Saaty's method is a special way of system analysis. Also, this method is aimed at helping in making decisions. The method of analysis of hierarchies by Thomas Saaty is extremely popular in forensic science, especially in the West, business, public administration. It is also often referred to as MAI.
Application
While it can be used by people working on simple solutions, the analytical hierarchy process is most useful when groups of people are working on complex problems, especially those with high stakes involving human perception and judgment. In this case, decisions have long-term consequences. The Saaty method has unique advantages when important elements of a solution are difficult to quantify or compare. Or when communication between team members is hampered by their different specializations, terminology, or perspectives.
The Saaty method is sometimes used in the development of very specific procedures for specific situations, such as valuation of buildings forhistorical significance. It has recently been applied to a project that uses videotape to assess highway conditions in Virginia. Road engineers first used it to determine the optimal scope for a project and then justify their budget to legislators.
Although the use of the Analytical Hierarchy Process does not require special academic training, it is considered an important subject in many higher education institutions, including engineering schools and graduate schools of business. This is a particularly important quality subject and is taught in many specialized courses including Six Sigma, Lean Six Sigma and QFD.
Value
The value of the Saaty method is recognized in developed and developing countries around the world. For example, China - about a hundred Chinese universities offer courses in AHP. And many doctoral students choose AHP as the subject of their research and dissertations. More than 900 articles have been published in China on this subject, and there is at least one Chinese scientific journal devoted exclusively to the Saaty hierarchical analysis method.
International status
The International Symposium on the Analytical Hierarchy Process (ISAHP) convenes biennially for scholars and practitioners with an interest in the field. Topics are different. In 2005, they ranged from "Setting Pay Standards for Surgical Specialists" to "Strategic Technology Planning", "Reconstruction of Infrastructure in Devastated Countries".
At the 2007 meeting inValparaiso, Chile, more than 90 papers were submitted from 19 countries, including the USA, Germany, Japan, Chile, Malaysia and Nepal. A similar number of papers were presented at the 2009 symposium in Pittsburgh, Pennsylvania, which was attended by 28 countries. Topics included economic stabilization in Latvia, portfolio selection in the banking sector, forest fire management to mitigate global warming, and rural micro-projects in Nepal.
Simulation
The first step in the hierarchy analysis process is to model the problem as a hierarchy. In doing so, participants explore aspects of the problem at different levels from general to detailed, and then express it in a multi-level way, as required by the decision-making (analysis of hierarchies) Saaty method. By working to build a hierarchy, they expand their understanding of the problem, its context, and each other's thoughts and feelings about both.
Structure
The structure of any AHP hierarchy will depend not only on the nature of the problem being addressed, but also on knowledge, judgments, values, opinions, needs, desires, etc. Building a hierarchy usually involves considerable discussion, research, and discovery from parties involved. Even after initial construction, it can be modified to meet new criteria or criteria that were not originally considered important; alternatives can also be added, removed or changed.
Choose a leader
It's time to move on to the Saaty method examples. Let's take a look at an example of the "Choose a leader" application. An important task for decision makers is to determine the weight to be given to each criterion when choosing a leader. Another important task of this application is to determine the weight to be given to candidates, taking into account each of the criteria. T. Saaty's method of analyzing hierarchies not only allows them to do this, but also makes it possible to assign a meaningful and objective numerical value to each of the four criteria. This example illustrates the essence of the technique well. In addition, the purpose of the Saaty method also becomes clear when reading the "Choose a Leader" application.
Promotion process
So far, we've only considered default priorities. As the analytic hierarchy process progresses, the priorities will change from their default values as decision makers enter information about the importance of the various nodes. They do this through a series of pairwise comparisons.
AHP is included in most textbooks in operations research and management and is taught in many universities; it is widely used in organizations that have carefully studied its theoretical foundations. While the general consensus is that it is technically sound and practical, the method has its own criticisms. In the early 1990s, a series of discussions between critics and proponents of Saaty's method problems was published inJournal of Management Science, 38, 39, 40, and the Journal of the Society for Operations Research.
