Question

A company wants to build a plant but is considering the size. The table below shows their payoffs under different states of demand.

	Demand
	Low (p=0.45)	High (p=0.55)
Small Plant	500000	500000
Medium Plant	200000	800000
Large Plant	-200000	1000000

They can hire a consultant who can conduct a survey to evaluate demand. The consultant will report to the company whether demand is strong or weak. The probabilities are 0.60 and 0.40 for strong and weak survey results respectively. The conditional probabilities for demand given survey results are as follow:

P(Low/Strong) = 0.35; P(High/Strong) = 0.65;

P(Low/Weak) = 0.70; P(High/Weak) = 0.30;

a) Draw the decision tree for this problem including with and without a survey.

b) What is the best decision without a survey?

c) What is the decision strategy when survey is conducted?

d) What is the EVPI?

e) What is the EVII

Answer 1

a) the decision tree is below

Moving from the right to left

when the prediction is strong result

choice node 6: (small plant)

The expected value is

choice node 7: (medium plant)

The expected value is

choice node 8: (Large plant)

The expected value is

when the prediction is weak result

choice node 9: (small plant)

The expected value is

choice node 10: (medium plant)

The expected value is

choice node 11: (Large plant)

The expected value is

when no survey is done

choice node 12: (small plant)

The expected value is

choice node 13: (medium plant)

The expected value is

choice node 14: (Large plant)

The expected value is

decision node 3:

Options are

1. small plant: EV=$500,000
2. medium plant, EV=$590,000
3. large plant, EV=$580,000

Optimum decision: Medium plant

decision node 4:

Options are

1. small plant: EV=$500,000
2. medium plant, EV=$380,000
3. large plant, EV=$160,000

Optimum decision: Small plant

decision node 5:

Options are

1. small plant: EV=$500,000
2. medium plant, EV=$530,000
3. large plant, EV=$460,000

Optimum decision: Medium plant

Choice node 2:

Node 1:

Options are

1. Do the survey: EV=$554,000
2. Do not do the survey, EV=$530,000

Optimum decision is Do the survey

b)the best decision without a survey is to build a medium plant

C) the decision strategy when survey is conducted is

• go for a medium plant if the survey results are strong
• go for a small plant if the survey results are weak

d) From the table we can see that the best decision if we know that the demand is low is to go for a small plant at a payoff of $500,000

the best decision if we know that the demand is high is to go for a large plant at a payoff of $1,000,000

the expected value with perfect information is

The expected value without perfect information is the EV when we do not conduct a survey

The expected value of perfect information is

EVPI=$245,000

e) The expected value with imperfect information is the EV when we conduct the survey (we would not get the perfect information but we will get more information than when no doing the survey)

The expected value without imperfect information is the EV when we do not conduct a survey

The expected value of imperfect information is

EVII = $24,000