Question

Brad Simpson is a farmer in the Moscow, Idaho area. Each year he tries to plant the crop that will make him the most money. He has a choice of three crops, barley, wheat or garbanzo beans. The amount he makes on each crop varies based on the amount of rain that comes during the season. A very rainy season is great for garbanzo beans (called garbos) but hurts the profit from barley. Wheat doesn’t vary much based on the rainfall. The estimated profit from each crop, based on the rainfall is in the following table:

Rainfall	Garbanzo Beans	Barley	Wheat
High (30% probability)	80,000	35,000	50,000
Low (70% probability)	20,000	60,000	40,000

Mr. Simpson only wants to plant one crop. Decide on the choice for him based on:

a) Maximin Strategy  

b) Maximax Strategy

c) Minimax Regret Strategy

d) Calculate the value of perfect information.  

Answer 1

a) The maximin rule involves selecting the alternative that maximises the minimum pay-off achievable. In this case, Mr Simpson would look to plant Wheat as it is the best alternative out of the worst possible payoffs.

	High Rainfall	Low Rainfall	Minimum Payoff
Garbanzo Beans	80,000	20,000	20,000
Barley	35,000	60,000	35,000
Wheat	50,000	40,000	40,000

b) The maximax rule involves selecting the alternative that maximises the maximum payoff available. In this case, Mr Simpson would plant Garbanzo Beans which promises him a profit of 80,000.

	High Rainfall	Low Rainfall	Maximum Payoff
Garbanzo Beans	80,000	20,000	80,000
Barley	35,000	60,000	60,000
Wheat	50,000	40,000	50,000

c) The minimax regret strategy is the one that minimises the maximum regret. This strategy's main idea is to ensure that the regret is minimum that a wrong decision is made. This Mr Simpson should plant Wheat which gives the minimum regret while maximising payoff.

	High Rainfall	Low Rainfall	Maximum Regret = Maxpayoff - Profit (High Rainfall)	Maximum Regret = Maxpayoff - Profit (Low Rainfall)	Maximum Regret
Garbanzo Beans	80,000	20,000	80,000 - 80,000 = 0	60,000 - 20,000 = 40,000	40,000
Barley	35,000	60,000	80,000 - 35,000 = 45,000	60,000 - 60,000 = 0	45,000
Wheat	50,000	40,000	80,000 - 50,000 = 30,000	60,000 - 40,000 = 20,000	30,000

d) Expected Value of Perfect Information is defined as the maximum additional value anyone is willing to pay for additional information to know the outcome.

EVPI = EVwPI - EVwoPI

EVPI = (80,000 x 0.3 + 60,000 x 0.7) - Max((80,000 x 0.3 + 20,000 x 0.7) ,(35,000 x 0.3 + 60,000 x 0.7), (50,000 x 0.3 + 40,000 x 0.7))

EVPI = 66,000 - Max(38,000, 52,500, 43,000)

EVPI = 66,000 - 52,500

EVPI = 13,500