Decision making with the analytic hierarchy process

Abstract

Decisions involve many intangibles that need to be traded off. To do that, they have to be measured along side tangibles whose measurements must also be evaluated as to, how well, they serve the objectives of the decision maker. The Analytic Hierarchy Process (AHP) is a theory of measurement through pairwise comparisons and relies on the judgements of experts to derive priority scales. It is these scales that measure intangibles in relative terms. The comparisons are made using a scale of absolute judgements that represents, how much more, one element dominates another with respect to a given attribute. The judgements may be inconsistent, and how to measure inconsistency and improve the judgements, when possible to obtain better consistency is a concern of the AHP. The derived priority scales are synthesised by multiplying them by the priority of their parent nodes and adding for all such nodes. An illustration is included.

Figures (14)

able 1 The fundamental scale of absolute numbers

Table 2 Relative consumption of drinks

There are 12 pairwise comparison matrices in all: One for the criteria with respect to the goal, which is shown here in Table 3, two for the subcriteria, the first of which for the subcriteria under flexibility: location, time and work, that is given in Table 4 and one for the subcriteria under opportunity that is not shown here. Then, there are nine comparison The following is a simple decision examined by someone to determine what kind of job would be best for him/her after getting his/her PhD: either to work in two kinds of companies or to teach in two kinds of schools. The goal is to determine the kind of job for which he/she is best suited as spelled out by the criteria. Because of space limitations we will not define them in detail here (for more detail see Saaty, 1994; Saaty and Vargas, 2000) (Figure 1).

able 3 Pairwise comparison matrix of the main criteria with respect to the Goal Pairwise comparison matrix for the subcriteria with respect to flexibility

Pairwise comparison matrix for the alternatives with respect to potential increase in salary

In Table 1, the criteria listed on the left are one by one compared with each criterion listed on top as to which one is more important with respect to the goal of selecting a best job. In Table 2, the subcriteria on the left are compared with the subcriteria on top as to their importance with respect to flexibility. In Table 3, the alternatives on the left are compared with those on top with respect to relative preference for potential increase in salary. The subcriteria priorities in Table 2 are weighed by the priority of their parent criterion flexibility (0.036) to obtain their global priority.

able 7 Final results shown as normalised priorities and idealised priorities

‘able 8 Deriving priorities for ratings on job security

There is in addition the possibility of the dependence of the criteria on the alternatives in addition to the mandatory dependence of the alternatives on the criteria or among themselves. In that case we have a decision with dependence and feedback. To determine the best course of action in such decisions needs a few days to do thoroughly. Its steps are carried out along the lines shown in Figure 2.

able 12 Comparing relative and rating results The process of paired comparisons has far broader uses for making decisions. We can deal with a decision from four different standpoints: the benefits (B), that the decision brings, the opportunities (O) it creates, the costs (C) that it incurs and the risks (R) that it might have to face. We refer to these merits together as BOCR. Some people in the field of strategic planning use similar factors known as SWOT (Strengths, Weaknesses, Opportunities and Threats) having switched the order of weaknesses and opportunities in making the correspondence with BOCR. The alternatives must be ranked for each of the four merits. The four rankings are then combined into a single overall ranking by rating the best alternative in each of the BOCR on strategic criteria that an individual or a government uses to decide whether or not to implement one or the other of the numerous decisions that they face. The results of the four ratings determine the priorities each of which is used to weigh all the priorities of all the alternatives with respect to that merit. a . e a4¢,e -) ey eae, nm aa a a me oa eo, . an