Thursday, September 15, 2011

Practical Decision Making: Decision Trees

quote



“If there are two courses of action,
you should take the third.”



Jewish Proverb.





A decision tree is a visual tool for analysing decisions. In using it you generate a tree-like graph of decisions and their consequences. In the simplest form of this technique:





  • Squares: represent decisions


  • Triangles: represent end points





When the graph is completed you can then add probabilities for each of the individual branches and from the the overall probabilities of the end points.



using the technique



As a simple example let's suppose that I decide that I want to travel from my home to a hotel in town A. So let's draw the options in a decision tree:







We can now add some %'s to reflect either our preferences or an estimate of some factor that we would like to consider (e.g. cost, estimated likelihood, etc.). In this case I will use personal preferences:








I am assuming here that the train station is close to my home. For 'walk' I have added 0% because it is a long distance to town A. The bus takes a long time but it is quite cheap so I have given it 10%.



Notice that I have also added end points to 'walk' and 'drive' as they both get me to my destination. 'Train' and 'bus' however do not get me to my final destination so I now extend my decision tree by adding more decision points, options and estimates:








We can now multiply the %'s and see what the final end point %'s are:






So our conclusion should be that we should take the train and a taxi (45%).



extending the %'s



In this example I have used personal preferences only. You could also do this based on cost (or any other factor) simply use another colour for another % on each branch.





caution



This is a very simple example but even here I have simplified the decision tree. I have not considered for instance how I would get from my home to the train station. Decision trees can rapidly become very complex, indeed this is one of their strengths as they allow us to consider options that we might normally ignore. Try using a large wall space covered with flip chart paper (or a large white board) for your decision trees.




tip



Before starting your decision tree decide on the level of detail you wish to consider and the number of %'s you want to take into account. For example it can get very complicated if you use more that two types of %'s. When you have decided on the level of detail that you require try to stick to this, don't be dragged off into too much detail. In fact deciding the detail you should go down to in each decision tree that you do is one of the skills that you will develop by using them. In some cases a very high degree of detail is needed, in others all but the major option branches can be ignored.



adding chance events



You can make your decision trees even more elaborate by adding:




  • Circles: Chance events



For example:







making your decision



The %'s at the end points should be all that you need to make a decision. If you feel that this is the wrong decision you should consider:




  • whether the %'s you have allocated are correct


  • whether the level of detail in the branches is too high or too low


  • whether you are using the correct estimate (e.g. your %'s may be 'increased sales' when they should be 'increased profits')










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