6 Roger Davis wants to open an independent gasoline station

6. Roger Davis wants to open an independent gasoline station. Roger must decide how large his station should be. The annual returns will depend upon both the size of his station and the demand for gasoline. After careful analysis, Roger developed the subsequent table.

Size of Station             Good Market                Fair Market                  Poor Market

$ (000)                                    $ (000)                        $ (000)                        $ (000)

Small                                        50                              20                                -10

Medium                                    80                              30                                -20

Large                                       100                              30                                -40

Very Large                              300                              25                                -160

a. Develop a decision table for this decision.

b. What is the Maximax decision?

c. What is the Maximin decision?

d. What is the Mini-max Regret decision?

e. Prepare a decision tree of this problem.

f. If the probabilities of the markets are good market, 30%; fair market, 50%; poor market, 20%, calculate the expected values and expected opportunities lost of each option, and make a recommendation.

Solution

b)

Hence the maximum pay off will be 300,000 decision is Very Large

c)MaxiMin

Maximum of Minimum payoff is -10,000, decision is Small

d)MinMax Regret

The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret. First select the maximum payoff under each state of nature and then all other payoffs under the respective natures are substracted from these amounts as follows

(-10+160)

150

These Values represent the regret for each decision that would be experienced by the decision maker if a decision were made that resulted in less than maximum payoff. The Max regret for each decision is determined as below

The Minimum of these regret values is the MiniMax regret=150,000, decsion is very large

F) The probability values are multplied to respective state and sum is done for the respective nature as below

Small=0.3*50+0.5*20-0.2*(-10)=27

Medium=0.3*80+0.5*30-0.2*(-20)=43

Large=0.3*100+0.5*30-0.2*(-40)=53

Very Large=0.3*300+0.5*25-0.2*(-160)=134.5 it means the recommended view is to have very large gas station