Problem solving

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Decision Theory and Decision Trees
Decision trees are excellent tools for making financial or number based decisions where a lot of complex information needs to be taken into account. They provide an effective structure in which alternative decisions and the implications of taking those decisions can be laid down and evaluated. They also help you to form an accurate, balanced picture of the risks and rewards that can result from a particular choice.

How to Draw a Decision Tree
You start a decision tree with a decision that needs to be made. This decision is represented by a small square towards the left of a large piece of paper. From this box draw out lines towards the right for each possible solution, and write that solution along the line. Keep the lines apart as far as possible so that you can expand your thoughts.
At the end of each solution line, consider the results. If the result of taking that decision is uncertain, draw a small circle. If the result is another decision that needs to be made, draw another square. Squares represent decisions, circles represent uncertainty or random factors. Write the decision or factor to be considered above the square or circle. If you have completed the solution at the end of the line, just leave it blank.

Starting from the new decision squares on your diagram, draw out lines representing the options that could be taken. From the circles draw out lines representing possible outcomes. Again mark a brief note on the line saying what it means. Keep on doing this until you have drawn down as many of the possible outcomes and decisions as you can see leading on from your original decision.

An example of the sort of thing you will end up with is shown below:




Once you have done this, review your tree diagram. Challenge each square and circle to see if there are any solutions or outcomes you have not considered. If there are, draw them in. If necessary, redraft your tree if parts of it are too congested or untidy.

You should now have a good understanding of the range of possible outcomes.


Starting to Evaluate Your Decision Tree
Now you are ready to evaluate the decision tree. This is where you can calculate the decision that has the greatest worth to you. Start by assigning a cash or numeric value to each possible outcome - how much you think it would be worth to you.
Next look at each circle (representing an uncertainty point) and estimate the probability of each outcome. If you use percentages, the total must come to 100% at each circle. If you use fractions, these must add up to 1. If you have data on past events you may be able to make rigorous estimates of the probabilities. Otherwise write down your best guess.

This will give you a tree like the one below:



Note that the tree looks less confused when different colours are used for numbers than for the structure of the tree.


Calculating Tree Values
Once you have worked out the value of the outcomes, and have assessed the probablity of the outcomes of uncertainty, it is time to start calculating the values that will help you make your decision.
We start on the right hand side of the decision tree, and work back towards the left. As we complete a set of calculations on a node (decision square or uncertainty circle), all we need to do is to record the result. All the calculations that lead to that result can be ignored from now on - effectively that branch of the tree can be discarded. This is called 'pruning the tree'.


Calculating The Value of Uncertain Outcome Nodes
Where we are assessing the value of an uncertain outcomes (circles on the diagram), we do this by multiplying the value of the outcomes by their probability, and noting the result. The total value of that node of the tree is gained by adding these together.
In the example above, the value for 'new product, thorough development' is:


0.4 (probability good outcome) x $500,000 (value) = $200,000
0.4 (probability moderate outcome) x $25,000 (value) = $10,000
0.2 (probability poor outcome) x $1,000 (value) = $200
--------
$210,200

This is shown across our example tree in the diagram below:



Note that the values calculated for each node are shown in the boxes.

Calculating The Value of Decision Nodes
When you are evaluating a decision node, write down the cost of each option along each decision line. Then subtract the cost from the value of that outcome that you have already calculated. This will give you a value which represents the benefit of that decision.
Sunk costs, amounts already spent, do not count for this analysis.

When you have calculated the benefit of each decision, select the decision which has the largest benefit, and take that as the decision made and the value of that node.

Calculation of decision nodes in our example is shown below:



In this example, the benefit we previously calculated for 'new product, thorough development' was $210,000. This example shows that we calculate the cost of this approach as $75,000. This gives a net benefit of $135,000. The benefit of 'new product, rapid development' was $15,700. On this branch we therefore choose the most valuable option, 'new product, thorough development', and allocate this value to the decision node.


Result
By applying this technique we can see that the best option for us may be to develop a new product. What the analysis shows which we might not have appreciated, is that it is worth much more to us to take our time and get the product right than to rush the product to market. In fact, it is better just to improve our existing products than to botch a new product, even though it costs us less.

Summary
Decision trees provide an effective method of decision making because they:
clearly lay out the problem so that all choices can be viewed, discussed and challenged
provide a framework to quantify of the values of outcomes and the probabilities of achieving them
help us to make the best decisions on the basis of our existing information and best guesses.
As with all decision making methods, though, decision tree analysis should be used in conjunction with common sense. They are just one important part of your decision-making tool kit.

