Question

Q. A Company has different investment options for their food business in Dubai. The table below shows conditional values for the investment in various options for the Company under different states of nature (demand conditions). All values are in US Dollars.

Alternatives	State of Nature
	High Demand	Low Demand
Option 1	7,000	-1,000
Option 2	12,000	4,000
Option 3	11,000	3,000

If the probabilities associated with the states of nature are 0.75 for high demand and 0.25 for a low demand, determine:

1. the decision under the Maximax criteria.
2. the decision under Mximin Criteria
3.   the decision under Hurwaiz criteria
4.   the decision under Laplace criteria
5.   the decision that provides the greatest expected monetary value (EMV).
6. the expected value of perfect information (EVPI).

Answer 1

Maximax, maximin, Hurwicz and Laplace are decision making approaches without considering probabilities.

a). Maximax is taking the maximum of each scenario (in this case, demand 1 and demand 2) and then choosing the maximum among all the maximum of each scenarios. In this case, maximum under demand 1 is option 2 (12,000) and maximum under demand 2 is option 2 (4,000). The maximum between 12,000 and 4,000 is 12,000 so using the maximax criteria, the company should choose option 2 under high demand.

b). Maximin is taking the minimum of each scenario (demand 1 and demand 2) and then choosing the maximum among all the minimum of each scenarios. In this case, minimum under demand 1 is option 1 (7,000) and minimum under demand 2 is option 1 (-1,000). The maximum between 7,000 and -1,000 is 7,000 so using the maximin criteria, the company should choose option 1 under high demand.

c). Hurwicz approach (or the realism approach) is a compromise between the best and worst payoffs. It chooses the best weighted average payoff based on coefficient of realism (0 <= <=1).

Note: Value of alpha has to be estimated to apply the Hurwicz approach. Since it is not provided, we will assume = 0.3 to apply the Hurwicz approach.

Expected payoff = *best payoff + (1-)*worst payoff

Expected payoff for option 1 = 0.3*7,000 + (1-0.3)*-1,000 = 1,400

Expected payoff for option 2 = 0.3*12,000 + (1-0.3)*4,000 = 6,400

Expected payoff for option 3 = 0.3*11,000 + (1-0.3)*3,000 = 5,400

The highest payoff among these 3, is option 2 so as per Hurwicz approach, the company should go for option 2.

d). Laplace approach is the equally likely approach which maximizes the average payoff.

Average of option 1 = (7,000 -1,000)/2 = 3,000

Average of option 2 = (12,000 + 4,000)/2 = 8,000

Average of option 3 = (11,000 + 3,000)/2 = 7,000

The maximum among these average is 8,000 so the Laplace decision should be to invest in option 2.

e). Expected Monetary value (EMV) is a probability weighted average of the payoffs.

Option 1 = (probability of high demand*payoff) + (probability of low demand*payoff)

= (0.75*7,000) + (0.25*-1,000) = 5,000

Option 2 = (0.75*12,000) + (0.25*4,000) = 10,000

Option 3 = (0.75*11,000) + (0.25*3,000) = 9,000

The highest EMV is for option 2 so it should be chosen by the company.

f). Expected value of perfect information (EVPI) = expected value with perfect information (EVwPi) - expected value without perfect information (EVwoPI)

EVwPI = probability weighted best payoffs for demand 1 and 2 = (0.75*12,000) + (0.25*4,000) = 10,000

EVwoPI is the best of the probability weighted total payoff between option 1, 2 and 3 (already calculation in part e)

Probability weighted payoff for option 1 = 5,000

Probability weighted payoff for option 2 = 10,000

Probability weighted payoff for option 3 = 9,000

So, EVwoPI = 10,000

EVPI = EVwPI - EVwoPI = 10,000 - 10,000 = 0