decision trees
Decision trees are used as a quantitative tool for making decisions and they provide a logical process. The technique makes use of diagrams where decisions are represented by squares and outcomes or chances represented by circles. Chances are estimated by assigning probability values. The expected values of each decision are calculated to reach the best decision.\
RULES TO CONSTRUCT THE DIAGRAM:
The diagram is constructed from left to right and calculations are performed from right to left.
The roots should be on the left while the branches on the right.
The branches consist of:
(1) Decision nodes
(2) Chance events or outcomes.
Decision nodes:
These are used when a decision has to be taken. Normally, the decision should be between at least two alternatives.
Chance nodes:
These are used to show the possible outcomes of a decision. The chances are beyond the decision maker’s control.
A chance event should have a probability.
The summation of all the probabilities for each chance event should add up to one.
Actual values should be placed at the end of each branch (these are forecasts of the net cash flow resulting from a sequence of decision and chance events through a decision tree).
Expected values (these are the forecast actual values adjusted by the probability of their occurrence) are calculated by taking the actual value x probability.
To calculate the expected profit, the cost should be deducted.
The decision maker should choose the branch producing the best value.
The rejected decision should be cut out with the following symbol ||.
ADVANTAGES OF DECISION TREES:
DISADVANTAGES OF DECISION TREES:
QUESTION WORKED IN CLASS:
Denham Potteries has a capital spending budget of £100, 000. The production manager has put abid for £100, 000 for a new tunnel kiln. The marketing manager has countered with a proposal tospend £80, 000 on the launching of a new product. This new
product is in line with the firm’s objective of diversifying, but may be rather risky given the firm’s past records of only one success
for every five new products.
RULES TO CONSTRUCT THE DIAGRAM:
The diagram is constructed from left to right and calculations are performed from right to left.
The roots should be on the left while the branches on the right.
The branches consist of:
(1) Decision nodes
(2) Chance events or outcomes.
Decision nodes:
These are used when a decision has to be taken. Normally, the decision should be between at least two alternatives.
Chance nodes:
These are used to show the possible outcomes of a decision. The chances are beyond the decision maker’s control.
A chance event should have a probability.
The summation of all the probabilities for each chance event should add up to one.
Actual values should be placed at the end of each branch (these are forecasts of the net cash flow resulting from a sequence of decision and chance events through a decision tree).
Expected values (these are the forecast actual values adjusted by the probability of their occurrence) are calculated by taking the actual value x probability.
To calculate the expected profit, the cost should be deducted.
The decision maker should choose the branch producing the best value.
The rejected decision should be cut out with the following symbol ||.
ADVANTAGES OF DECISION TREES:
- Help to set out problems in a clear and logical manner and encourages a logical approach as well.
- By considering all outcomes, the decision maker gets all the options in front of him,thereby speeding up the decision making process.
- Risks are not ignored because decision trees consider negative outcomes as well.
- The probability of each outcome occurring is an advantage and makes calculations easier.
- Decision trees take into consideration the costs of the decision as well.
- This method is scientific and does not rely on imagination or intuition. It allows for informed decision.
DISADVANTAGES OF DECISION TREES:
- The estimated probabilities might not always be meaningful since forecasting errors may occur.
- Decision trees are numerical/quantitative in nature and ignore qualitative data.
- Data can easily be manipulated deliberately in order to justify a particular department's preference.
- The external business environment is not taken into consideration when drawing decision trees.
- The diagram only helps in calculation but not reduction of risks in decision making.
QUESTION WORKED IN CLASS:
Denham Potteries has a capital spending budget of £100, 000. The production manager has put abid for £100, 000 for a new tunnel kiln. The marketing manager has countered with a proposal tospend £80, 000 on the launching of a new product. This new
product is in line with the firm’s objective of diversifying, but may be rather risky given the firm’s past records of only one success
for every five new products.
CALCULATION OF EXPECTED VALUES:
Now that the probability values and actual values have been filled in, the first option would give:
(900 000x0.1)+(500 000x0.1)+(30 000x0.8) = £164 000
Since the case study gives costs of £ 80 000 for new product launching, it should be deducted.164 000-80 000 = £84 000
The second option would give:
(200 000*0.8)+(60 000*0.2) = £172 000
Since the case study gives costs of £ 100 000 for tunnel kiln, it should be deducted. 172 000-100000 = £ 72 000
MAKING THE QUANTITATIVE DECISION:
Now that the net expected incomes for both options have been calculated, it is found out that the option of launching a new product should be selected because it gives a net expected income of £ 84 000.
QUALITATIVE REASONING FOR DENHAM POTTERIES:
Whenever a decision has to be taken, both quantitative and qualitative factors have to be taken into account. The management must first of all investigate the quality of the data collected by the marketing manager. They may be less reliable and biased in favour of his department. The production manager must also verify the validity of the figures collected by the marketing manager.
The company has as objective to diversify which plays in favour of the marketing manager especially in addition to the numerate considerations. However the management must not forgetthat the probability of failure for the new product is 80 %. This implies that the firm has 80 %risk of losing £ 50 000 (calculated as 80 000 - 30 000). This represents a high risk. Is the company ready to take such a high risk?
The state of the existing kiln must also be checked. Is there any problem with the kiln? Is thequality and efficiency negatively affected? All these areas must be verified before investing in the new kiln. The new efficiency and productivity level must be known to check whether theproduct is really a priority.
The other departments must also be considered and involved in the decision making process. Inthe case study, it seems that the other departments have not given their proposals. It must bewell coordinated else the board will be seen as favouring one department and this may result inlow morale and misunderstanding
Now that the probability values and actual values have been filled in, the first option would give:
(900 000x0.1)+(500 000x0.1)+(30 000x0.8) = £164 000
Since the case study gives costs of £ 80 000 for new product launching, it should be deducted.164 000-80 000 = £84 000
The second option would give:
(200 000*0.8)+(60 000*0.2) = £172 000
Since the case study gives costs of £ 100 000 for tunnel kiln, it should be deducted. 172 000-100000 = £ 72 000
MAKING THE QUANTITATIVE DECISION:
Now that the net expected incomes for both options have been calculated, it is found out that the option of launching a new product should be selected because it gives a net expected income of £ 84 000.
QUALITATIVE REASONING FOR DENHAM POTTERIES:
Whenever a decision has to be taken, both quantitative and qualitative factors have to be taken into account. The management must first of all investigate the quality of the data collected by the marketing manager. They may be less reliable and biased in favour of his department. The production manager must also verify the validity of the figures collected by the marketing manager.
The company has as objective to diversify which plays in favour of the marketing manager especially in addition to the numerate considerations. However the management must not forgetthat the probability of failure for the new product is 80 %. This implies that the firm has 80 %risk of losing £ 50 000 (calculated as 80 000 - 30 000). This represents a high risk. Is the company ready to take such a high risk?
The state of the existing kiln must also be checked. Is there any problem with the kiln? Is thequality and efficiency negatively affected? All these areas must be verified before investing in the new kiln. The new efficiency and productivity level must be known to check whether theproduct is really a priority.
The other departments must also be considered and involved in the decision making process. Inthe case study, it seems that the other departments have not given their proposals. It must bewell coordinated else the board will be seen as favouring one department and this may result inlow morale and misunderstanding