## Monday, March 11, 2013

### An Introduction to Decision Tree Analysis

Summary

Craig Kirkwood, a member of the Department of Supply Chain Management of Arizona State University, published a primer on the use of decision tree analysis in 2002. The first chapter provides increasingly complex examples of decision trees and the various factors that can effect analysis.

Kirkwood begins by giving a simple example of a decision tree. This example involves the decision of a company on whether or not it should manufacture a temperature sensor, pressure sensor, or neither. The costs differ for the sensors, as does the potential profit. This is the most basic decision tree that he presents, and the examples become increasingly complex as more factors are added.

After the basic set-up of a decision tree is given, Kirkwood adds the first new "node": chance. What went from a relatively simple analysis of costs now include the probability that a product will sell or not. With the addition of this variable, a new concept is introduced: the expected value. Depending on the situation, the best expected value is either the highest number or the lowest number. By finding the expected value, it allows for a decision maker to know the best and worst decision with a quick glance at that number.

A second variable that Kirkwood introduces is dependent uncertainties   Dependent uncertainties further complicate decision trees, as they add a new degree of uncertainty. The example given discusses the uncertainty of a trading company in dealing with minerals from a nation that could face trade sanctions from the United States. This leads to the application of the term 'decision tree rollback', which is calculating the expected values from the endpoint of a decision tree to the root node, or beginning.

Sequential decisions is the last variable that Kirkwood discusses. These further complicate decision trees by adding a second layer (or more) of decisions that must be made after an initial decision has been decided. The example Kirkwood uses is a computer company bidding for a government contract. The company must first decide if it wants to bid for the contract or not, as there is a cost to creating a prototype to enter the bidding process. The company then must decide how much it will bid. Thirdly, the company then has to decide on whether or not to use a new, untested manufacturing process that will either save or lose money.

Kirkwood used diagrams of decision trees throughout the chapter. The most complex example (using all of the variables that he discussed) was presented at the end.
 Figure 1: Final Dicission Tree Example
Critique

Kirkwood gives a very good introduction to decision tree analysis. While his explanation of concepts can be vague, the examples he provides makes up for this. He also successfully demonstrated that decision trees can be used for increasingly complex scenarios. Though this is a good introduction to decision trees, there are two main criticisms that should be mentioned.

First, he does not explain sufficiently the formulas used to obtain the expected values that he bases decisions.  on. While he explains the first equation used to determine the expected value, this was done with only one variable (chance). With each new variable he introduces, the equation gets longer. Though there is no fundamental change in the equation, his discussion could have benefited from an explanation of each equation. As it was, it was difficult to remember how the equation he used came about.

Second, while his examples are very good at demonstrating the different variables that he discusses, they all have the same goal: profit. At no point did he discuss the application of decision trees to situations that did not have the endpoint of profit. Admittedly it would be much more difficult to give examples where the goal was something other than profit, but it would be interesting to see decision tree analysis applied to a problem that was not based on profit and costs.

Source

Kirkwood, C.W. (2002). Decision Trees. Decision Tree Primer, 1-18. Retrieved from
http://www.public.asu.edu/~kirkwood/DAStuff/decisiontrees/DecisionTreePrimer-1.pdf