The Saati method is a special way of system analysis. Also, this method is aimed at assisting in making decisions. The method of analyzing hierarchies by Thomas Saati is extremely popular in forensics, especially in the West, business, and government. It is also often called the MAI.
Application
Although it can be used by people working on simple solutions, the analytic hierarchy process is most useful when groups of people work on complex problems, especially at high rates, including human perception and judgment. In this case, the decisions have a long-term nature of the consequences. The Saati method has unique advantages when important elements of a decision are difficult to quantify or compare. Or when communication between team members is hindered by their various specializations, terminology or perspectives.
The Saati method is sometimes used to develop very specific procedures for specific situations, such as assessing buildings for historical significance. It has recently been applied to a project that uses video recording to assess the condition of highways in Virginia. Road engineers first used it to determine the optimal scale of the project, and then justify their budget to lawmakers.
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 business schools. This is an especially important subject in the field of quality and is taught in many specialized courses, including Six Sigma, Lean Six Sigma and QFD.
Value
The value of the Saati method is recognized in developed and developing countries around the world. For example, China - about a hundred Chinese universities offer AHP courses. And many doctoral students choose AHP as the subject of their research and dissertations. More than 900 articles on this subject have been published in China, and there is at least one Chinese scientific journal devoted exclusively to the method of analyzing Saati hierarchies.
International status
The International Symposium on the Process of Analytical Hierarchy (ISAHP) holds biennial meetings of scientists and practitioners interested in this field. Themes are different. In 2005, they ranged from “Setting Payment Standards for Surgical Specialists” to “Strategic Technology Planning”, “Reconstruction of Infrastructure in Devastated Countries”.
At a 2007 meeting in Valparaiso, Chile, more than 90 reports were submitted from 19 countries, including the USA, Germany, Japan, Chile, Malaysia and Nepal. A similar number of papers were presented at a 2009 symposium in Pittsburgh, PA, in which 28 countries participated. The topics covered included economic stabilization in Latvia, portfolio selection in the banking sector, forest fire management to mitigate the effects of global warming, and rural microprojects in Nepal.
Modeling
The first step in the process of hierarchy analysis is to model the problem in the form of a hierarchy. At the same time, participants study aspects of the problem at different levels from general to detailed, and then express it in a multi-level way, as required by the Saati decision-making method (hierarchy analysis). Working to build a hierarchy, they expand their understanding of the problem, its context, as well as 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 in question, but also on knowledge, judgment, values, opinions, needs, desires, etc. The construction of a hierarchy usually involves considerable discussion, research, and discovery by those involved. Even after the initial construction, it can be changed to meet new criteria or criteria that were not initially considered important; Alternatives can also be added, deleted or modified.
“Choose a leader”
It's time to move on to examples of the Saati method. Consider an example of the Select Leader application. An important task of decision makers is to determine the weight that must be given to each criterion when choosing a leader. Another important task of this application is to determine the weight that must be given to candidates based on each of the criteria. The method of analyzing hierarchies of T. Saati not only allows them to do this, but also makes it possible to attach meaningful and objective numerical value to each of the four criteria. This example reveals the essence of the technique well. In addition, the task of the Saati method also becomes clear when familiarizing yourself with the Select Leader application.
Promotion process
So far, we have considered only default priorities. As the analytic hierarchy process advances, 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 paired comparisons.
AHP is included in most textbooks on operations research and management and is taught at many universities; It is widely used in organizations that have carefully studied its theoretical foundations. Although the general opinion is that it is technically sound and practically useful, the method has its criticisms. In the early 1990s, a series of discussions between critics and proponents of the Saati method was published in the journal Management Science, 38, 39, 40, and Journal of Operations Research Society.
Two schools
There are two schools of thought about changing rank. One argues that new alternatives that do not introduce any additional attributes should not cause a change in rank under any circumstances. Another is convinced that in some situations it is reasonable to expect a change in rank. Saati’s initial decision-making formulation allowed a change in rank. In 1993, Foreman introduced the second AHP synthesis mode, called the ideal mode for solving situations of choice in which adding or removing an “irrelevant” alternative should not and will not change the ranks of existing alternatives. The current version of AHP can accommodate both of these schools: its ideal mode keeps the rank, and its distribution mode allows you to change the rank. Any mode is selected in accordance with the existing problem.
The change of rank and solution by the Saati method are discussed in detail in a 2001 article in Operations Research. And also can be found in the chapter entitled "Saving and changing the rank." And all this in the main book on the method of paired comparisons Saati. The latter presents published examples of changes in rank due to the addition of copies of an alternative, due to the intransigence of decision rules, due to the addition of phantom and bait alternatives, and due to the switching phenomenon in utility functions. It also discusses the distribution and ideal decision modes by the Saati method.
Comparison matrix
In the comparison matrix, you can replace the judgment with a less favorable opinion, and then check whether specifying a new priority becomes less favorable than the original priority. In the context of tournament matrices, Oscar Perron proved that the method of the main right eigenvector is not monotonic. This behavior can also be demonstrated for inverse matrices nxn, where n> 3. Alternative approaches are discussed elsewhere.
Who was Thomas Saati?
Thomas L. Saati (July 18, 1926 - August 14, 2017) was an emeritus professor at the University of Pittsburgh, where he taught at the Graduate School of Business. Joseph M. Katz. He was the inventor, architect and chief theorist of the Analytical Hierarchy Process (AHP), the decision-making structure used for large-scale, multi-part, multi-criteria analysis of decisions, as well as the Analytical Network Process (ANP), its generalization to decisions with dependence and feedback. He later generalized the mathematics of ANP for a neural network process (NNP) with application to neural triggering and synthesis, but none of them gained such popularity as the Saati method, examples of which were discussed above.
