## What Is the AHP and Why Is It Useful?

The Analytic Hierarchy Process (the AHP) is a theory of measurement, developed by Thomas L. Saaty in 1970s, that is used to provide structured techniques necessary for making complex decisions. The approach is based on ratio scales from discrete and continuous paired comparisons that can be taken both from fundamental scale, reflecting feelings or preferences, and practical measurements (Saaty 161).

Since the theory manages to unite mathematical and psychological methods, it is now widely applied in multicriteria decision making, conflict resolution, resource allocation, and many other spheres, including business, government, industry, healthcare, education, etc. The major reasons the approach is considered useful can be summed up as follows (Aragonés-Beltrán et al. 225-228):

- It is comprehensive. The major advantage of the suggested technique is that it allows uniting deductive and inductive thinking, analyzing a number of factors simultaneously.
- It is well-proven. Thousands of companies across the world successfully implement the AHP in their decision-making practice.
- It has a broad range of applications. The AHP can provide a solution to wide variety of problems including vendor, technology, site, and employee selection, project prioritization, etc.
- It is easy to use. People are much more eager to take recommendations from a machine if it is clear for them how the system works. The AHP makes it possible to break complex processes into smaller units, consider alternatives, and prioritize criteria. This makes it much more useful than complex mathematical black boxes.
- It does not require initial prioritizing. Multiple conflicting criteria can be used as input data. The AHP will help organize them hierarchically.
- It simplifies the process of decision making by relying on pairwise comparisons. Deadlocks are eliminated by making respondents choose only between two options each time. The results of these comparisons are reviewed afterwards.
- It validates consistency. There is an algorithm that eliminates inconsistent and redundant data.

Thus, as compared to other mathematical methods, the AHP features a number of considerable advantages since it allows simplifying the process of decision making to ensure full understanding on behalf of respondents, while covering all important criteria and eliminating redundancies.

## How Does It Work?

Basically, the AHP analyzes a determined number of evaluation parameters together with alternatives suggested and figures out the most suitable decision to be made if all of them are taken into account. However, it would be wrong to state that the best option in this case is the one that would ensure optimization of each selected criterion. Since some of them can be contrasting, the major task of the AHP is to arrive at the decision that would reach the most beneficial compromise.

The decision maker is required to perform pairwise comparisons of different criteria evaluating them according to his/her preferences. The system generates weight for each of them: The higher it is, the more significant the criterion is. For a fixed criterion, a score is assigned to every alternative based on the results of the comparisons performed (Aragonés-Beltrán et al. 231). Thus, the bigger the identified score is, the better the performance of the alternative is expected to be. At the final step of the analysis, the AHP combines both results (criteria weights and options scores) and comes out with a respective ranking, which takes into account global scores for each option.

## Application Examples

The AHP is applied in thousands of industries due to the above-mentioned advantages. The approach allows achieving impressive results in solving problems related to resource allocation, planning, priority setting, forecasting, business process re-engineering, total quality management, quality function deployment, etc. These are the examples (Durbach 555):

- Resource allocation is one of the major issues for all industries. Since any organization has limited resources and unlimited needs, the AHP can help decide on the most preferable options.
- Since environmental problems are gaining popularity, the AHP is highly useful in deciding what strategies can be implemented to reduce the negative impact of climatic changes.
- Another aspect of high concern is atomic energy. It is highly complicated to evaluate nuclear reactors decommissioning. The problem is that there are no clearly defined evaluation procedures as well as those concerning identification of appropriate quantification methodologies. Since there are more than 20 indicators that have to be taken into consideration, the AHP is the most optimal solution for evaluating decommissioning.

## Criticisms of AHP

Despite evident advantages of the AHP, there are still some points that are subject to criticism (Aragonés-Beltrán et al. 232):

- It is possible that ranking irregularities can happen in case AHP is implemented and a copy of an option is added to the current alternatives.
- The approach can be regarded as a complete aggregation technique of the additive kind, which means that the compensation between positive and negative scores can happen. This leads to information losses.
- A great number of pairwise comparisons have to be completed when the problem is divided into a big number of subsystems.
- The artificial limitation created by the 9-point scale makes it difficult to distinguish between the options.

## Extensions of AHP: Example

Due to the popularity of the AHP, there appeared a lot of elaborations of the theory. One of them is DS-AHP framework that combines the AHP with Dempster-Shafer (DS) theory. In most general terms, it allows comparing not only single options but also groups of alternatives. The theory makes it possible to create a decision matrix and allows making judgments on groups of decision options. Furthermore, there is also a possibility of measuring uncertainty of the results (Durbach 556). Thus, this elaboration enables understanding of the appropriateness and accuracy of the rating scale.

## Works Cited

Aragonés-Beltrán, Pablo, et al. “An AHP (Analytic Hierarchy Process)/ANP (Analytic Network Process)-Based Multi-Criteria Decision Approach for the Selection of Solar-Thermal Power Plant Investment Projects.” *Energy*, vol. 66, no. 1, 2014, pp. 222-238.

Durbach, Ian, et al. “The Analytic Hierarchy Process with Stochastic Judgments.” *European Journal of Operational Research*, vol. 238, no. 2, 2014, pp. 552-559.

Saaty, Roseanna W. “The Analytic Hierarchy Process—What It Is and How It Is Used.” *Mathematical Modelling, *vol. 9, no. 3-5, 1987, pp. 161-176.