Two Schools
There are two schools of thought about changing rank. One states that new alternatives that do not introduce any additional attributes should not cause a rank change under any circumstances. Another believes that in some situations it is reasonable to expect a change in rank. The original formulation of Saaty's decision making allowed for rank changes. In 1993, Foreman introduced a second mode of AHP synthesis called the ideal mode for solving choice situations in which the addition or removal of an "irrelevant" alternative should not and will not change the ranks of the existing alternatives. The current version of AHP can accommodate both of these schools: its ideal mode preserves rank, while its distributive mode allows rank to be changed. Either mode is selected according to the problem.
Rank reversal and the Saaty solution are discussed in detail in a 2001 article in Operations Research. And also can be found in the chapter called "Saving and changing the rank." And all this is in the main book on the method of paired comparisons of Saaty. The latter presents published examples of rank change due to the addition of copies of an alternative, due to intransitive decision rules, due to the addition of phantom and decoy alternatives, and due to switching phenomena in utility functions. It also discusses distributive and ideal modes of Saaty's solutions.
Comparison matrix
In the comparison matrix, you can replace the judgment lessfavorable opinion, and then check whether the indication of the new priority becomes less favorable than the original priority. In the context of tournament matrices, Oscar Perron proved that the principal right eigenvector method is not monotonic. This behavior can also be demonstrated for inverse nxn matrices, where n>3. Alternative approaches are discussed elsewhere.
Who was Thomas Saaty?
Thomas L. Saaty (July 18, 1926 - August 14, 2017) was Distinguished Professor at the University of Pittsburgh, where he taught at the Graduate School of Business. Joseph M. Katz. He was the inventor, architect, and principal theorist of the Analytical Hierarchy Process (AHP), a decision framework used for large-scale, multi-party, multi-objective decision analysis, and the Analytical Network Process (ANP), its generalization to dependency and feedback decisions. He later generalized the mathematics of ANP to Neural Network Process (NNP) with application to neural firing and synthesis, but none of them gained as much popularity as Saaty's method, examples of which were discussed above.
He died on August 14, 2017 after a year-long battle with cancer.
Before joining the University of Pittsburgh, Saaty was professor of statistics and operations research at the Wharton School at the University of Pennsylvania (1969–1979). Prior to that, he spent fifteen years working for US government agencies and publicly funded research companies.
Problems
One of the major challenges facing organizations today is their ability to select the most appropriate and consistent alternatives in a way that maintains strategic alignment. In any given situation, making the right decisions is probably one of the most difficult tasks for science and technology (Triantaphyllou, 2002).
When we consider the ever-changing dynamics of the current environment as we have never seen before, making the right choice based on adequate and consistent goals is critical even to the survival of an organization.
Essentially, prioritizing projects in a portfolio is nothing more than an ordering scheme based on the benefit-cost ratio of each project. Projects with higher benefits compared to their cost will be given priority. It is important to note that benefit-to-cost ratio does not necessarily mean the use of exclusive financial criteria, such as the well-known cost-benefit ratio, but instead a broader concept of project benefits and associated efforts.
Because organizations belong to a complex and volatile "fellow", often even chaotic, the problem with the above definition lies precisely in determining the costs and benefits for any particular organization.
Project standards
The Project Management Institute Standard for Portfolio Management (PMI, 2008) states that the size of the project portfolio should be based on strategicorganization goals. These goals must be aligned with the business scenario, which in turn may be different for each organization. Therefore, there is no ideal model that would fit the criteria that any type of organization would use to prioritize and select its projects. The criteria to be used by an organization should be based on the values and preferences of decision makers.
Although a set of criteria or specific targets can be used to prioritize projects and determine the true value of the optimal benefit/cost ratio. The main criterion of the group is financial. It is directly related to cost, performance and profit.
For example, return on investment (ROI) is the percentage of profit from a project. This allows you to compare the financial return of projects with different investments and profits.
Transformation
Saaty's analysis method converts comparisons, which are most often empirical, into numerical values, which are then processed and compared. The weight of each factor allows you to evaluate each of the elements within a certain hierarchy. This ability to convert empirical data into mathematical models is the main distinguishing contribution of the AHP method compared to other comparison methods.
After making all comparisons and determining the relative weights between each of the criteria to be evaluated, the numerical probability of each alternative is calculated. This probability determines the probabilitythat the alternative should fulfill the expected purpose. The higher the probability, the more likely the alternative is to reach the end goal of the portfolio.
