EXPECTED VALUE AND UNCERTANTY Problem 1: Expected Value Determine whether you wo

Question

EXPECTED VALUE AND UNCERTANTY Problem 1: Expected Value Determine whether you would decide, based on profitability, to go with the product cluster of Product A, Product B, and Product C or the product cluster of Product X, Product Y, and Product Z. Product cluster ABC has a fixed cost of 8.7% of revenue. Product cluster XYZ has a fixed cost of 9.3% of revenue. Product A is expecting revenues of $900,000 and variable costs of $300,000. Product B is expecting revenues of $700,000 and variable costs of $200,000 Product C is expecting revenues of $800,000 and variable costs of $400,000. The probability of achieving these revenues and costs are 5% for Product A and 25% for Product C? Product X is expecting revenues of $700,000 and variable costs of $300,000. Product Y is expecting revenues of $800,000 and variable costs of $250,000. Product Z is expecting revenues of $600,000 and variable costs of $300,000. The probability of achieving these revenues and costs are 35% for Product X and 15% for Product Z? Your goal is to maximize profits. Which product cluster would you choose? For any credit, you must show all your work. ANSWER: Focu

Explanation / Answer

There are four strategies . S1, S2, S3 and S4.

One of them is to be choosen based on psychological approaches.

1) Optimistic Approach:

It says one needs to choose the maximum value of all the strategies.

Let's consider strategy S1 ,

The value of R1 is 22

The value of R2 is 12

And the value of R3 is 11

The maximum value of S1 is maximum of all the responses. So value is 22.

Similarly for S2, the R1 , R2 , R3 values are 20 , 15, 15 . So maximum value is 20.

Similarly for S3 , it is 25 and S4 , it is 26.

So in optimistic approach. One must consider the maximum of maximum values of strategies to select the best strategy.

The maximum value of S, S2, S3 and S4 are 22, 20 , 25 and 26 respectively.

So the value of S4 is the maximum to select it as best strategy in Optimistic Approach.

2) Pessimistic Approach:

Unlike in Optimistic Approach, one must consider the minimum values of all the strategies.

Let's consider S1, the values of R1 , R2 and R3 are 22, 12 and 11 resp.

The lowest value is 11.

Similarly for S2 , the lowest value is 15. For S3 and S4 , the lowest values are 14 and 19 respectively.

Lowest values of S1 ,S2 , S3 and S4 are 11, 15 , 14 and 19.

The lowest value among these is 11 which is of Strategy S1. So S1 is considered in pessimistic approach.

3 Maxmin Regret Approach :

In this approach we select the regret from all the responses. THe best value of a response is considered and the remaining values of the response are deducted from the best one to find the regret.

Lets consider the R1 ,

The maximum value is 22 . The regret value of Strategy S1 , 22( Max )-22 ( Acutal value) = 0

The regret value of S2 is 22- 20 = 2

The regret value of S3 = 22-14 = 8

The regret value of S4 = 22-19 = 3

The regret table for R1 is

Similarly Regret table for R2 and R3 are shown below

The complete regret table is as follows

Then we need to select the maxmum regret of all the four strategies.

The value of regret of S1 for all the 3 strategies are 0, 11 and 12 resp

The maximum regret of Stretegy S1 is 12

Similarly maximum regret values of all the four strategies are shown below

We need to consider the minimum regret out of these to slect the best strategy . The minimu regret value is 14 , which is of strategy S3. The best strategy is S3.

Response R1 R2 R3 Strategy S1 22 12 11 S2 20 15 15 S3 14 16 25 S4 19 21 26

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