Question

Please use Excel and show steps!! Greentrop Pharmaceutical Products are the world leader in the area of sleep aids. Its major product is “Dozealot”. The Research-and-Development Division has defined two alternatives to improve the quality of the product. These alternatives are simple reformulations of the product to minimize the side effects and to improve the product efficacy. To conduct an analysis, management has decided to consider the possible demands for the drug under each alternative. The following payoff table shows the projected profit in millions of dollars.If the decision maker knows nothing about the probabilities of three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

	Demand
Decision Alternatives	Low	Medium	High
d1	$500	$350	$525
d2	$875	$300	$765

Answer 1

ANSWER:

In the problem, two quality improvment products d1 and d2 can be maufactured. Each of them will face three different evironment viz, low , medium and high. The demand are shown in dollar. Based on given figures, following decision tree has been developed.

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Answer (b): If probabilities of each alternatives are known, then decision maker can calculate expected value to determine, optimum product. But when probabilties are not known, he has to apply different methods of taking decision under uncertain evironment. They are-

Optimistic method: In this method, decision maker will assume that nature is always kind to him. So it will behave in a manner to optimize the demand. If decision maker select d1, then nature behaving optimistically will create high evironment where demand is highest i.e. $525. On the other hand, if he select strategy d2, then nature will recommend low evironment, so that optimum demand is $875. Now compare $525 and $875. Highest is $875. So d2 will be selected.

Note that here decision maker has first selected maximum payoff of each row. Then he has selected maximum of row maxima. Due to this reason, this principle is known as maximax.

Conservative: It is just opposite of first one. Here nature is expected to behave in a conservative manner. So it will create a situation, which will minimize his pay off. Thus decision maker will select minimum value of each row. Then from minimum row value best one is selected. It is known as maximin technique.

Minimum pay off of each row is $350 and $300. Among these two maximum value is $350. It is related with d1. So d1 is selected under Conservative method.

Minimax regret: It is also known as Savage method. Steps are-

1. First calculate regret value of each cell of two rows. It is the deviation of cell value from maximum value of the row. In row 1, maximum value is $525. Now first cell value is $500. So deviation is $525-$500=$25. It is known as regret value. Develop regret matrix first. It is shown below:

2.Here regret is like a loss that decision maker will suffer from optimum payoff. So he will try to minimize regret value. But nature ise xpected to behave in a conservative manner. It will always try to maximize regret value. If d1is selected, then nature will create medium, so that regret is highest for row 1. It is $175. Similarly for row 2, it is $575.

3. Finally, decision maker will select minimum of row maxima. It is $175. So d1 is selected.

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