# Decision tree

### INTRODUCTION

**What Is Decision Tree?**

- Decision Tree is a visual or graphical representation of all Decision-Making Process.
- Basically, Decision Trees are composed of Nodes and Branches.
- There are three types of nodes in each and every Decision Tree, they are
- Decision Nodes - indicates the point at which decisions must be made and it is represented by squares.
- Outcome Nodes - indicates the point at which outcomes or states of nature occur and it is represented by circles.
- End Nodes - indicates the point at which the final outcome occurs and it is represented by triangle. But this is optional.

**How to Use Decision Tree?**

- Decision tree can be used to predict a figure or pattern, classify the class of data.
- They also helps to form a equalised or balanced picture of the venture and remuneration associated with each practicable course of action.
- It provides a framework for capturing and using judgement and experience to understand and interpret.

**When and Where to use Decision Trees?**

- Decision trees are used in complex and multi-staged problems where it is very essential.
- It is used *when we plan or organize to have sequence of decisions,
- considering the choices made at starting stages, *events at later stages of that sequence.
- This is efficiently used while choosing two different strategies, projects and in limited resources.

### ROLE OF DECISION TREE:

**Capacity Of Decision Tree:**

- The decision tree is a decision tree support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcome resource costs and utility.
- The main difference between the table and the decision tree is the tree is more flexible and makes the decisions simple when compared with table.
- It is a technique for determining the overall risk associated with a series of related risks.

### BENEFITS OF DECISION TREE:

- Decision Trees are simple to understand and to frame it.
- Decision trees can be combined with any other decision techniques.
- It is easy to map nicely to set a business rules.
- It doesn't make prior assumptions about the data.
- Decisions tree applies to real-time problems.

### WEAKNESS OF DECISION TREE:

- The main weakness of decision tree is that its algorithms are unstable.
- Trees which created from the numerical datasets can be complex.
- Decision trees are limited to one output attribute.

### EXAMPLE OF DECISION TREE:

**Question:**

- Ford car company bid for government contract for manufacturing 5000 cars at the cost 4750, 4250, 3750 per car. And its only competitor is Chevrolet cars whose bids 5000, 4500, 4000. Fords current manufacturing process cost 4000 per car. In new manufacturing process there is a 0.25 probability that costs 2500 and 0.50 probability which costs 3750. Unfortunately there is also 0.25 probability that cost 4250 per car.

Q** Should the ford company submit a bid and if so what should they bid per car?

(The detailed question is given in appendix 1)

**Answer:**

**Evaluating the Decision Tree:**- For this situation the decision tree should be constructed as shown in the figure 5.1 below.
- First ford car company should decide whether to bid and how much to bid.
- If Fords bid is lower than Chevrolet cars then ford has to decide which manufacturing process to use.
- If Ford uses the proposed new manufacturing process then the cost of manufacturing is uncertain.
- The estimated net profit of the ford company is shown at the end point of the tree by considering the Cost of preparing the bid, Cost of manufacturing the cars, The revenue cost that ford will receive for the cars.
**Calculating the Net Income:**- For example: examine the topmost end value.
- It cost half a million pounds to prepare for bid and Ford bids 4750 which is lower than Chevrolet cars bid of 5000 and hence Ford wins the contract.
- Then the propose new manufacturing process is used and it costs 4250 per car to manufacture the 5000 cars.
- Therefore at this endpoint, ford makes a ne profit of (-500000-5000*4250+5000*4750) = 2 million.
- Similarly it is done for other end points to find the other net profit values.
**Calculating The Estimated Value:**- Calculating the expected value shown on the figure decision tree requires addressing a new issue, namely what to do when there are multiple decision nodes in the tree.
- In this decision the amount of the bid is first decision.
- And if this is lower than the Chevrolet bid then there is a second decision involving the type of manufacturing process to use.
- The calculation procedure for this situation is a straight forward extension of the calculation procedure.
- This procedure will be illustrated by considering the topmost set of nodes in the tree figures.
- Start at the rightmost side of tree and calculate the expected value for the top rightmost chance node.
- This is determined by (1/4)* 2+(1/2)* 4.5+(1/4)* 10.75 = 5.43 million
- At the top rightmost decision node, Compare the expected values for the two branches.
- The expected value for the top branch of this decision tree is 5.43 and the expected value for the bottom branch is 3.25
- Since the top branch has higher expected value, it is the preferred branch.
- Hence the expected value for the "manufacturing process" decision node is equal to the expected value for new manufacturing process, which is 5.43.
- Now continue back toward the root of decision tree calculating the expected value for the top most chance node in the tree.
- The expected value of left most chance node is (1/3)*( 5.43)+(2/3)* (- 0.5) = 1.32
- A similar process is used for calculating the expected value for other three branches of the root node and the results are shown in the decision tree figure and the calculation part in appendix.
**Result and Key Points:**- In addition the calculations also show that Ford should use the proposed new manufacture process if it wins the contract.
- The less preferred branches for each decision node have been indicated on the decision tree with cross hatching.
- The complete specification of the alternatives that should be selected at all decision nodes in a decision tree is called a Decision Strategy.
- The decision strategy shown in decision tree figure can be summarized as follows.
- Bid 4250 million and if Ford wins the contract, it should use the proposed new manufacturing process.

