 Probability 0.3 0.5 0.2 Part 2 The best decision is ▼ a. alternative Upper A 1alternative A1 b. alternative Upper A 2alternative A2 , with an EMV=$________(enter your response as a whole number).
Southern Gas Company (SGC) is preparing to make a bid for oil and gas leasing right in a newly opened drilling area in the Gulf of Mexico. SGC is trying to decide whether to place a high bid of $16 million or a low bid of $7 million. SGC expects to be bidding against its major competitor, Northern Gas Company (NGC) and predicts NGC to place a bid of $10 million with probability 0.4 or a bid of $6 million with probability 0.6. Geological data collected at the drilling site indicates a 0.15 probability of the reserves at the site being large, a 0.35 probability of being average, and a 0.50 probability of being unusable. A large or average reserve would most likely represent a net asset value of $120 million or $28 million, respectively, after all drilling and extraction costs are paid. The company that wins the bid will drill an exploration well at the site for a cost of $5 million. a. Develop a decision tree for this problem. b. What is the optimal decision according to the EMV…
(Show Solution): ABC Construction Company is going to decide whether they are going to expand their business, build an additional facility, or subcontract a partner company. The research and development department forecasted the following payoff values which are summarized in the table below. The values are expressed as GAINS and alpha = 0.6. Come up with a decision using the different criteria under conditions of uncertainty:
If you want to invest in a project that cost $3.5 million. As we are unsure about the future demand, there is a 40% probability of high demand with a present value for the project $3 million. There is a 25% probability of moderate demand with a present value of $2.5 million. In addition, there is a 35% probability of low demand with a present value is $1.5 million. Draw a decision tree for this problem. What is the expected net present value of the business? Should you invest? Explain. Assume that you can expand the project by investing another $0.6 million after you learn the true future demand state. This would make the present value of the business $3.9 million in the high‐demand state, $3.5 million in the moderate demand state, and $1.80 million in the low demand state. Draw a decision tree to reflect the option to expand. Evaluate the alternatives. What is the net present value of the business if you consider the option to expand? How valuable is the option to expand?
The following payoff table shows a profit for a decision analysis problem with two decision alternatives and three states of nature. In order to get full credit, show your all work done step by step including cell calculations using excel functions. State of Nature Decion Alternatives s1 s2 s3 d1 250 100 50 d2 100 75 100 a) Construct a decision tree for this problem. b) Suppose that the decision-maker obtains the probabilities P(s1)=0.65, P(s2)=0.15, and P(s3)=0.20. Use the expected value approach to determine the optimal decision.
Southern Gas Company (SGC) is preparing to make a bid for oil and gas leasing rights in a newly opened drilling area in the Gulf of Mexico. SGC is trying to decide whether to place a high bid of $16 million or a low bid of $7 million. SGC expects to be bidding against its major competitor, Northern Gas Company (NGC) and predicts NGC to place a bid of $10 million with probability 0.4 or a bid of $6 million with probability 0.6. Geological data collected at the drilling site indicates a 0.15 probability of the reserves at the site being large, a 0.35 probability of being average, and a 0.50 probability of being unusable. A large or average reserve would most likely represent a net asset value of $120 million or $28 million, respectively, after all drilling and extraction costs are paid. The company that wins the bid will drill an exploration well at the site for a cost of $5 million. a. Develop a decision tree for this problem. b. What is the optimal decision according to the EMV…
The research department of Unilever Ltd has recommended to the marketing departmentto launch a shampoo of three different types. The marketing manager has to decide one ofthe types of shampoo to be launched under the following estimated pay offs for variouslevels of sales:Estimated levels of sales15, 000 10,000 5, 0001. Egg shampoo2. Clinic shampoo3. Deluxe shampoo3040551015201053What will be the marketing manager’s decision ifiv. Laplace criterion is used?v. Regret criterion is used?