Example Problem Solution


[Page 547 ( continued )]

The following example will illustrate the solution procedure for a decision analysis problem.

Problem Statement

T. Bone Puckett, a corporate raider, has acquired a textile company and is contemplating the future of one of its major plants, located in South Carolina. Three alternative decisions are being considered : (1) expand the plant and produce lightweight, durable materials for possible sales to the military, a market with little foreign competition; (2) maintain the status quo at the plant, continuing production of textile goods that are subject to heavy foreign competition; or (3) sell the plant now. If one of the first two alternatives is chosen , the plant will still be sold at the end of a year. The amount of profit that could be earned by selling the plant in a year depends on foreign market conditions, including the status of a trade embargo bill in Congress. The following payoff table describes this decision situation:


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State of Nature

Decision

Good Foreign Competitive Conditions

Poor Foreign Competitive Conditions

Expand

$ 800,000

$ 500,000

Maintain status quo

1,300,000

150,000

Sell now

320,000

320,000


  1. Determine the best decision by using the following decision criteria:

    1. Maximax

    2. Maximin

    3. Minimax regret

    4. Hurwicz ( a = .3)

    5. Equal likelihood

  2. Assume that it is now possible to estimate a probability of .70 that good foreign competitive conditions will exist and a probability of .30 that poor conditions will exist. Determine the best decision by using expected value and expected opportunity loss.

  3. Compute the expected value of perfect information.

  4. Develop a decision tree, with expected values at the probability nodes.

  5. T. Bone Puckett has hired a consulting firm to provide a report on future political and market situations. The report will be positive (P) or negative (N), indicating either a good (g) or poor (p) future foreign competitive situation. The conditional probability of each report outcome, given each state of nature, is

    P (Pg) = .70

    P (Ng) = .30

    P (Pp) = .20

    P (Np) = .80

    Determine the posterior probabilities by using Bayes's rule.

  6. Perform a decision tree analysis by using the posterior probability obtained in (e).

Solution

Step  1.
(part A): Determine Decisions Without Probabilities

Maximax:

   

Expand

$ 800,000

 

Status quo

1,300,000

Maximum

Sell

320,000

 

Decision: Maintain status quo.


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Maximin:

   

Expand

$ 500,000

Maximum

Status quo

-150,000

 

Sell

320,000

 

Decision: Expand.

Minimax regret:

   

Expand

$500,000

Minimum

Status quo

650,000

 

Sell

980,000

 

Decision: Expand.

Hurwicz ( a = .3):

 

Expand

$800,000(.3) + 500,000(.7) = $590,000

Status quo

$1,300,000(.3) 150,000(.7) = $285,000

Sell

$ 320,000(.3) + 320,000(.7) = $ 320,000


Decision: Expand.

Equal likelihood:

 

Expand

$800,000(.50) + 500,000(.50) = $650,000

Status quo

$1,300,000(.50) 150,000(.50) = $575,000

Sell

$320,000(.50) + 320,000(.50) = $320,000


Decision: Expand.

Step  2.
(part B): Determine Decisions with EV and EOL

Expected value:

 

Expand

$800,000(.70) + 500,000(.30) = $710,000

Status quo

$1,300,000(.70) 150,000(.30) = $865,000

Sell

$320,000(.70) + 320,000(.30) = $320,000


Decision: Maintain status quo.

Expected opportunity loss:

Expand

$500,000(.70) + 0(.30) = $350,000

Status quo

$0(.70) + 650,000(.30) = $195,000

Sell

$980,000(.70) + 180,000(.30) = $740,000


Decision: Maintain status quo.

Step  3.
(part C): Compute EVPI

expected value given perfect information

= 1,300,000(.70) + 500,000(.30)

 

= $1,060,000



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expected value without perfect information

= $1,300,000(.70) 150,000(.30)

 

= $865,000

EVPI

= $1,060,000 865,000 = $195,000


Step  4.
(part D): Develop a Decision Tree

Step  5.
(part E): Determine Posterior Probabilities


[Page 551]
Step  6.
(part F): Perform Decision Tree Analysis with Posterior Probabilities




Introduction to Management Science
Introduction to Management Science (10th Edition)
ISBN: 0136064361
EAN: 2147483647
Year: 2006
Pages: 358

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