Question

Andrew Thomas, a sandwich vendor at Hard Rock Cafe's annual Rockfest created a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd):

 

Alternatives	States of Nature                   Big Average Small
Large Stock	$22,000	$12,000	-$2,000
Average Stock	$14,000	$10,000	$6,000
Small Stock	$9,000	$8,000	$4,000

 

The probabilities associated with the states of nature are 0.3 for a big demand, 0.5 for an average demand, and 0.2 for a small demand.

1. Determine the alternative that provides Andrew the greatest Expected Monetary Value. What is this EMV?

2. What is the expected value under certainty?

3. Compute the expected value of perfect information, (EVPI)

4. Determine the appropriate alternative under uncertainty using Maximin. Provide support for your answer.

 

 

Answer 1

Big demand probability =0.3

Average demand probability=0.5

Small demand probability= 0.2

a)

Expected monetary value for each alternative:

EMV (large stock) =0.3*22000+ 0.5*12000+0.2*(-2000) = 12200

EMV (Average stock) =0.3*14000+ 0.5*10000+0.2*(6000) =10400

EMV (small stock) =0.3*9000+ 0.5*8000+0.2*(4000) =7500

The alternative that provide Andrew Thomas the greatest expected monetary value(EMV) is large stock

The EMV of this decision is $12,200

b)

In order to calculate expected value under certainty, consider highest value under each option

Expected Value under certainty = 0.3*22000+0.5*12000+0.2*6000=$13,800

c)

Expected value of perfect information (EVPI)

EVPI = EVwPI – Maximum EMV

=Expected value under certainty – Maximum EMV

= 13800-12200

=1600

The expected value of perfect information for Andrew Thomas is $1,600

d)

Maxmin Criteria is pessimistic. With this criterion, the decision makers select the decision that will reflect the maximum of minimum payoffs. For each decision alternative, the decision maker assumes that the minimum payoff will occur, of these, the maximum is selected as follows:

Large stock =-$2,000

Average stock =$6,000

Small stock =$4,000

Maximum value is for average stock which is $6,000

Therefore, appropriate alternative under uncertainty using Maximin is Average stock