During the past years a number of mainly mathematical techniques have been developed to assist the decision maker. These techniques are called decision aids and their use is intended to maximize the probability that the chosen decision is the best one. Among the better known are the following:
- decision trees
- decision matrices
- linear programming
- game theory
- linear regression
- mathematical modelling
- PERT (program evaluation review technique)
- critical path method
Of these, decision trees and decision matrices must be considered genuinely basic and are the only ones treated here. Decision trees and decision matrices are not dependent on advanced mathematics or the use of computers.
A decision tree is a model which gives a visual presentation of the structure of a decision situation. It has branches spreading out from nodes like a tree. The nodes are of two types: decision nodes (usually presented as a small square) and event nodes (usually presented as a small circle). From each decision node all the potential decisions branch out. Seen as series of decisions, the second step is dependent upon the first step, the third depends upon the second, etc. If risk or uncertainty is associated with each step, these qualities are gradually accumulated. An example of a decision tree is shown in Figure 9.1. Note the probability assignment given for each branch.
Figure 9.1 A decision tree.
To make a decision involves in practice cuting off a branch of the tree that is no longer possible to reach. A transition takes place from openness to closure, something which presupposes a moment in time when all necessary information is collected.
A decision matrix is another aid for enhancing the choice of the best alternative when the various options have been sufficiently identified. The value of a decision matrix increases when the number of alternatives increases. The use of the matrix can be clarified by explaining four consecutive user steps. Step one is to identify all the alternatives which seem reasonable in the pertinent situation and to assign them to the matrix.
In the second step, criteria are established to provide a basis for the selection of one alternative over another. Here, each quality is given a number in relation to its order of importance. The numbers are summed, and weighting factors are assigned by dividing this total into each item’s individual number. An example with eight criteria is given in Table 9.2.
The third step is to assign rating factor values to all the present alternatives considering the selection criteria. A scale from 1 to 10 is applied, where 10 is best. The assignment of these values is best done one criterion at a time, evaluating each alternative according to that particular criterion.
The fourth and final step in completion of the matrix is to multiply each ranking factor by its corresponding weighting factor and to record the product to the right in the column. Ultimately, all products are summed as in the completed matrix of Table 9.3.
Mathematically, the highest sum can be 10, since all weighting factors together must be 1 and the highest ranking factor value is 10. In this example, the third alternative had the highest value and was thus chosen. The great advantage with this matrix is that all steps in the decision process are clearly documented and the idea behind a given choice can easily be demonstrated.
Besides the techniques described here as decision aids (used inside or outside a computer), the computer itself is a kind of decision aid if sensibly used. The general principles for use of this type of assistance is presented in Table 9.4.
The horizontal axis shows an increasing degree of computer processing. The least processed output is data which can be further processed together with human supplements. By this means, what- if questions can be asked and sensitivity analysis can be performed. Of course, the computer may be able to recommend a certain course of action if enough information and structure has been programmed into it.
The vertical axis shows how output from the computer can be used by man with increased degree of human processing. On the lowest level the computer is only used as a source of inspiration while at the highest it is used as a decision adviser.
The table can also be used to describe how the good decisionmaker can interact with his assistants. The computer, however, has a tremendous advantage in that it has no ambition for a career of its own. It can never be a yes-man.
Source: Skyttner Lars (2006), General Systems Theory: Problems, Perspectives, Practice, Wspc, 2nd Edition.