1. 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.

2. Terminology Alternatives = strategies = decision variables = d i States of nature = random variables = s j Criterion = objectives = r(d i, s j ) The payoff matrix summarizes the final outcome for each alternative under each state of nature

3. Expected Monetary Value (EMV) A probability distribution for the states of nature must exist such that P(s j )>=0 for all j and ΣP(s j )=1 EMV(d i )= Σr(d i, s j )* P(s j ) Often times, decision-makers select the decision d i that maximizes EMV.

4. 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.

5. 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…

6. 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.

7. (Note: All numbers are in millions of dollars) Land Near Location A Land Near Location B Current purchase price $18$12 Present value of future cash flows if hotel and airport are built at this location $31$23 Present value of future sales price of parcel if the airport is not built at this location $6$4

8. 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.

9. The Possible States of Nature 1) The new airport is built at location A. 2) The new airport is built at location B.

10. A Decision Tree for Magnolia Inns 0 1 2 3 4 Buy A -18 Buy B -12 Buy A&B -30 Buy nothing 0 Land Purchase Decision Airport Location A B A B B B A A Payoff

11. A Decision Tree for Magnolia Inns 0 1 2 3 4 Buy A -18 Buy B -12 Buy A&B -30 Buy nothing 0 Land Purchase Decision Airport Location A B A B B B A A Payoff 13 -12 -8 11 5 0 0 31 6 4 23 35 29 0 0

12. Rolling Back the Decision Tree 0 1 2 3 Buy A -18 Buy B -12 Buy A&B -30 Buy nothing 0 Land Purchase Decision Airport Location A B A B B A Payoff 13 -12 -8 11 5 31 6 4 23 35 29 0.4 0.6 0.4 0.6 0.4 0.6 EMV=-2 EMV=3.4 EMV=1.4 EMV=3.4 0