Project #10856 - Decision Analysis

Must  Word-process formulas using Equation Editor and diagrams using excel Drawing Tool. All problems must be complete for release of payment

 

Problem 1

Adele Weiss manages the campus flower shop. Flowers must be ordered three days in advance from her supplier in Mexico. Advance sales are so small that Weiss has no way to estimate the demand for the red roses. She buys roses for $15 per dozen and sells them for $40 per dozen. Pay-off table for the problem is given below.

 

 

Demand for Red Roses

Alternative

Low (25 dozen)

Medium (60 dozen)

High (130 dozen)

Do nothing

0

0

0

Order 25 dozen

300,000

300,000

300,000

Order 60 dozen

100,000

600,000

600,000

Order 130 dozen

-100,000

400,000

900,000

Probability

0.3

0.4

0.3

 

What is the decision based on each of the following criteria? Show work in making the decision for each criterion.

a)      EMV approach

b)      EOL approach

 

Use the tables given below.

a)      EMV Approach

 

 

Demand for Red Roses

 

Alternative

Low (25 dozen)

Medium (60 dozen)

High (130 dozen)

EMV

Do nothing

 

 

 

 

Order 25 dozen

 

 

 

 

Order 60 dozen

 

 

 

 

Order 130 dozen

 

 

 

 

Probability

0.3

0.4

0.3

 

 

b)      EOL Approach

 

 

Demand for Red Roses

 

Alternative

Low (25 dozen)

Medium (60 dozen)

High (130 dozen)

EOL

Do nothing

 

 

 

 

Order 25 dozen

 

 

 

 

Order 60 dozen

 

 

 

 

Order 130 dozen

 

 

 

 

Probability

0.3

0.4

0.3

 

 

Problem 2

Build-Rite construction has received favorable publicity from guest appearances on a public TV home improvement program. Public TV programming decisions seem to be unpredictable, so Build –Rite cannot estimate the probability of continued benefits from it relationship with the show. Demand for home improvements next year may be either low or high. But Build-Rite must decide now whether to hire more employees, do nothing, or develop subcontracts with other home improvement contractors. Build-Rite has developed the following payoff table.

Payoffs

Demand For Home Improvements

Alternative

Low

Moderate

High

Hire

($250,000)

$100,000

$625,000

Subcontract

$100,000

$150,000

$415,000

Do nothing

$50,000

$80,000

$300,000

What is the decision based on each of the following criteria? Show work in making the decision for each criterion:

a)      Maximax

b)      Maximin

c)       Criterion of realism with coefficient of realism = 0.7

d)      Equally likely

e)      Minimax regret

 

Use the tables given below.

a)      Optimistic or Maximax Criterion

 

Payoffs

Demand For Home Improvements

 

Alternative

Low

Moderate

High

Hire

 

 

 

 

Subcontract

 

 

 

 

Do nothing

 

 

 

 

 

b)      Pessimistic or Maximin Criterion

 

Payoffs

Demand For Home Improvements

 

Alternative

Low

Moderate

High

Hire

 

 

 

 

Subcontract

 

 

 

 

Do nothing

 

 

 

 

 

c)       Criterion of realism with coefficient of realism = 0.7

 

Payoffs

Demand For Home Improvements

 

Alternative

Low

Moderate

High

Hire

 

 

 

 

Subcontract

 

 

 

 

Do nothing

 

 

 

 

 

d)      Equally likely or Principle of Insufficient Reason Criterion

 

Payoffs

Demand For Home Improvements

 

Alternative

Low

Moderate

High

 

 

Hire

 

 

 

 

 

Subcontract

 

 

 

 

 

Do nothing

 

 

 

 

 

               

 

e)      Minimax Regret Approach

 

Regrets

Demand For Home Improvements

 

Alternative

Low

Moderate

High

Hire

 

 

 

 

Subcontract

 

 

 

 

Do nothing

 

 

 

 

 

Problem 3

Planwell Corporation

Planwell Corporation is considering whether to build a large plant or a small plant for new product, which has an estimated life of 7 years.  A small plant requires an investment of $3.4 million and a large plant of $4 million.  The following estimates are available for annual income.

Plant Size

Demand

Annual Income

Large

High

$900,000

 

Low

$300,000

Small

High

$600,000

 

Low

$500,000

The probability of high demand in first year is 0.75.  If the demand is high in the first year, the probabilities of high and low demands in subsequent years are 0.7 and 0.3 respectively.  The probability of low demand in the first year is 0.25.  If the demand is low in the first year, the probabilities of high and low demands in subsequent years are 0.2 and 0.8 respectively.

Evaluate the decision alternatives open to the company using decision trees.  Which alternative should be followed by the Planwell company and what return can be expected?

Use this space for the Decision Tree

Decision Tree for Planwell Corporation

 

Subject Mathematics
Due By (Pacific Time) 08/17/2013 10:00 pm
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