Question

McHuffter Condominiums, Inc., of Pensacola, Florida, recently purchased land near the Gulf of Mexico and is attempting to determine the size of the condominium development it should build. Three sizes of develop-ment are being considered; Small, d1; Medium, d2; and large, d3. At the same time, an uncertain economy makes it difficult to ascertain the demand for the new condominiums. McHuffter's management realizes that a large development followed by a low demand could be very costly to the company. However, if McHuffter makes a conservative small-development decision and then finds a high demand, the firm's profits will be lower than they might have been. With the three levels of demand-low, medium and high. McHuffter's management has prepared the following profit ($000). (20 pts.) 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. Suppose that before making a final decision, McHuffter is considering conducting a survey to help evaluate the demand for the new condominium development. The survey report is anticipated to indicate one of two levels of demand: weak(W) or strong(S). The relevant probabilities are as follows: (25 pts) P(W)= 0.3 P(low/W) = 0.50 P(low/S) = 0.10 P(S)= 0.7 P(medium/W)= 0.40 P(medium/S)= 0.25 P(high/W) = 0.10 P(high/S) = 0.65 BDSC 340.001-3 d) Construct a decision tree for this problem and analyze it. e) What is McHuffter’s optimal decision? f) What is the expected value of the survey(sample) information? McHuffter Condominiums, Inc., of Pensacola, Florida, recently purchased land near the Gulf of Mexico and is attempting to determine the size of the condominium development it should build. Three sizes of develop-ment are being considered; Small, d1; Medium, d2; and large, d3. At the same time, an uncertain economy makes it difficult to ascertain the demand for the new condominiums. McHuffter's management realizes that a large development followed by a low demand could be very costly to the company. However, if McHuffter makes a conservative small-development decision and then finds a high demand, the firm's profits will be lower than they might have been. With the three levels of demand-low, medium and high. McHuffter's management has prepared the following profit ($000). (20 pts.) 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. Suppose that before making a final decision, McHuffter is considering conducting a survey to help evaluate the demand for the new condominium development. The survey report is anticipated to indicate one of two levels of demand: weak(W) or strong(S). The relevant probabilities are as follows: (25 pts) P(W)= 0.3 P(low/W) = 0.50 P(low/S) = 0.10 P(S)= 0.7 P(medium/W)= 0.40 P(medium/S)= 0.25 P(high/W) = 0.10 P(high/S) = 0.65 BDSC 340.001-3 d) Construct a decision tree for this problem and analyze it. e) What is McHuffter’s optimal decision? f) What is the expected value of the survey(sample) information?

Answer 1

a)

i) Maximax - in this criterion, we find the Maximum payoff of each decision alternative and then select the alternative, whose Maximum payoff is the Maximum of all.

ii) Maximin - in this criterion, we find the Minimum payoff of each decision alternative and then select the alternative, whose Minimum payoff is the Maximum of all.

iii) MiniMax regret - in this criterion, we find the Maximum Regret of each decision alternative and then select the alternative, whose Maximum regret is the Minimum of all. Regret for each decision under each state of nature is calculated in a separate table. It is calculated by subtracting the maximum payoff under each state of nature out of the three decision alternatives - payoff for particular state of nature for the particular decision alternative. For example, regret value for decision Small (d1) under Low Demand = MAX(400,100,-300) - 400 = 400-400=0; for decision Small (d1) under High Medium Demand = MAX(400,600,300) - 400 = 600-400=200;  Small (d1) under High Demand = MAX(400,600,900) - 400 = 900-400=500

Maximum Regret for decision Small (d1) = MAX(0,200,500) = 500

b) Expected Value approach

Expected Value for decision Small (d1) = 0.2*400+0.35*400+0.45*400 = 400

Expected Value for decision Medium (d2) = 0.2*100+0.35*600+0.45*600 = 500

Expected Value for decision Large (d3) = 0.2*-300+0.35*300+0.45*900 = 450

Maximum Expected Value = 500

Therefore, recommended decision is Medium (d2)

c) EVPI

Expected regret value for decision Small (d1) = 0.2*0+0.35*200+0.45*500 = 295

Expected regret value for decision Medium (d2) = 0.2*300+0.35*0+0.45*300 = 195

Expected regret value for decision Large (d3) = 0.2*700+0.35*300+0.45*0 = 245

Minimum expected regret value = 195. This is EVPI

EVPI = 195