Figure 5.1 Ford Car Company Decision Tree:

Figure 5.2 Ford Car Company Decision Tree With Net Profit:

Figure 5.3 Ford Car Company Decision Tree with Net Value and Estimated Value:

### Conclusion:

- Decision trees provide an effective method of decision making.
- Clear layout of the problem.
- A problem can be fully analysed in all possible options.
- Used for making the best decisions from the existing outcomes.

As with all decision making methods, decision tree analysis should be used in conjunction with common sense - decision trees are just one important part of the decision making process.

### APPENDIX:

Question:

Ford car company is taking into account of submitting a bid for a government contract to provide 5000 cars for senior officers. There is only one other potential bidder for this contract is Chevrolet cars. Now the low bidder will receive the contract. Ford cars bidding decision is complicated by the fact that ford is currently working on a new process to manufacture the cars. If this process works as hoped then it may substantially lower the cost of making the cars. However there is some chance that the new process will actually be more expensive than the current manufacturing process. Unfortunately ford will not be able to determine the cost of the new process without actually using to manufacture the cars. If ford decides to bid it will male one of three bids: 4750 per car; 4250 per car; 3750 per car. Chevrolet cars are certain to bid and it is equally that Chevrolet will bid 5000, 4500, 4000 per car. If ford decides to bid then it will cost 500000 to prepare the bid due to the requirement that a prototype car be included with the bid. This 500000 will be totally lost regardless of whether ford wins or loses the bidding competition. With fords current manufacturing process it is certain to cost 4000 per car. With the proposed new manufacturing process there is 0.25 probability that the manufacturing cost will be 2500 per car and 0.50 probability that the cost will be 3750 per car. Unfortunately there is also a 0.25 probability that the cost will be 4250 per car.

Calculations:

Net Income:

- (-500000-5000*4250+5000*4750) = 2 million.
- (-500000-5000*3750+5000*4750) = 4.5 million.
- (-500000-5000*2500+5000*4750) = 10.75 million.
- (-500000-5000*4000+5000*4750) = 3.25 million.
- (-500000-5000*4750+5000*4750) = -0.5 million.
- (-500000-5000*4250+5000*4250) = -0.5 million.
- (-500000-5000*3750+5000*4250) = 2 million.
- (-500000-5000*2500+5000*4250) = 8.25 million.
- (-500000-5000*4000+5000*4250) = 0.7 million.
- (-500000-5000*4250+5000*4250) = -0.5 million.
- (-500000-5000*4250+5000*3750) = -3 million.
- (-500000-5000*3750+5000*3750) = -0.5 million.
- (-500000-5000*2500+5000*3750) = 5.75 million.
- (-500000-5000*4000+5000*3750) = -1.75 million.

**Estimated Value:**

- (1/4)* 2+(1/2)* 4.5+(1/4)* 10.75 = 5.43 million
- (1/4)* (-0.5)+(1/2)* 2+(1/4)* 8.255 = 2.93 million
- (1/4)* (-3)+(1/2)* (-0.5)+(1/4)* 5.75 = 0.43 million
- (1/3)*( 5.43)+(2/3)*(- 0.5) = 1.32 million
- (2/3)*( 2.93)+(1/3)*(- 0.5) = 1.81million

### REFRENCES:

- http://www.public.asu.edu/~kirkwood/DAStuff/decisiontrees/DecisionTreePrimer-1.pdf
- http://people.revoledu.com/kardi/tutorial/DecisionTree/how-to-use-decision-tree.htm
- http://www.mindtools.com/dectree.html
- http://www.time-management-guide.com/decision-tree.html
- http://people.revoledu.com/kardi/tutorial/DecisionTree/how-to-train-decision-tree.htm
- An Introduction to Management Science (David R. Anderson, Dennis J. Sweeney, Thomas A. Williams)
- Borison, A. (1995). Oglethorpe Power Corporation decides about investing in a major transmission system. Interfaces, 25 (2), 25-36.
- Managerial Economics and Organizational Architecture (Brickley, Smith, Zimmerman)