The company believes that there is a 60% chance that the volume of demand will be high. a. Construct a decision tree to identify the best choice with its net expected payoff. b. Suppose that the company engages an economic expert to provide an opinion about the volume of work based on a forecast of economic conditions. Historically, the number of times actually high volume out of the times the expert predicted upward was 75%, and the number of times actually low volume out of the times he predicted downward was 90%. In contrast to the company’s assessment, the expert believes that the chance for high demand is 70%. Determine the best strategy if their predictions suggest that the economy will improve or will
CW Logistics has decided to build a new warehouse to support its supply chain activities. They have the option of building either a large warehouse or a small one. Construction costs for the large facility are $8 million versus $3 million for the small facility. The profit (excluding construction cost) depends on the volume of work the company expects to contract for in the future. This is summarized in the following table (in millions of dollars):
|
High Volume |
Low Volume |
||
|
Large Warehouse |
$35 |
$20 |
|
|
Small Warehouse |
$25 |
$15 |
|
The company believes that there is a 60% chance that the volume of demand will be high.
a. Construct a decision tree to identify the best choice with its net expected payoff.
b. Suppose that the company engages an economic expert to provide an opinion about the volume of work based on a forecast of economic conditions. Historically, the number of times actually high volume out of the times the expert predicted upward was 75%, and the number of times actually low volume out of the times he predicted downward was 90%.
In contrast to the company’s assessment, the expert believes that the chance for high demand is 70%. Determine the best strategy if their predictions suggest that the economy will improve or will deteriorate. Given the information, what is the probability that the volume will be high?
Guide:
For part a, construct the branches with each of the available options. Enter the parameters to calculate the expected profit. After that, be sure to subtract the construction cost to reflect the net expected profit for each option.
For part b, match the probabilities with the given values. We can ignore the original 60% and rely on the expert’s prediction. Use the given conditional probabilities P(high | predicts up) and P(low | predicts down) to build the decision tree and estimate the inherent probability of high volume.
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