


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.

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



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 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.




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…


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
1)
2)
3)
4)
Buy
Buy
Buy
Buy
the parcel of land at location A.
the parcel of land at location B.
both parcels.
nothing.
1) The new airport is built at location A.
2) The new airport is built at location B.
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
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
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