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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 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. 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 .... 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