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   

Use of Rehabilitation Decision-Making For Buildings In the Wenchuan Area

Rehabilitation Decision-Making For Buildings In the Wenchuan Area

Summary:

            In 2008 an 8.0 magnitude earthquake occurred in the Wenchuan area of China.  The Earthquake left over 88,000 people dead or missing, and resulted in economic losses up to $125.6 billion.  After the earthquake, talks occurred within building owners in the Wenchuan area if seismic rehabilitation measures should be pursued.  Most individuals worried that spending the money to make their properties upgraded in terms of seismic design would prove futile if another earthquake didn’t occur.  To present possible decision options to building owners in the Wenchuan area of China, the authors present a Decision-Making Tree Model (DMT) to develop both risks and rewards for each option of action for the building owners. 

            The DMT model used by the authors consists of five components: decision nodes, decision options, uncertainty nodes, possible outcomes, and end nodes.  With the use of the DMT model, the authors broke down possible outcomes into three distinctions that building owners would want answers on: possible damage states and possibilities, possible earthquake intensities and probabilities, and rehabilitation options and costs.  The overall goal of the use of the DMT model is to inform building owners which of the three options is the most viable: restoring the buildings to original seismic consistency, repair and strengthen building seismic resistance, and upgrade seismic resistance to the highest level. 

            Overall, the use of the DMT model was able to demonstrate that upgrading building levels to the highest seismic resistance was economically justified.  When the authors examined whether seismic rehabilitation would occur, the DMT models displayed cost as the key factor influencing decision-makers.  The other factors of building vulnerability and the probability of seismic activity the authors concluded as remaining constant among regions.  Thus, the DMT model demonstrated that reducing rehabilitative costs made it more likely for building owners to choose to rehabilitate their building to higher standards of seismic resistance.  

Critique:

            The use of DMT modeling as a tool for risk assessment of earthquake probabilities and different options for economic improvement initiatives was a manner in which to reduce uncertainty and unwillingness to improve building quality.  For the purposes of this study, decision-makers needed to have a willingness to be open to the outcomes of the DMT model results despite their perceptions beforehand.  To make the DMT model as an analytical technique more reliable, the authors could have considered incorporating the building owners overall attitude to improving seismic stability of their buildings.  Incorporating the building owners’ attitudes might offer intriguing insights of the situation in the Wenchuan area of China as it relates to earthquake probability and citizen perceptions.      

            However, DMT modeling could be applied to any situation in which a decision-maker considers both the risks and benefits of a proposed action.  DMT models would be especially relevant in analysis endeavors in the intelligence community.  DMT modeling not only is a way to display visually different outcomes of action for a decision-maker, but also effective at analyzing information in probabilistic thinking terms.   DMT modeling allows for probabilistic thinking that creates more reliable measures that uses words of estimative probability within their estimates.  Overall, DMT modeling is an effective manner in which to display the possible options available to the decision-maker and has the capability to display both the risks and benefits in terms of probability measures.  In the intelligence field probability measures are the most crucial aspect of intelligence estimates and what decision-makers look for to reduce their uncertainty in actions proposed to them.    

Source:

Zhang, Hong, Xing, Feng, and Liu, Juan. (2011). Rehabilitation Decision-Making For Buildings In the Wenchuan Area. Construction Management and Economics, 29, 569-578. Retrieved from http://content.ebscohost.com/pdf25_26/pdf/2011/1JM/01Jun11/62872628.pdf?T=P&P=AN&K=62872628&S=R&D=bsh&EbscoContent=dGJyMNHr7ESep644y9fwOLCmr0ueqK5Sr6u4SLGWxWXS&ContentCustomer=dGJyMPGstFGwprVLuePfgeyx44Dt6fIA.