# Decision Analysis develop a career planning strategy BSBHRM512: Assessment 1 develop a career planning strategy

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Chapter 4
Decision Analysis
MA609 Business Analytics and Data Intelligence Week 6: TUT6
Solutions:
The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature:
State of Nature
Decision alternatives
S1
S2
S3
d 1
250
100
25
d 2
100
100
75
Construct a decision tree for this problem.
If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?
Decision
Maximum Profit
Minimum Profit
d1
250
25
d2
100
75
Optimistic approach: select d1
Conservative approach: select d2
Regret or opportunity loss table:

s1
s2
s3
d1

50
d2
150

Maximum Regret:  50 for d1 and 150 for d2; select d1
Video Tech is considering marketing one of two new video games for the coming holiday season: Battle Pacific or Space Pirates. Battle Pacific is a unique game and appears to have no competition. Estimated profits (in thousands of dollars) under high, medium, and low demand are as follows:

Demand
Battle Pacific
High
Medium
Low
Profit
\$1000
\$700
\$300
Probability
0.2
0.5
0.3
Video Tech is optimistic about its Space Pirates game. However, the concern is that profitability will be affected by a competitor’s introduction of a video game viewed as similar to Space Pirates. Estimated profits (in thousands of dollars) with and without competition are as follows:
Space Pirates with competition
Demand

High
Medium
Low
Profit
\$800
\$400
\$200
Probability
0.3
0.4
0.3
Space Pirates without competition
Demand

High
Medium
Low
Profit
\$1600
\$800
\$400
Probability
0.5
0.3
0.2
Develop a decision tree for the Video Tech problem.
For planning purposes, Video Tech believes there is a 0.6 probability that its competitor will produce a new game similar to Space Pirates. Given this probability of competition, the director of planning recommends marketing the Battle Pacific video game. Using expected value, what is your recommended decision?
EV(node 2) = 0.2(1000) + 0.5(700) + 0.3(300) = 640
EV(node 4) = 0.3(800) + 0.4(400) + 0.3(200) = 460
EV(node 5) = 0.5(1600) + 0.3(800) + 0.2(400) = 1120
EV(node 3) = 0.6EV(node 4) + 0.4EV(node 5) = 0.6(460) + 0.4(1120) = 724
Space Pirates is recommended. Expected value of \$724,000 is \$84,000 better than Battle Pacific.

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