Mathematical calculation included in the AHP process may seem simple at first glance, but when working with more complex cases, the analysis and calculations become deeper and more comprehensive.
Comparing two items using AHP can be done in a variety of ways (Triantaphyllou & Mann, 1995). However, the scale of relative importance between two alternatives proposed by Saaty (SAATY, 2005) is the most widely used. By assigning values that range from 1 to 9, the scale determines the relative importance of an alternative compared to another alternative.
Odd numbers are always used to determine a reasonable difference between measurement points. The use of even numbers should only be accepted if negotiation is required between raters. When a natural consensus cannot be reached, it becomes necessary to define the midpoint as an agreed solution (compromise) (Saaty, 1980).
To serve as an example of AHP's calculations for prioritizing projects, a fictitious decision-making model for the ACME organization was chosen. As the example develops further, concepts, terms, and approaches to AHP will be discussed and analyzed.
The first step in building an AHP model is to define the criteria to be used. As already mentioned, each organization develops and structures its ownown set of criteria, which, in turn, should be consistent with the strategic goals of the organization.
For our fictitious ACME organization, we will assume that research has been done along with the areas of funding, planning strategy and project management criteria to be used. The following set of 12 criteria was adopted and grouped into 4 categories.
Once the hierarchy is established, the criteria should be evaluated in pairs to determine the relative importance between them and their relative weight for the global goal.
Evaluation begins with determining the relative weight of the initial criterion groups.
Contribution
The contribution of each criterion to the organizational goal is determined by calculations performed using the priority vector (or eigenvector). The eigenvector shows the relative weight between each criterion; it is obtained in an approximate way by calculating the mathematical average for all criteria. We can observe that the sum of all values from a vector is always equal to one. The exact calculation of the eigenvector is determined only in specific cases. This approximation is used in most cases to simplify the calculation process, since the difference between the exact value and the approximate value is less than 10% (Kostlan, 1991).
You may notice that the approximate and exact values are very close to each other, so calculating the exact vector requires mathematical effort (Kostlan, 1991).
Values found in the eigenvector have directphysical value in AHP - they determine the contribution or weight of this criterion in relation to the overall result of the goal. For example, in our ACME organization, strategic criteria have a weight of 46.04% (accurate eigenvector calculation) relative to the overall goal. A positive score on this factor is about 7 times more than a positive score on stakeholder commitment (weight 6.84%).
The next step is to look for any inconsistencies in the data. The goal is to collect enough information to determine whether the decision makers were consistent in their choices (Teknomo, 2006). For example, if decision makers argue that strategic criteria are more important than financial criteria and that financial criteria are more important than stakeholder commitment criteria, it would be inconsistent to argue that stakeholder commitment criteria are more important than strategic criteria. (if A>B and B>C, it would be inconsistent if A<C).
As with the initial set of criteria for the ACME organization, it is necessary to estimate the relative weights of the criteria for the second level of the hierarchy. This process is exactly the same as the step for evaluating the first level of the hierarchy (criteria group).
After structuring the tree and establishing priority criteria, it is possible to determine how each of the candidate projects meets the selected criteria.
In the same way as when prioritizing criteria, candidate projects are compared in pairs withtaking into account each established criterion.
AHP has attracted the interest of many researchers, mainly due to the mathematical nature of the method and the fact that data entry is quite simple (Triantaphyllou & Mann, 1995). Its simplicity is characterized by pairwise comparison of alternatives according to specific criteria (Vargas, 1990).
Its use to select portfolio projects allows decision makers to have a specific and mathematical decision support tool. This tool not only supports and qualifies decisions, but also allows decision makers to justify their choices as well as model possible outcomes.
Using the Saaty decision/hierarchy analysis method also involves using a software application specifically designed to perform mathematical calculations.
Another important aspect is the quality of the assessments made by decision makers. For a decision to be as adequate as possible, it must be consistent and consistent with organizational results.
Finally, it is important to emphasize that decision making involves a broader and more complex understanding of the context than the use of any particular method. He suggests that portfolio decisions are the product of negotiations in which methods such as Saaty's hierarchy method support and guide performance, but they cannot and should not be used as universal criteria.
