Question

The example involves a capacity-planning problem in which a company must choose to build a small, medium, or large production facility. The payoff obtained will depend on whether future demand is low, moderate, or high, and the payoffs are as given in the following table:

  

	Possible Future Demand
Alternatives	Low	Moderate	High
Small facility	$11*	$11	$11
Medium facility	8	13	13
Large facility	-6	0	14

*Present value in $ millions.

Suppose that the company assigns prior probabilities of .3, .5, and .2 to low, moderate, and high demands, respectively.

(a) Find the expected monetary value for each alternative (small, medium, and large). (Round your answers to 1 decimal place. Enter your answers in millions.)

  

Maximum payoff for each alternative:
EMV (Small)	$  M
EMV(Medium)	$  M
EMV(Large)	$  M

(b) What is the best alternative if we use the expected monetary value criterion?

  Best alternative:   (Click to select)
Medium facility
Large facility
Small facility

Answer 1

(A) Suppose that the company assigns prior probabilities of .3, .5, and .2 to low, moderate, and high demands, respectively

Expected value for Small facility is E[x] =

using the given data table for x value

this implies

= (11*0.3)+(11*0.5)+(11*0.2)

= 3.3 + 5.5 +2.2

= $11.0

Expected value for Medium facility is E[x] =

using the given data table for x value

this implies

= (8*0.3)+(13*0.5)+(13*0.2)

= 2.4 + 6.5 +2.6

= $11.5

Expected value for Large facility is E[x] =

using the given data table for x value

this implies

= (-6*0.3)+(0*0.5)+(14*0.2)

= -1.8 + 0 +2.8

= $1.0

(B)  the best alternative if we use the expected monetary value criterion is medium facility because it has highest expected monetary value

Medium facility is correct answer