In the theory of decision making, the analytic hierarchy process (AHP), also analytical hierarchy process, is a structured technique for organizing and analyzing complex decisions, based on mathematics and psychology. It was developed by Thomas L. Saaty in the 1970s; Saaty partnered with Ernest Forman to develop Expert Choice software in 1983, and AHP has been extensively studied and refined since then. It represents an accurate approach to quantifying the weights of decision criteria. Individual experts’ experiences are utilized to estimate the relative magnitudes of factors through pair-wise comparisons. Each of the respondents compares the relative importance of each pair of items using a specially designed questionnaire. The relative importance of the criteria can be determined with the help of the AHP by comparing the criteria and, if applicable, the sub-criteria in pairs by experts or decision-makers. On this basis, the best alternative can be found.
Uses and applications AHP is targeted at group decision making, and is used for decision situations, in fields such as government, business, industry, healthcare and education.
Rather than prescribing a "correct" decision, the AHP helps decision makers find the decision that best suits their goal and their understanding of the problem. It provides a comprehensive and rational framework for structuring a decision problem, for representing and quantifying its elements, for relating those elements to overall goals, and for evaluating alternative solutions.
Users of the AHP first decompose their decision problem into a hierarchy of more easily comprehended sub-problems, each of which can be analyzed independently. The elements of the hierarchy can relate to any aspect of the decision problem—tangible or intangible, carefully measured or roughly estimated, well or poorly understood—anything at all that applies to the decision at hand.
Once the hierarchy is built, the decision makers evaluate its various elements by comparing them to each other two at a time, with respect to their impact on an element above them in the hierarchy. In making the comparisons, the decision makers can use concrete data about the elements, and they can also use their judgments about the elements' relative meaning and importance. Human judgments, and not just the underlying information, can be used in performing the evaluations.
The AHP converts these evaluations to numerical values that can be processed and then compared over the entire range of the problem. A numerical weight or priority is derived for each element of the hierarchy, allowing diverse and often incommensurable elements to be compared to one another in a rational and consistent way. This capability distinguishes the AHP from other decision making techniques.
In the final step of the process, numerical priorities are calculated for each of the decision alternatives. These numbers represent the alternatives' relative ability to achieve the decision goal, so they allow a straightforward consideration of the various courses of action.
While it can be used by individuals working on straightforward decisions, the Analytic Hierarchy Process (AHP) is most useful where teams of people are working on complex problems, especially those with high stakes, involving human perceptions and judgments, whose resolutions have long-term repercussions.
Decision situations to which the AHP can be applied include: Choice – The selection of one alternative from a given set of alternatives, usually where there are multiple decision criteria involved. Ranking – Putting a set of alternatives in order from most to least desirable. Prioritization – Determining the relative merit of members of a set of alternatives, as opposed to selecting a single one or merely ranking them Resource allocation – Apportioning resources among a set of alternatives Benchmarking – Comparing the processes in one's own organization with those of other best-of-breed organizations Quality management – Dealing with the multidimensional aspects of quality and quality improvement Conflict resolution – Settling disputes between parties with apparently incompatible goals or positions
The applications of AHP include planning, resource allocation, priority setting, and selection among alternatives. Other areas have included forecasting, total quality management, business process reengineering, quality function deployment, and the balanced scorecard. Other uses of AHP are discussed in the literature:
Deciding how best to reduce the impact of global climate change (Fondazione Eni Enrico Mattei) Quantifying the overall quality of software systems (Microsoft Corporation) Selecting university faculty (Bloomsburg University of Pennsylvania) Deciding where to locate offshore manufacturing plants (University of Cambridge) Assessing risk in operating cross-country petroleum pipelines (American Society of Civil Engineers) Deciding how best to manage U.S. watersheds (U.S. Department of Agriculture) More Effectively Define and Evaluate SAP Implementation Approaches (SAP Experts) Integrated evaluation of a community's sustanaibility in terms of environment, economy, society, institution, and culture. Accelerated Bridge Construction Decision Making Tool to assist in determining the viability of accelerated bridge construction (ABC) over traditional construction methods and in selecting appropriate construction and contracting strategies on a case-by-case basis.Salem, O., Salman, B., & Ghorai, S. (2017). Accelerating construction of roadway bridges using alternative techniques and procurement methods. Transport, 33(2), 567-579. https://doi.org/10.3846/16484142.2017.1300942
AHP is sometimes used in designing highly specific procedures for particular situations, such as the rating of buildings by historical significance. It was recently applied to a project that uses video footage to assess the condition of highways in Virginia. Highway engineers first used it to determine the optimum scope of the project, and then to justify its budget to lawmakers.
