Tim Thompson's article Management Accounting - Decision Management discusses the use of decision trees involving probabilities with combinations of events and decisions.
In the article the author discusses how a decision tree can help solve a problem, specifically situations where there is no control over what follows in an event sequence. In this type of scenario, the decision maker needs to know the possible outcomes as well as the probabilities of the outcomes.
To demonstrate how a decision tree can be used to solve a problem, the author used an example of a student deciding how to get to class. One alternative is for the student to take public transportation, which would cost £5. The second option is walk and save the cost of the transportation fare. The situation is complicated by adding other factors to the decision making process. In this scenario there is a 25 percent chance of rain. If the student is caught in the rain the student will have to pay £10 to have their clothes cleaned.
In this example there is one decision, to walk or to take public transportation, and one event, rain or no rain. If the student take the public transit option there is an £5 financial impact. If the student walks there is no immediate financial impact. The decision tree (shown below) will recognize the key event once for each potential decision.
- Public Transportation: (£0 x 0.25) + (£0 x 0.75) = £0
- Walk: (-£10 x 0.25) + (£0 x 0.75) = -£2.50
Using a decision tree a rational choice can be made. Looking at the public transportion option, there is a £5 cost but the expected value of the node is zero. Totaling the actual cost and expected value, the cost to the student of public transportation option is £5. The walk option has no cost, but the expected value of the event node is £2.50. Totaling the actual cost and expected value, the cost to the student of the walking option is £2.50. Since the total cost of walking is less than the total cost of public transportation, the student should decide to walk.
The author adds more complexity to this relatively simple model by adding a third option, the student takes an umbrella. Another event is also added, the student loses the umbrella. The author indicates that there is a 10 percent chance of the student losing the umbrella. If umbrella is lost, the student will incur a £20 cost to replace it. The updated decision tree with the third option is below.
The expected value for the new event was calculated as follows:
- Lose Umbrella: (-£20 x 0.10) + (£0 x 0.90) = -£2.00
The updated decision tree shows the rational choice the student should make is to carry an umbrella when walking. Total cost for walking with an umbrella is £2.00, versus £2.50 for walking without an umbrella and £5.00 for taking public transportation.
Decision trees are well suited for repeat decisions and can be applied to a variety of decision-making scenarios. In the business world, for example, decision trees can be used to launch a new product. Decision trees can also be used to determine when and where products should be launched.
Thompson, T. (2007, May). Management Accounting - Decision Management. Financial Management, 41-41.