Easy Decision Tree Tutorial from SilverDecisions

978

This article is a contribution from SilverDecisions.

For many people, decision trees are something unfamiliar. What follows is an example illustrating the application of decision trees in management, to provide you with some insight into how effective they can be when used in practice. The decision tree diagram in this article was created with SilverDecisions – a Free and Open Source tool for manually creating and analyzing decision trees. The SilverDecisions application, along with its browser-based interface, provides a rich set of layout, graphics and export options and functionalities.

Let us consider the management board of a certain company that is considering two R&D investment options, both of which may generate profits. R&D investments are associated with extra costs and risks but in an optimistic scenario each of them could produce as much as €1 000 000 in profits, which certainly appears tempting at first glance.

The following options are considered:

  • An R&D project conducted by an internal R&D department with an estimated cost of €100 000. A successful project would generate income of €800 000 on the domestic market, while failure would result in no investment profit whatsoever. The likelihood of success is estimated at 50%.
  • The second alternative is to outsource R&D activities – such services are more expensive and cost €500 000 but they are more efficient too: the probability of a successful project generating €800 000 on the domestic market is estimated at 70%. In the case of success, the company may expand the outsourced R&D project abroad for another €500 000. High demand on the external market, with a probability of 50%, would generate an additional €1 200 000. If demand on the external market is low, the income generated abroad would only be €300 000.

Abandoning the R&D project is the alternative scenario that results in no extra profit or costs. Which is the best step to take?

At first sight such a problem seems to be clear, but when it comes to presenting and analyzing optimal decisions – this is where the difficulties arise. Let us try to describe this situation formally: the decision maker (we) makes different decisions step-by-step, which is commonly referred to as sequentiality. Then there are the so-called “states of the world” associated with the term called uncertainty. This means that there are some independent events (investment success or failure) that may happen with a certain probability level. Finally, each decision to be made and independent event that may occur, has its outcome interpreted as the consequence of a decision or a state of the world. Of course, this could be either profit or loss.

It turns out that the model described above enables the understanding and solving of the sequential decision problems under uncertainty. It can be presented in a tree-like directed graph, in which 3 types of nodes may be distinguished: in decision nodes (typically represented as squares) it is the decision maker who makes the choice. Edges emanating from the chance nodes (shown as circles) represent the set of available randomly occurring events. Terminal nodes (presented as triangles) are the endpoints containing the outcome. The decision tree model created for this R&D problem is presented in the diagram below:

The above diagram was created with SilverDecisions and can be opened in the application by clicking here. The tool has several decision making algorithms built-in (e.g. a classic rule, based on expected value maximization, a pessimistic maxi-min approach or an optimistic maxi-max approach) and, for each constructed tree, the set of optimal decisions is determined and highlighted in green. In our decision problem, based on an optimistic algorithm approach, the R&D project should be outsourced and, in the case of a success on the domestic market, we should also expand abroad. €1 000 000 is the expected profit associated with these decisions. The decision tree generated, along with all of its characteristics, can be exported as a PNG/SVG image or a PDF file or even to a JSON document for document storage or further processing.

In summary, the decision tree model is an easy-to-interpret method that represents the possible decisions to be made, the independent events that may happen, and the outcomes associated with combinations of these two. It is an extremely useful tool for decision analysis problems as it helps in finding the optimal decision from the set of possible decisions.

The SilverDecisions development was financed by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 645860.