A company that is introducing a new product has to choose between four different

Question

A company that is introducing a new product has to choose between four different manufacturing methods, referred to as methods A, B, C and D. Depending on the demand for the product, they forecast different levels of expenses for the year (values are in thousands). The company has identified three possible states of nature for economic growth, and named them High, Medium, and Low.

High

Medium

Low

Method A

$450

$670

$780

Method B

$950

$320

$200

Method C

$375

$575

$775

Method D

$800

$400

$300

Using the information in Table A.2, which alternative is BEST in accordance with an optimistic outlook? (maximax)

Using the information in Table A.2, which alternative is BEST in accordance with a pessimistic outlook? (maximin)

Using the information in Table A.2, which alternative is BEST in accordance with a decision criterion of Laplace?

Using the information in Table A.2, which alternative is BEST in accordance with a decision criterion of minimax regret?

High

Medium

Low

Method A

$450

$670

$780

Method B

$950

$320

$200

Method C

$375

$575

$775

Method D

$800

$400

$300

Explanation / Answer

Answer: This question is part of Decision Analysis, before going to answering would like to explain a bit about the decision table.

Given Table comprises of 3 elements

1. Methods(A, B etc) Known as Decision Alternatives

2. High, Medium & Low Known as States of Nature or Outcome

3. Expenses which are known as payoffs

First Part

That is choosing an alternative with Optimistic Outlook or Maximax method we need to select the alternative with Best Possible payoff

Since we need best payoffs in terms of expenses we need to select the alternative with lowest expenses or cost and looking at the table for Best Payoffs we get that for

Method A is $450

Method B is $200 (Best Among Best)

Method C is $375

Method D is $300      

Out of above best payoff i.e. lowest expense is in Method B, so we would select Method B

Second Part

Pessimistic outlook which is also known as conservative approach or Maximin approach method we need to select the best alternative of worst possible payoff

Since we need best available alternative out of worst payoffs in terms of expenses we need to select the alternative with maximum expenses or cost and looking at the table for Best Payoffs we get that for

Method A is $780

Method B is $950

Method C is $775            (Best Among Worst)

Method D is $800

Out of above best alternative i.e. lowest expense is in Method C, so we would select Method C

Third Part

Moving to next question of Decision analysis, in which we need alternative which is best in accordance with decision criterion of Laplace

Laplace approach is also known as Equally Likey approach we first calculate the average of payoffs of available alternatives and select the best out of it.

For calculating average of Payoffs we add payoffs in decision alternatives and divide by numbers of Payoffs.

By doing so our table will look like this

High

Medium

Low

Total of payoffs

Average of Payoffs = total of Payoffs/Number of Payoffs (3 in our case)

Method A

$450

$670

$780

$450+$670+$780= $1,900

$1900/3 = $633

Method B

$950

$320

$200

$950+$320+$200= $1,470

$1470/3 = $490

Method C

$375

$575

$775

$375+$575+$775= $1,725

$1725/3 = $575

Method D

$800

$400

$300

$800+$400+$300= $1,500

$1500/3 = $500

Since we see best alternative in terms of cost will be $490 i.e. Method B

Fourth Part

Now moving to last question of Decision analysis we need alternative which is best in accordance with a decision criterion of minimax regret

Minimax Regret also known as Minimum of Maximum Regrets where

Regret = Payoff Received – Best Payoff

High

Medium

Low

Method A

$450

$670

$780

Method B

$950

$320

$200

Method C

$375

$575

$775

Method D

$800

$400

$300

We would first select Minimum cost for every state of nature and calculate Regrets for every alternative.

High

(Minimum cost 375)

Medium

(Minimum cost 320)

Low

(Minimum cost 200)

Method A

$450-$375= $75

$670-$320= $350

$780-$200= $580

Method B

$950-$375= $575

$320-$320= $0

$200-$200= $0

Method C

$375-$375= $0

$575-$320= $255

$775-$200= $575

Method D

$800-$375= $425

$400-$320= $80

$300-$200= $100

So the Regret Table would look like this

High

Medium

Low

Method A

$75

$350

$580

Method B

$575

$0

$0

Method C

$0

$255

$575

Method D

$425

$80

$100

Now we have the regret table and for selecting best alternative under Minimax regret approach we need to first find maximum regret of each alternative and then select the minimum out of it.

So we get Maximum regret for each alternative is as following

Method A is $580

Method B is $575

Method C is $575

Method D is $420 (Best among maximum regrets)           

so we would select Method D

High

Medium

Low

Total of payoffs

Average of Payoffs = total of Payoffs/Number of Payoffs (3 in our case)

Method A

$450

$670

$780

$450+$670+$780= $1,900

$1900/3 = $633

Method B

$950

$320

$200

$950+$320+$200= $1,470

$1470/3 = $490

Method C

$375

$575

$775

$375+$575+$775= $1,725

$1725/3 = $575

Method D

$800

$400

$300

$800+$400+$300= $1,500

$1500/3 = $500

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