He died on August 14, 2017 after a year-long battle with cancer.
Prior to joining the University of Pittsburgh, Saati was a professor of statistics and operations research at the Wharton School of the University of Pennsylvania (1969–1979). Prior to that, he spent fifteen years working for US government agencies and state-funded research companies.
Issue
One of the main challenges organizations face today is their ability to choose the most appropriate and consistent alternatives in ways that support 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, which we have never seen before, the right choice based on adequate and agreed goals is a critical factor even for the survival of the organization.
In fact, prioritizing projects in a portfolio is nothing more than an ordering scheme based on the ratio of the benefits and costs of each project. Projects with higher benefits compared to their cost will be a priority. It is important to note that the ratio of benefits to costs does not necessarily mean the use of exceptional financial criteria, such as the well-known ratio of benefits to costs, but instead a broader concept of the benefits received from the project and its associated efforts.
Since organizations belong to a complex and variable “comrade”, often even chaotic, the problem of the above definition lies in determining the costs and benefits for any particular organization.
Project Standards
The Institute for Project Management's Portfolio Management (PMI, 2008) standard states that project portfolio size should be based on the organization’s strategic objectives. These goals should be consistent with the business scenario, which, in turn, may differ for each organization. Therefore, there is no ideal model that meets the criteria that will be used for any type of organization in determining priorities and choosing its projects. The criteria that should be used by the organization should be based on the values and preferences of decision makers.
Although, when determining project priorities and determining the real value of the optimal ratio between benefits and costs, a set of criteria or specific goals can be used. The main criterion of the group is financial. It is directly related to costs, productivity, and profit.
For example, return on investment (ROI) is the percentage of return on a project. This allows you to compare the financial returns of projects with different investments and profits.
Conversion
Saati's analysis method converts comparisons, which are most often empirical, into numerical values that are then processed and compared. The weight of each factor allows you to evaluate each of the elements within a particular hierarchy. This ability to transform empirical data into mathematical models is the main distinguishing contribution of the AHP method compared to other comparison methods.
After all comparisons are made and relative weights are determined between each of the criteria to be evaluated, the numerical probability of each alternative is calculated. This probability determines the likelihood that the alternative should fulfill the expected goal. The higher the probability, the more chances the alternative has to achieve the ultimate goal of the portfolio.
The mathematical calculation included in the AHP process may seem simple at first glance, but when dealing with more complex cases, analysis and calculations become deeper and more comprehensive.
Comparison of two elements using AHP can be performed in various ways (Triantaphyllou & Mann, 1995). However, the scale of relative importance between the two alternatives proposed by Saati (SAATY, 2005) is the most widely used. By attributing values that range from 1 to 9, the scale determines the relative importance of the alternative compared to another alternative.
Usually, odd numbers are always used to determine a reasonable difference between measurement points. The use of even numbers should only be accepted if negotiations between appraisers are necessary. When natural consensus cannot be reached, it becomes necessary to define the middle point as a coordinated solution (compromise) (Saaty, 1980).
To serve as an example of AHP calculations for prioritizing projects, a fictitious decision-making model for ACME was selected. 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 determine the criteria that will be used. As already mentioned, each organization develops and structures its own set of criteria, which, in turn, must correspond to the strategic goals of the organization.
For our fictitious ACME organization, we will assume that a study has been conducted along with the areas of financing, planning strategies, and project management criteria to be used. The following set of 12 criteria was adopted and grouped into 4 categories.
Once a hierarchy has been established, criteria should be evaluated in pairs to determine the relative importance between them and their relative weight for a global goal.
The assessment begins by determining the relative weight of the original criteria groups.
Contribution
The contribution of each criterion to the organizational goal is determined by calculations performed using the priority vector (or eigenvector). An 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 the vector is always equal to unity. 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).
The values found in the eigenvector have a direct physical meaning in the AHP - they determine the participation or weight of this criterion in relation to the overall result of the target. For example, in our ACME organization, strategic criteria have a weight of 46.04% (accurate calculation of the eigenvector) with respect to a common goal. A positive rating on this factor gives about 7 times more than a positive rating on the criterion of commitment to stakeholders (weight 6.84%).
The next step is to look for any data inconsistencies. The goal is to gather enough information to determine if decision makers are consistent in their choices (Teknomo, 2006). For example, if decision makers claim that strategic criteria are more important than financial criteria, and that financial criteria are more important than criteria of commitment to stakeholders, it would be inconsistent to argue that criteria of commitment to stakeholders are more important than strategic criteria (if A> B and B> C, it would be inconsistent if A <C).
As in the case of the initial group of criteria for organizing ACME, it is necessary to evaluate the relative weights of the criteria for the second level of the hierarchy. This process is performed in the same way as a step for evaluating the first level of a hierarchy (group of criteria).
After structuring the tree and setting priority criteria, you can determine how each of the candidate projects meets the selected criteria.
In the same way as in determining the priority of criteria, candidate projects are compared in pairs taking into account each established criterion.
AHP , - , (Triantaphyllou & Mann, 1995). (Vargas, 1990).
Its use for selecting projects for a portfolio 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 choice and also to model possible results.
Using the decision-making method / analysis of Saati hierarchies also involves the use of a software application specifically designed to perform mathematical calculations.
Another important aspect is the quality of evaluations made by decision makers. To make the decision 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 a portfolio decision is the result of negotiations during which methods such as the Saati hierarchy method support and guide the execution of work, but they cannot and should not be used as universal criteria.