Choosing between Alternatives
Decision Trees are excellent tools for helping you to choose between several courses of action. They provide a highly effective structure within which you can lay out options and investigate the possible outcomes of choosing those options. They also help you to form a balanced picture of the risks and rewards associated with each possible course of action. Decision trees can be used when making a wide variety of choices, from the simplest decisions to very complex ones regarding: product planning and process management.
Decision Tree Formulation
The name Decision Tree comes from the tree-like appearance of the model. A decision tree consists of a number of square nodes, which represent decision points. The nodes grow branches, which show multiple alternatives. Branches also come out of circular event nodes, which represent the likelihood where more than one event is possible that influences the decision. The probability of each event is written above each branch. The probabilities for all branches leaving an event node must add up to exactly one.
Calculating Tree Values
After drawing the decision tree and working out the value of the outcomes as well as the probability of the outcomes uncertainty, we can now start calculating the values that will help make the best decision.
The decision tree is solved from right to left, calculating the expected results for each node.
Calculating the results for each node is as follows:
1. For an event node, multiply the outcome of each event branch by the events probability. The product is then added up in order to attain the event nodes expected results.
2. For the decision node, the alternative that has the best expected outcome is chosen. If this alternative leads to an event node, its outcome is equal to that nodes expected outcome. The branches that have not been chosen are “sawed off”. The decision nodes expected payoff is the one associated with the single remaining branch that has not been sawed off.
The method of calculation is continued along the branches of the tree until the decision node to the furthest left is reached. The branch extending from it that has not been sawed off is the best alternative to follow. Refer to Figure 1 below, for an illustration and calculation of a decision tree.
Key points
Decision trees provide an effective method of Decision Making because they:
- Clearly lay out the problem so that all options can be challenged.
- Allow us to analyze fully the possible consequences of a decision.
- Provide a framework to quantify the values of outcomes and the probabilities of achieving them.
- Help us to make the best decisions on the basis of existing information and best guesses.
- Below is an example of a decision tree and the calculations .
The tree approach is most useful in a sequential decision situation. For example, assume XYZ Corporation wishes to introduce one of two products to the market this year. The probabilities and present values (PV) of projected cash inflows follow:
A decision tree analyzing the two products follows:
Figure 1:
Based on the expected net present value, the company should choose product A over product B.
External Links
http://www.dtreg.com/dtintro.htm
http://en.wikipedia.org/wiki/Special:Recentchanges
http://www.public.asu.edu/~kirkwood/DAStuff/decisiontrees/index.html
http://www.cs.ubc.ca/nest/lci/CIspace/Version4/dTree/
Further Readings
Foundations of Operations Management-2nd Canadian Edition
http://books.google.ca/books?id=9HAmJQAACAAJ&source=gbs_book_other_versions_r&cad=3_1
http://www.decisiontrees.net/node/19
References
Ritzman, L. P., Krajewski, L. J., Malhotra, M. K., & Klassen, R. D. (2007). Foundations of Operations Management - 2nd Canadian ed. Toronto: Pearson Education Canada.
Critical thinking. (2008). Retrieved january 22, 2008, from http://philosophy.hku.hk/think/strategy/chart.php#b
