# Introduction to Decision Trees A decision tree can be used instead of a table to show alternatives, outcomes, and payoffs. Trees are much more powerful than tables, which are limited to two dimensions. For example, alternatives and outcomes. It consists of nodes and arcs. A square represents a decision node, a circle represents an outcome node, and a line indicates the decision alternatives or outcomes. A decision tree shows the order of decisions and outcomes. Let’s look at our first example. The Duncan Manufacturing Company must decide whether to manufacture a component part at its Mississauga plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit. The decision alternatives are to manufacture or purchase the component, and the following outcomes are low demand, medium demand, and high demand. So, if the company were to manufacture the component when it is in high demand, the projected profit is \$100,000. Show the order of decisions and outcomes using a decision tree. We start off with decision node. If the company decides to manufacture the component, then there are three following outcomes. If it is in low demand, the company is projected to lose \$20,000. If it is in medium demand, the company is projected to profit \$40,000. And when it is in high demand, the company is projected to profit \$100,000. If the company decides to purchase the component, then we can see the projected payoff when it is in low demand, medium demand, and high demand. Recall that a square represents a decision node, so node 1 shows the decision to either manufacture or purchase the component. Nodes 2 and 3 shows the outcomes: when there is a low demand, medium demand, and high demand. Folding back a decision tree is a process of identifying the optimal decision. The process begins after a complete decision tree has been developed. Moving from right to left, we calculate the expected payoff at each outcome node. At each decision node, we then select the best decision alternative based on the expected payoff at each outcome node. For a maximization problem, we would select the largest payoff, and for a minimization problem, we would select the lowest cost. Continuing on from Example 1, suppose that the probability of a low demand is 35%, the probability of a medium demand is also 35%, and the probability of a high demand is 30%. Calculate the expected payoff at each outcome node and identify the best decision alternative based on the expected payoff. So first, let’s calculate the expected payoff if the company were to manufacture the component. Let’s look a piece of the decision tree to help us out. The expected payoff is 35% times negative \$20,000 for a low demand, plus 35% times \$40,000 for a medium demand, plus 30% times \$100,000 for a high demand. This equals to an expected payoff of \$37,000. Now let’s calculate the expected payoff if the company were to purchase the component. The expected payoff is 35% times \$10,000 for a low demand, plus 35% times \$45,000 for a medium demand, plus 30% times \$70,000 for a high demand. This gives us an expected payoff of \$40,250. So when we are folding back the decision tree, we need to first look at the payoff at each outcome, then multiply it by the probability of each outcome, which will give us the expected payoff at each outcome node. Now we can make a decision based on the expected payoff at each outcome node. Since we would want to maximize profit, the best decision would be the outcome with the largest expected payoff. Therefore, the best decision alternative would be to purchase the component since it yields the largest expected payoff of \$40,250. Here is an exercise that you can try. Make sure that you pause the video before you check your solution. Good luck!

### 3 thoughts on “Introduction to Decision Trees”

• Nabeel says:

great video. thanks for sharing the knowledge!!

• Linda Eze says:

Hello. Could you help out with the problem below.
. A large steel manufacturing company has three options with regards to production: (i) produce commercially (ii) build pilot plant (iii) stop producing steel. The management has estimated that their pilot plant, if built, has 0.8 chance of high yield and 0.2 chance of low yield. If the pilot plant does show a high yield, management assigns a probability of 0.75 that the commercial plant will also have a high yield. If the pilot plant shows a low yield there is only a 0.1 chance that the commercial plant will show a high yield. Finally, management’s best assessment of the yield on a commercial –size plant without building a pilot plant first has a 0.6 chance of high yield. A pilot plant will cost N300,000. The profits earned under high and low yield conditions are N12,000,000 and N1,200,000 respectively. Find the optimum decision for the company.

• aya mikbel says:

hi waffa