QUESTION 3 The Charm City Consultants Inc. wants to build a new network of compu

Question

QUESTION 3

The Charm City Consultants Inc. wants to build a new network of computers for its employees. The management of the company is considering three network sizes for the possible purchase: large, medium, or small. The management believes that the demand for their services will be either high level, medium level, or low level. The payoff (profit in dollars) table for the situation is given below:

Demand Level

Decision High Medium Low

Large Size $150,000 $ 60,000 $20,000

Medium Size $100,000 $110,000 $50,000

Small Size $ 60,000 $ 70,000 $80,000

(a) What is the best decision using the maximax criterion? What is the payoff for it?

(b) What is the best decision using the maximin criterion? What is the payoff for it?

(c) What is the best decision using the minimax regret criterion? What is the payoff for it?

(d) What is the best decision using the Hurwicz’s criterion if = 0.4? What is the payoff for it?

QUESTION #4

For the problem given in Question 3, assume that the probability of high demand level is 0.3, the probability of medium demand level is 0.4, and the probability of low demand level is 0.3. (a) Calculate the expected value of each decision alternative. What is your recommendation using the expected value criterion? (b) Calculate the expected opportunity loss value of each decision alternative. What is your recommendation using the expected opportunity loss criterion? (c) Calculate and interpret the value of perfect information.

Explanation / Answer

3a. Under the maximax criteria, that alternative is selected that maximises the maximum payoff available. We start with determining the maximum payoff related with each network size. The maximum payoffs are - large size $150,000; medium size $110,000 and small size $80,000. The maximum of these three is related to large size and high demand level and the payoff is $150,000

b. Under the maximin criteria, that alternative is selected the maximises the minimum payoffs. We start with determining the minimum payoff related with each network size. The minimum payoffs are - large size $20,000; medium size $50,000 and small size $60,000. The maximum of these three is related to small size and high demand level and the payoff is $60,000

c. The minimax regret is the one that minimises the maximum regret. Regret is the opportunity loss through having made the wrong decision. Regret is calculated by using the biggest payoff for each row and then substracting each from the payoffs of that row.

Regret table:

Now, we will determine the maximum regret for each demand level. High: 20,000; Medium: 90,000 and low: 130,000. We now have to select the minimum of these values. The minimum is $20,000 and this happens when there is high demand for small size networks.

d. alpha = 0.4 and 1-alpha = 0.6. For each decision alternative, the maximum payoff is multiplied by alpha and the minimum payoff is multiplied by 1 - alpha.

Thus, for large size = 0.4*150,000 + 0.6*20,000 = 72,000

for medium size = 0.4*110,000 + 0.6*50,000 = 44,000+30,000 = 74,000

for small size = 0.4*80,000 + 0.6*60,000 = 32,000+36,000 = 68,000

Now, the maximum of the above values is selected. So, the payoff is $74,000 for medium size networks.

4. a. expected value = sum of (probability*payoff). expected value of large size = 150,000*0.3 + 60,000*0.4 + 20,000*0.3 = 75,000

Medium size should be selected as it has the highest expected value.

b. Opportunity loss = expected value - payoff

Maximum regrets or opportunity loss: High 10,000 ; Medium 15,000 and low 55,000. minimum opportunity loss = 10,000 for high demand for small size networks.

c. The expected value without perfect information is calculated in 4a above = $89,000.

expected value given perfect information = 110,000*0.4 + 60,000*0.4 + 60,000*0.3 = 44,000+24,000+18,000 = 86,000

Thus EVPI = 86,000 - 89,000 = -3,000

High Medium Low Large 0 90,000 130,000 Medium 10,000 0 60,000 Small 20,000 10,000 0

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