Getting Started with the Decision Tree
A decision tree can be used to plan a strategy, analyze the uncertainties and come to conclusions. The key elements of a decision tree are called nodes and appear as a square or circle with lines connecting them. A square represents a decision node, a circle represent an uncertainty, which is called a 'chance' node.
When you start the Decision Tree stand along application or whenever you click the "Decision Tree" button in Rational Will, you will see the following screen.
Now, you can start creating the decision tree by adding a start Node. A Start node can be a Decision Node, a Chance node or a Simultaneous node.
If you click the Decision Node, you will see the Decision Tree diagram view started as shown in the following screenshot.
Say, you added few options in this way. Select an option node, and you will see several buttons in the flyover menu of that option node.
Double-click a node to edit the text of a node.
From the flyover the menu, you see a note option. You can add a note like this.
You can select an option node and from there, you can add a chance node. Once you add a chance node and select the node, you will see the choices valid for that chance node. For example, a chance node can have Uncertain events. So, you will see the menu button for adding an uncertain event.
Once you add some events, the tree may look like the following screenshot.
If you click this button "I know the probability", then you will see a probability slider shows up.
A decision tree can be formed by chaining decision node, option node, chance node, event node and finally terminated as a terminal node. Even though, the terminal node is not really necessary for the calculation's perspective, yet, using a terminal node is intuitive.
What is a Simultaneous node?
You must be familiar with a Decision node and a Chance node. But what is a simultaneous node? A simultaneous node is a node where it's children are considered simultaneous. For example, you may think about 2 decision problem at the same time. Or you may have 2 mutually non-exclusive chance events. Then you can use the Simultaneous node. A simultaneous event shows up with Summation icon, because, the values of the children are summed up at that simultaneous node.
Add Payoff to a Node
Now, it is time to analyze the options numerically. Select an option node (children of a decision node) or an event node (children of a chance node), you will see the option to add a reward.
Once you click that button to add a reward, the Multi-criteria objective wizard will show up. Select "Minimize" from the drop-down menu, and name your criteria "Cost", as shown below. In that way, you define an objective "Minimize Cost".
Then Click the "Proceed" button and choose this objective as Money Type. You can choose the "Numerical Type" as well for the simple purpose. Or, choose Subjective if you simply don't want to dig deep with actual numbers.
After that, screen, you will be presented with the following wizard screen. Simply click no for this simple example.
Then, you will be presented with the following wizard screen. Set the minimum possible cost and maximum possible cost. Let's use the default value shown here and click proceed button.
Once you click the proceed button, you will be asked if you have any more objective (or criteria). Click "No" for this simple example. Yes, you can add more than one objectives. Please visit this page for learning Multi-Criteria modeling.
Once you click "No", you will be taken to the Decision Tree. Now, set the Cost value for the node "Car breaks down". Say, you estimate the cost as 500$. Set it by clicking the number box.
Practically, the cost can be a range rather than a fixed number. You can use a probability distribution to model that cost. Click the Probability Distribution button as shown here.
Clicking the Probability Distribution button will show the probability distribution gallery. You can choose a common distribution, or you can click the Custom button to model a custom distribution. For simplicity, let's choose the Normal Distribution. You will see the following window. Say, you think that, on average, your car breaks down cost can be 500$, but it can be as low as 200$ to maximum 800$.
Click OK, and your decision tree will show the Normal Distribution symbol on the Car breaks down event node.
Now, set the cost for 'Go by car' node and 'Go by plane' node. Say, you expect the fuel cost for "car" is 200$ and "plane" ticket is 500$. Set the values for these nodes as shown earlier. This time, you won't have to go thru the wizard for setting up objectives again. Simply click the reward button on flyover menu and set the cost.
Your tree will look like this.
You can see the expected value of a node by hovering the mouse on a node. The tooltip will show metrics.
By default, the Maximize Expected Value strategy is selected. You can change the strategy based on your risk attitude. Notice that, when you change the strategy to "LexiMin", the "Go By Plane" path is highlighted. LexiMin criterion is a criterion that evaluates an option based on the Worst Case Scenario. If you go by Car, from the above diagram, we can see that the worse case can be a cost of 998.53$. But if you take the plane, the worst case is the same ticket price, which is -500. As 500$ is less than 998.53$, the "Go by plane" option is recommended.
The Result Panel has a lot of analysis feature that help you to gain further insights. As this tree contains probability distribution, Monte Carlo Simulation was performed automatically, without needing you anything to configure.
Node Analysis (Risk Profile)
Select a node, and you will see all possible states (Risk Profile) generated base on the Monte Carlo Simulation.
Finally, you need to perform a sensitivity analysis, to understand which variable affects more than another variable that can change your decision. Expand the Sensitivity Analysis tab,
Clicking the chart button opens up the variable that is in question.