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Force Field Analysis
Force Field Analysis is a method used to get a whole view of all the forces for or against a plan so that a decision can be made which takes into account all interests. In effect this is a specialised method of weighing pros and cons.
Where a plan has been decided on, force field analysis allows you to look at all the forces for or against the plan. It helps you to plan or reduce the impact of the opposing forces, and strengthen and reinforce the supporting forces.


Carrying Out a Force Field Analysis
To carry out a force field analysis, follow the following steps:
List all forces for change in one column, and all forces against change in another column.
Assign a score to each force, from 1 (weak) to 5 (strong).
Draw a diagram showing the forces for and against, and the size of the forces.
Example Force Field Analysis
An example of the analysis is shown below:



Once you have carried out an analysis, you can decide on the viability of the project.

Where you have decided to carry out a project, it can help you to analyse how you can push through a project that may be in difficulty. Here you have two choices:

To reduce the strength of the forces opposing a project
To increase the forces pushing a project
Often the most elegant solution is the first: just trying to force change through may cause its own problems as e.g. staff can be annoyed into active opposition to a plan instead of merely not welcoming it.
If you were faced with the task of pushing through the project in the example above, the analysis might suggest a number of points:

By training staff (increase cost by 1) fear of technology could be eliminated (reduce fear by 2)
It would be useful to show staff that change is necessary for business survival (new force in favour, +2)
Staff could be shown that the new machines will introduce variety and interest to their jobs (new force, +1)
Wages could be raised to reflect new productivity (cost +1, loss of overtime -2)
Slightly different machines with filters to eliminate pollution could be installed (environmental impact -1)
These changes swing the balance from 11:10 (against the plan), to 8:13 (in favour of the plan)
Summary
Force Field Analysis is an effective method of getting a picture of all the forces for and against a plan. It helps you to weigh the importance of these factors and asses whether a plan is worth pursuing.
Where you have decided to proceed with a plan, carrying out a Force Field Analysis helps you identify changes that might be made to improve the plan.

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PMI - Plus/Minus/Interesting

What is PMI?
PMI stands for 'Plus/Minus/Interesting'. It is a valuable development (by Edward de Bono) of the 'pros and cons' technique used for centuries.
PMI is a basic decision making tool. When you are facing a difficult decision, simply draw up a table headed up 'Plus', 'Minus', and 'Interesting'. In the column underneath the 'Plus' heading, write down all the positive points of taking the action. Underneath the 'Minus' heading write down all the negative effects. In the 'Interesting' column write down the extended implications of taking the action, whether positive or negative.


Scoring your PMI table
You may be able to make a decision just from the table you have drawn up. Alternatively, consider each of the points you have written down and assign a positive or negative score to each appropriately. The scores you assign can be entirely subjective. Once you have done this, add up the score. A strongly positive score indicated that an action should be taken, a strongly negative score that it should be avoided.
An example is shown below:


Should I move to the big city?

Plus Minus Interesting
--------------------------------------------------------------------------------------------------------------
More going on Have to sell my Easier to find a new job? (+1)
(+5) house (-6)
Easier to see More pollution (-3) Meet more people? (+2)
my friends
(+5) Less space (-3) More difficult to get work done?(-4)
No countryside (-2)
Easier to get More difficult to get to work? (-4)
places (+3)
----------------------------------------------------------------------------------------------------------------
13 -14 -5 = - 6
Total = -6 - I'm happier living just outside the city.


For further information
Edward de Bono, Serious Creativity, HarperBusiness, New York, US, 1992.

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SWOT Analysis - Strengths, Weaknesses, Opportunities, Threats
SWOT Analysis is an effective method of identifying your Strengths and Weaknesses, and to examine the Opportunities and Threats you face. Often carrying out an analysis using the SWOT framework will be enough to reveal changes which can be usefully made.
To carry out a SWOT Analysis write down answers to the following questions:


Strengths:
What are your advantages?
What do you do well?
Consider this from your own point of view and from the point of view of the people you deal with. Don't be modest, be realistic. If you are having any difficulty with this, try writing down a list of your characteristics. Some of these will hopefully be strengths!

Weaknesses:
What could be improved?
What is done badly?
What should be avoided?
Again this should be considered from an internal and external basis - do other people perceive weaknesses that you don't see? Do your competitors do any better? It is best to be realistic now, and face any unpleasant truths as soon as possible.

Opportunities
Where are the good chances facing you?
What are the interesting trends?
Useful opportunities can come from such things as:
Changes in technology and markets on both a broad and narrow scale
Changes in government policy related to your field
Changes in social patterns, population profiles, lifestyle changes, etc.
Local Events

Threats
What obstacles do you face?
What is your competition doing?
Are the required specifications for your job, products or services changing?
Is changing technology threatening your position?
Do you have bad debt or cash-flow problems?
Carrying out this analysis is will often be illuminating - both in terms of pointing out what needs to be done, and in putting problems into perspective.