Even though independent gasoline stations have been having a difficult time, Hac

Question

Even though independent gasoline stations have been having a difficult time, Hachya Mehta has been thinking about starting her own independent gasoline station. Hachya’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Hachya developed the following table:

Size of First Station

Good Market ($)

Fair Market ($)

Poor Market ($)

For example, if Hachya constructs a small station and the market is good, she will realize a profit of $50,000.

a.Develop a decision table for this decision.

b.What is the maximax decision?

c.What is the maxmin decision?

d.What is the equally likely decision?

e. is the criterion of realism decision? Use an value of 0.8.

f.Develop an opportunity loss table.

g.What is the minimax regret decision?

Size of First Station

Good Market ($)

Fair Market ($)

Poor Market ($)

small 50,000 20,000 -10,000 medium 80,000 30,000 -20,000 large 100,000 30,000 -40,000 very large 300,000 25,000 -160,000

Explanation / Answer

.Develop a decision table for this decision.

What is the maximax decision?

Maximax we can find by using best value of the of the three alternatives or Size of First Station.

The largest value in the last column is 30000 against very large.

Decision : Invest in very large.

What is the maxmin decision?

Here the largest value in the worst column is -10000 against small.

Decision : Invest in small.

What is the equally likely decision?

We can calculate equally likely decision by using average of each altervative.

The largest value of last column is 55000 against column vary large.

Decision : Invest in very large.

is the criterion of realism decision? Use an value of 0.8.

It finds a compromise between the best and worst payoffs.

Choose the best weighted average payoff based on .

= 0.8

1 - = 1 - 0.2 = 0.8

Calculate weighted average by using formula :

weighted average = *best payoff + (1-)*worst payoff

The largest value of the last column if table is 208000 against very large.

Decision : Invest in very large.

What is the minimax regret decision?

Regret = opportunity loss

Regret = best payoff - payoff received

We can find regret table by using following steps :

i) FInd maximum of all the table entries.

ii) Divide each observation from maximum entry.

Therefore the regret table is,

The smallest value of the last column is 310,000 against very large.

Size of First Station Good Market ($) Fair Market ($) Poor Market ($) small 50,000 20,000 -10,000 medium 80,000 30,000 -20,000 large 100,000 30,000 -40,000 very large 300,000 25,000 -160,000

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