Transcript Document

Decision Analysis
• Defines a structured approach for making a
good decision under uncertainty
• Does not guarantee a good outcome
• Allows you to measure and control the
inherent risk by understanding the impact of
different available decision options.
Terminology
• Alternatives = strategies = decision
variables = di
• States of nature = random variables = sj
• Criterion = objectives = r(di, sj)
• The payoff matrix summarizes the final
outcome for each alternative under each
state of nature
Expected Monetary Value (EMV)
• A probability distribution for the states of
nature must exist such that P(sj)>=0 for all j
and ΣP(sj)=1
• EMV(di)= Σr(di, sj)* P(sj)
• Often times, decision-makers select the
decision di that maximizes EMV.
Decision Tree Terminology
• Decision nodes are represented by squares and
represent a decision where the decision-maker
may prune back branches that represent the less
desirable options
• Event nodes are represented by circles and
represent uncertain events where the EMV will
need to be calculated
• Terminal nodes are the final outcomes that can be
expected if the path through the tree is followed to
that point. It should correspond to the payoff
matrix value.
An Example: Magnolia Inns
• Hartsfield International Airport in Atlanta, Georgia, is
one of the busiest airports in the world.
• Commercial development around the airport prevents
it from building more runways to handle future air
traffic demands.
• Plans are being made to build another airport outside
the city limits.
• Two possible locations for the new airport have been
identified, but a final decision will not be made for a
year.
Continued…
Magnolia Inns (continued)
• The Magnolia Inns hotel chain intends to build a
new facility near the new airport once its site is
determined.
• Land values around the two possible sites for the
new airport are increasing as investors speculate
that property values will increase greatly in the
vicinity of the new airport.
(Note: All numbers are in
millions of dollars)
Current purchase price
Present value of future cash
flows if hotel and airport
are built at this location
Present value of future sales
price of parcel if the airport
is not built at this location
Land Near Land Near
Location A Location
B
$18
$31
$12
$23
$6
$4
The Decision Alternatives
1) Buy the parcel of land at location A.
2) Buy the parcel of land at location B.
3) Buy both parcels.
4) Buy nothing.
The Possible States of Nature
1) The new airport is built at location A.
2) The new airport is built at location B.
A Decision Tree for Magnolia Inns
Land Purchase Decision
Buy A
-18
Buy B
-12
Airport Location
A
1
B
A
2
B
0
Buy A&B
-30
Buy nothing
0
A
3
B
A
4
B
Payoff
A Decision Tree for Magnolia Inns
Land Purchase Decision
Buy A
-18
Buy B
-12
Airport Location
1
2
0
Buy A&B
-30
Buy nothing
0
Payoff
A 31
13
B 6
-12
A 4
-8
B 23
11
A 35
5
B 29
-1
A 0
0
B 0
0
3
4
Rolling Back the Decision Tree
Land Purchase Decision
Airport Location
0.4
Buy A
-18
EMV=-2
1
A 31
13
6
B 0.6
-12
0.4
Buy B
-12
EMV=3.4
2
0
EMV=3.4
A 4
-8
23
B 0.6
11
0.4
Buy A&B
-30
EMV=1.4
A 35
5
B 29
-1
3
0.6
Buy nothing
0
Payoff
0