The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.States of NatureDecisionAlternative$15253d1d22409015909065Suppose that the decision maker obtained 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.EV(d₁)EV(d2)==The optimal decision is --?--✓

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Answered: The following payoff table shows profit…

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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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.
Which investment should Warren make under each of the following criteria? a. Maximax criterion. b. Maximin criterion. c. Maximum likelihood criterion. d. Bayes’ decision rule. e. The investor decides that Bayes’ decision rule is his most reliable decision criterion. He believes that 0.1 is just about right as the prior probability of an improving economy, but is quite uncertain about how to split the remaining probabilities between a stable economy and a worsening economy. Therefore, he now wishes to do some sort of sensitivity analysis with respect to these latter two prior probabilities. If he still wants to choose the alternative from the Bayes’ decision rule (part d): e1. How much would be the maximum amount of the prior probability of a stable economy? e2. How much would be the minimum amount of the prior probability of a worsening economy?
Many decision problems have the following simplestructure. A decision maker has two possible decisions,1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utility.
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?
A manager is deciding whether to build a small or a large facility. Much depends on the future demand that the facility must serve, and demand may be small or large. The manager knows with certainty the payoffs that will result under each alternative, shown in the following payoff table. The payoffs (in $000) are the present values of future revenues minus costs for each alternative in each event. Possible Future DemandAlternative Low HighSmall facility 200 270Large facility 160 800Do nothing 0 0What is the best choice if future demand will be low?
A store owner must decide whether to build a small or a large facility at a new location. Demand at a location can be either small or large, which probabilities estimated to be 0.4 and 0.6, respectively. If small facility is built and demand proves to be high, the manager may choose not to expand (payoff=P235,000) or to expand (payoff=P275,000). If a small facility is built and demand is low, there is no reason to expand and the payoff is P220,000. If a large facility is built and demand proves to be low, the choice is to do nothing (P60,000) or to stimulate demand through local advertising. The response to advertising may be either modest or sizable, with their probabilities estimated to be 0.3 and 0.7, respectively. If it is modest, the payoff grows to P230,000 if the response is sizable. Finally, if a large facility is built and demand turns out to be high, the payoff is P900,000.a.) Draw a decision tree.b.) Determine the expected payoff for each decision and event node.c.)…
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.
Maximus Steel plans to introduce one of three new products code-named: Wren, Hawk, and Nightingale. The marketing department indicated that the success of any product depends on the market conditions (Favorable, Neutral, or Unfavorable). The profit the company will earn also depends on the market conditions. The table below shows the probability estimated for each market condition and the profits Maximus Steel will realize within those conditions: Product Code Market Conditions Favorable P = 0.2 Neutral P = 0.7 Unfavorable P = 0.1 Wren $120,000 $70,000 ($30,000) Hawk $60,000 $40,000 $20,000 Nightingale $35,000 $30,000 $30,000 Maximus Steel is considering hiring a market research firm to do a survey to determine future market conditions. The results of the survey will indicate either positive or negative market conditions. There is a 0.60 probability of a positive report, given favorable conditions; a 0.30 probability of a positive…
Maximus Steel plans to introduce one of three new products code-named: Wren, Hawk, and Nightingale. The marketing department indicated that the success of any product depends on the market conditions (Favorable, Neutral, or Unfavorable). The profit the company will earn also depends on the market conditions. The table below shows the probability estimated for each market condition and the profits Maximus Steel will realize within those conditions: Product Code Market Conditions Favorable P = 0.2 Neutral P = 0.7 Unfavorable P = 0.1 Wren $120,000 $70,000 ($30,000) Hawk $60,000 $40,000 $20,000 Nightingale $35,000 $30,000 $30,000 Part 1 Instructions: Develop the opportunity loss table and compute the expected opportunity loss for each product.
Suppose that a decision is faced with three decision alternatives and four states of nature.The following profit payoff table is constructed: ALTERNATIVES STATE OF NATURE S1 S2 S3 S4 A1 18 12 15 8 A2 15 14 10 11 A3 13 16 19 15 Assuming that the decision maker has no knowledge about the probabilities of occurrenceof the four states of nature, find the decisions to be recommended under each of thefollowing criteria:i. Maximin criterionii. Maximax criterioniii. Minimax Reject criterioniv. Hurwicz criterion with α = 0.6
A firm that plans to expand its product line must decide whether to build a small or a large facilityto produce the new products. If it builds a small facility and demand is low, the net present valueafter deducting for building costs will be $400,000. If demand is high, the firm can either maintainthe small facility or expand it. Expansion would have a net present value of $450,000, and maintaining the small facility would have a net present value of $50,000.If a large facility is built and demand is high, the estimated net present value is $800,000. If demandturns out to be low, the net present value will be – $10,000.The probability that demand will be high is estimated to be .60, and the probability of low demandis estimated to be .40.a. Analyze using a tree diagram.
A firm that plans to expand its product line must decide whether to build a small or a large facilityto produce the new products. If it builds a small facility and demand is low, the net present valueafter deducting for building costs will be $400,000. If demand is high, the firm can either maintainthe small facility or expand it. Expansion would have a net present value of $450,000, and maintaining the small facility would have a net present value of $50,000.If a large facility is built and demand is high, the estimated net present value is $800,000. If demandturns out to be low, the net present value will be – $10,000.The probability that demand will be high is estimated to be .60, and the probability of low demandis estimated to be .40. 1- Compute the EVPI 2- Determine the range over which each alternative would be best in terms of the value of P ( low demand )

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