Question

payoff table ------------------------------------------- Demand Decision ---------------------------- Alternatives Low Medium High ------------------------------------------- Small, d1 400 400 400 Medium, d2 100 600 600 Large, d3 -300 300 900 -------------------------------------------- a) If nothing is known about the demand probabilities, what are the recommended decision using the Maximax(optimistic), Maximin (pessi- mistic), and Minimax regret approaches? b) If P(low) = 0.20, P(medium) = 0.35, and P(high) = 0.45, What is the recommended decision using the expected value approach? c) What is the expected value of perfect information (EVPI)? You have to use regret table to get EVPI.

Answer 1

The problem is as shown below:-

a) If nothing is known about the demand probabilities, what are the recommended decision using the Maximax(optimistic)

In this approach, we look at each alternative and choose the best possible alternative as shown in the last column and as highlighted in each cell:-

Among all these now the best is the decision D3, so we choose D3.

Maximin (pessimistic)

In this approach, we look at each alternative and choose the worst possible alternative as shown in the last column and then from those we choose the best option which means - Choose the maximum among the minimums.

Minimax Regret Approach

We need to find the regret for each state (Low, Med, High) first, regret = best pay off - Pay off received as shown below:-

The formula sheet for the above table is:-

Then use the Minimax approach again to choose the Minimum of the Maximum value we get:-

So, D2 is the best approach as per this method.

b) If P(low) = 0.20, P(medium) = 0.35, and P(high) = 0.45, What is the recommended decision using the expected value approach?

We find the Expected Value by Multiplying the value in each column with their probabilities:-

According to this, the best option is D2 as it has the maximum value.

c) What is the expected value of perfect information (EVPI)?

In order to get EVPI, we need to Find EV with PI which is the value of the above table when we know all the information, this can be found using multiplying the maximum payoff in each column with the corresponding probabilities as

EV with PI = 0.2 * 400 + 0.35 * 600 + 0.45 * 900 = 695

Therefore EVPI = EV with PI - EV without PI ( As calculated in part b)

= 695-500 = 195

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