1. Decision Trees MHA 6350 Dr. Burton

2. A B A square with two or lines branching from the square represents a decision. This diagram represents two alternatives.

3. Source: Clemen, 1990 A B A circle at the end of the branch from decision square represents a chance event.

4. Source: Clemen, 1990 A B A chance event must be followed by two or more possible outcomes.20 10 6 5 5 Each outcome has a weighted value.

5. 200.70.3 Source: Clemen, 1990 0.1 0.1 10 A B 6 5 5 0.6 0.2 Each outcome associated with a chance event has a probability. The sum of all probabilities for each event must = 1.

6. 0.7 20 0.3 Source: Clemen, 1990 0.1 0.1 10 A B 6 5 5 0.6 0.2 0.1 x 20 = 2 0.2 x 10 = 2 0.6 x 6 = 3.6 0.1 x 5 = 0.5 0.1 x 5 = 3.5 0.3 x -1 = -0.3

7. 0.7 20 0.3 Source: Clemen, 1990 0.1 0.1 10 A B 6 5 5 0.6 0.2 0.1 x 20 = 2 0.2 x 10 = 2 0.6 x 6 = 3.6 0.1 x 5 = 0.5 0.7 x 5 = 3.5 0.3 x -1 = -0.3 3.2 = 3.5 – 0.3 8.1 = 2 + 2 + 3.6 + 0.5

8. 0.45 $8 $0 0.55 Source: Clemen, 1990 A 1 $0 A B 0.5 $10 A 2 0.5 $15 0.73 $4

9. Safety, Low Cost Adapted from: Clemen, 1990 Danger, Low Cost Forecast: Will hit New Orleans Hurricane hits N.O. Stay Evacuate Safety, High Cost Hurricane misses N.O. Safety, Low Cost Danger, Low Cost Forecast: Will miss New Orleans Hurricane hits N.O. Stay Evacuate Safety, High Cost Hurricane misses N.O.

10. Real-estate decision Purchase an apartment complex for $400,000 Expected net revenue after operating and finance costs is $6000 per month. Revenue could vary from low of -$1000 to a high of $10,000 per month. A ten year certificate of deposit would earn 9.5% per year. Source: Clemen, 1990

11. Invest $400,000 at 9.5% Purchase complex for $400,000 $6000 per mo Highest $10,000 per mo Lowest -$1000 per mo $380,000 $1,200,000 $720,000 -$120,000

12. You need to upgrade your facility’s software for medical records and billing. You have the option of upgrading your current system at a cost of $350,000. Your CIO has evaluated the upgrade and estimated that there is a 75% chance that the upgrade will work. If the upgrade works it is expected to have a life expectancy of 5 years. If the upgrade does not work you will have to replace the existing software at a cost of $1,200,000. If you purchase a new software package now, the vendor is willing to discount the cost to $950,000. However, this version is programmed for revision in five years and will no longer be supported at that time. Your CIO estimates that there is a 95% probability that the new package will work without any cost for debugging. If debugging is required the cost is projected to be $50,000. A third option is to outsource the system. A five year contract for an outsourced system would cost $200,000 annually. The outsource vendor will include upgrades when needed at no additional cost. Develop a decision tree for this scenario. Which alternative would you recommend? Software Purchase Decision

13. $350,000 $200,000 x 5 years = $1,000,000 0.75 $950,000 Upgrade System Outsource 0.25 0.5 $950,000 + $50,000 0.95 $1,200,000 +$350,000 Purchase New