The weights of the AHP judgement matrix may be corrected with the ones calculated through the Entropy Method. This variant of the AHP method is called AHP-EM.
Education and scholarly research Though using the analytic hierarchy process requires no specialized academic training, it is considered an important subject in many institutions of higher learning, including schools of engineering and graduate schools of business. It is a particularly important subject in the quality field, and is taught in many specialized courses including Six Sigma, Lean Six Sigma, and QFD.
The International Symposium on the Analytic Hierarchy Process (ISAHP) holds biennial meetings of academics and practitioners interested in the field. A wide range of topics is covered. Those in 2005 ranged from "Establishing Payment Standards for Surgical Specialists", to "Strategic Technology Roadmapping", to "Infrastructure Reconstruction in Devastated Countries". At the 2007 meeting in Valparaíso, Chile, 90 papers were presented from 19 countries, including the US, Germany, Japan, Chile, Malaysia, and Nepal. A similar number of papers were presented at the 2009 symposium in Pittsburgh, Pennsylvania, when 28 countries were represented. Subjects of the papers included Economic Stabilization in Latvia, Portfolio Selection in the Banking Sector, Wildfire Management to Help Mitigate Global Warming, and Rural Microprojects in Nepal.
Use As it can be seen in the material that follows, using the AHP involves the mathematical synthesis of numerous judgments about the decision problem at hand. It is not uncommon for these judgments to number in the dozens or even the hundreds. While the math can be done by hand or with a calculator, it is far more common to use one of several computerized methods for entering and synthesizing the judgments. The simplest of these involve standard spreadsheet software, while the most complex use custom software, often augmented by special devices for acquiring the judgments of decision makers gathered in a meeting room.
The procedure for using the AHP can be summarized as:
Model the problem as a hierarchy containing the decision goal, the alternatives for reaching it, and the criteria for evaluating the alternatives. Establish priorities among the elements of the hierarchy by making a series of judgments based on pairwise comparisons of the elements. For example, when comparing potential purchases of commercial real estate, the investors might say they prefer location over price and price over timing. Synthesize these judgments to yield a set of overall priorities for the hierarchy. This would combine the investors' judgments about location, price and timing for properties A, B, C, and D into overall priorities for each property. Check the consistency of the judgments. Come to a final decision based on the results of this process.
These steps are more fully described below.
Model the problem as a hierarchy The first step in the analytic hierarchy process is to model the problem as a hierarchy. In doing this, participants explore the aspects of the problem at levels from general to detailed, then express it in the multileveled way that the AHP requires. As they work to build the hierarchy, they increase their understanding of the problem, of its context, and of each other's thoughts and feelings about both. (This book is the primary source for the sections in which it is cited.)
Hierarchies defined A hierarchy is a stratified system of ranking and organizing people, things, ideas, etc., where each element of the system, except for the top one, is subordinate to one or more other elements. Though the concept of hierarchy is easily grasped intuitively, it can also be described mathematically. Diagrams of hierarchies are often shaped roughly like pyramids, but other than having a single element at the top, there is nothing necessarily pyramid-shaped about a hierarchy.
Human organizations are often structured as hierarchies, where the hierarchical system is used for assigning responsibilities, exercising leadership, and facilitating communication. Familiar hierarchies of "things" include a desktop computer's tower unit at the "top", with its subordinate monitor, keyboard, and mouse "below."
In the world of ideas, we use hierarchies to help us acquire detailed knowledge of complex reality: we structure the reality into its constituent parts, and these in turn into their own constituent parts, proceeding down the hierarchy as many levels as we care to. At each step, we focus on understanding a single component of the whole, temporarily disregarding the other components at this and all other levels. As we go through this process, we increase our global understanding of whatever complex reality we are studying.
Consider the hierarchy that medical students use while learning anatomy: they separately consider the musculoskeletal system (including parts and subparts like the hand and its constituent muscles and bones), the circulatory system (and its many levels and branches), the nervous system (and its numerous components and subsystems), etc., until they have covered all the systems and the important subdivisions of each. Advanced students continue the subdivision all the way to the level of the cell or molecule. In the end, the students understand the "big picture" and a considerable number of its details. They also understand the relation of the individual parts to the whole. By working hierarchically, they've gained a comprehensive understanding of anatomy.
Similarly, when we approach a complex decision problem, we can use a hierarchy to integrate large amounts of information into our understanding of the situation. As we build this information structure, we form a better and better picture of the problem as a whole.
Hierarchies in the AHP