Question

Mary developed the following payoff table based on the plan to build housing units. Mary has 3 decision alternatives to build 30 units, 50 units, and 60 units. The probabilities of strong, fair, and poor housing market are provided.

Housing Units  Good Market Fair Market  Poor Market

30, d1 $50,000 . $20,000 $10,000

50, d2 80,000 30,000 -10,000

60, d3 150,000 35000 -30,000

Probability .5 .3 .2

Question # 1: If Mary wanted to make a decision based on the expected value (EV) of the decision alternatives, what would be the value ($) of the housing units chosen?

Construct a regret table based on the payoff table above and calculate the expected value of the opportunity loss for each decision alternatives using the regret payoff amounts.

Question #2: If Mary can't make a decision as to what alternative to choose, what is the minimum expected value (S) of the opportunity loss for Mary?

Answer 1

Question # 1

Expected value for 30 units = 0.5 * 50,000 + 0.3 * 20,000 + 0.2 * 10,000 = $33,000

Expected value for 50 units = 0.5 * 80,000 + 0.3 * 30,000 + 0.2 * -10,000 = $47,000

Expected value for 60 units = 0.5 * 150,000 + 0.3 * 35000 + 0.2 * -30,000 = $79,500

Since the highest EMV is for housing units 60, the decision based on the expected value (EV) is 60 units.

Regret = Best Payoff - Payoff Received

Regret table is,

Housing Units	Good Market	Fair Market	Poor Market
30	150,000 - 50,000 = 100,000	35000 - 20,000 = 15000	10,000 - 10,000 = 0
50	150,000 - 80,000 = 70,000	35000 - 30,000 = 5000	10,000 - (-10,000) = 20,000
60	150,000 - 150,000 = 0	35000 - 35000 = 0	10,000 - (-30,000) = 40,000

Question #2:

For 30 units, the maximum opportunity loss (Regret) is 100,000

For 50 units, the maximum opportunity loss (Regret) is 70,000

For 60 units, the maximum opportunity loss (Regret) is 40,000

The minimum of these opportunity loss is $40,000 which is for house for 60 units.

Mary should choose housing units 60 to minimize the expected value of the opportunity loss.