Question

1.     Precision Manufacturing, Inc. plans to open a new plant in Missouri. The company can open a full-sized plant now or a medium-sized plant now or a small-sized plant now depending on the levels of future demand. The future demand levels may be high, medium, or low. The following table gives the estimated annual income for each decision alternative under each level of future demand:

DECISION ALTERNATIVES	STATES OF NATURE (Future Demand Levels)
	High Demand	Medium Demand	Low Demand
Full-sized plant now	$1,000,000	$500,000	-$300,000
Medium-sized plant now	$900,000	$600,000	-$150,000
Small-sized plant now	$400,000	$280,000	-$125,000

a.      Which decision alternative should Precision Manufacturing select using the MAXIMAX approach? What is the corresponding annual income?

b.     Which decision alternative should Precision Manufacturing select using the MAXIMIN approach? What is the corresponding annual income?

c.      Which decision alternative should Precision Manufacturing select using the Laplace (or equally likely) approach? What is the corresponding annual income?                                

Precision’s analysis resulted in the following probabilities for the three future demand levels: P(high demand) = 0.70; P(medium demand) = 0.20; and P(low demand) = 0.10.

d.     Construct a decision tree for this problem.

e.      If maximum expected monetary value (EMV) is used as the decision criterion, which decision alternative should Precision Manufacturing select? What is the corresponding expected annual income?

f.      Suppose a marketing research firm is trying to sell the perfect information about the future demand to Precision Manufacturing, which will help Precision select the best alternative. What would be the expected value of perfect information (EVPI) for Precision?

If the marketing research firm were asking $39,000 for the perfect information, would you advise Precision to buy the information? Explain your reasoning.             

Answer 1

a)

Maximax: here the maximum payoff is selected, that maximizes the total payoff.

Here, the maximum payoff is 1000000. This payoff or imcome comes from full size plant when there is high demand. Hence we select this option under maximax.

b)

Maximin we select that alternative which maximizes the minimum payoff.

For full size plant minimum payoff is = -300000

for  Medium-sized plant minimum payoff is = -150000

for Small-sized plant minimum payoff = -125000

Hence since we are trying to maximize the minimum payoff, we select -125000, since this is the minimum of the three options.

Hence we select small sized plant for maximin

c)

Under laplace all natures are equal likely.

Hence all have a probability of 1/3

expected income of full sized plant = 1000000*1/3 + 500000*1/3 - 300000*1/3

= 400000

expected income of medium sized plant = 900000*1/3 + 600000*1/3 - 150000*1/3

= 450000

expected income of small sized plant = 400000*1/3 + 280000*1/3 - 125000*1/3

= 185000

maximum income from medium sized plant, hence select this. income = 450000

d)

e) EMV of Full size: 1000000*0.7 + 500000*0.2 - 300000*0.1 = 770000

EMV of medium size = 900000*0.7 + 600000*0.2 - 150000*0.1 = 735000

EMV of small size = 400000*0.7 + 280000*0.2 - 125000*0.1 = 323500

maximum EMV for full size plant.