Question

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff (profit in thousands of dollars) table based on whether a business will be brisk, medium, or slow.

                                           Business Level

Decision               Brisk           Medium                Slow

────────────────────────────────────────

Buy                          90                 50                       30                                         

Rent                         50                 60                       45                                         

Lease                       40                55                       50

Assume that the probability of a brisk business level is 0.4, the probability of a medium business level is 0.4 and the probability of a slow business level is 0.2.

(1) Calculate the expected value of each decision alternative. What is your recommendation using the expected value criterion?

(2) Calculate the expected opportunity loss value of each decision alternative. What is your recommendation using the expected opportunity loss criterion?

(3) Calculate and interpret the value of perfect information for this problem.

Answer 1

1) The Expected monetary value of each decision alternative is given by the sum of product of probabilities of state of nature and the profit values.

The following table summarizes the EMV of each decision alternative:

EMV of Buy = 0.4*90+0.4*50+0.2*30=62

EMV of Rent = 0.4*50+0.4*60+0.2*45=53

EMV of Lease = 0.4*40+0.4*55+0.2*50=48

The best decision alternative is the maximum of EMV, which is to take "Buy Decision" at $62,000

2) Expected Regret = Sumproduct (Probability, Regret)

Regret = Profit of each alternative - Maximum value of each state for all the alternatives

Maximum values of states being 90,60,50 for Brisk, medium, slow respectively.

The following is the regret table:

Expected Regret for Buy = .4*0+.4*10+.2*20 = 8

Expected Regret for Rent = .4*40+.4*0+.2*5 = 17

Expected Regret for Buy = .4*50+.4*5+.2*0 = 22

The best decision is to minimize the expected regret, which is for Buy decision at $8,000

3. Perfect information:

The above table gives the perfect information which is the maximum of values for each state, which when multiplied with probability gives the expected value

Best expected value under perfect information = 90*.4+60*.4+50*.2 = 70

EMV = 62

EVPI = 70-62 = 8

The Expected value of Perfect information = $8000 which gives the value of additional information required to make a decision regarding the best alternative.