Analytic Hierarchy Process

Analytic Hierarchy Process
Lou Sander · Public domain · source
Name	Analytic Hierarchy Process
Inventor	Thomas L. Saaty
Introduced	1970s
Applications	Multi-criteria decision making, resource allocation, project selection

Analytic Hierarchy Process The Analytic Hierarchy Process is a structured technique for complex decision making that decomposes problems into a hierarchy and derives priorities through pairwise comparisons. It combines quantitative computation with qualitative judgment to rank alternatives and allocate resources, and it is applied across domains from business to public policy. The method’s formalism supports group decision making, sensitivity analysis, and the incorporation of expert judgment in engineering projects and strategic planning.

Introduction

The framework was formalized to assist decision makers such as Thomas L. Saaty and practitioners at institutions like the United States Department of Defense and World Bank in comparing alternatives under multiple criteria. It has been taught in programs at universities including Harvard University, Massachusetts Institute of Technology, Stanford University, and University of Cambridge and used by corporations such as General Electric, Siemens, Shell, and Procter & Gamble. Variants and extensions have been developed in collaboration with organizations like the International Organization for Standardization and research centers at Carnegie Mellon University, University of California, Berkeley, and London School of Economics.

History and Development

The method originated from the work of Thomas L. Saaty in the 1970s and matured through applications at institutions such as the United Nations and RAND Corporation. Early adopters included agencies like the National Aeronautics and Space Administration and firms engaged with projects at Bell Labs, Royal Dutch Shell, and Boeing, which stimulated methodological refinements. Subsequent theoretical and applied developments involved collaborations with scholars at Columbia University, Yale University, Princeton University, and University of Oxford, influencing standards and textbooks circulated by publishers such as Cambridge University Press and Springer Science+Business Media.

Methodology and Steps

The process structures a decision into a hierarchy of goal, criteria, subcriteria, and alternatives, a format used by analysts at McKinsey & Company, Boston Consulting Group, Deloitte, and PricewaterhouseCoopers. Practitioners perform pairwise comparisons using scales introduced by Thomas L. Saaty and synthesize priorities through eigenvector methods familiar to researchers at Institute for Operations Research and the Management Sciences and IEEE. Typical steps mirror workflows in project management at Project Management Institute settings and include problem structuring similar to methods in studies from Oxford Brookes University and INSEAD: define goal, model hierarchy, elicit judgments, compute weights, check consistency, aggregate results, and perform sensitivity analysis.

Mathematical Foundations and Consistency

The underpinning relies on positive reciprocal matrices and principal eigenvector computation, areas studied by mathematicians at Princeton University and Massachusetts Institute of Technology. Consistency indices and ratios derived by Saaty are evaluated alongside alternative metrics developed in scholarship at University of California, Berkeley, University of Washington, and ETH Zurich. Linear algebraic properties connect to the Perron–Frobenius theorem investigated by researchers at Institute for Advanced Study and consistency testing parallels approaches in statistical inference found at London School of Hygiene & Tropical Medicine and Johns Hopkins University.

Applications and Case Studies

AHP has been applied to portfolio selection at Goldman Sachs and Morgan Stanley, supplier selection in firms such as Toyota and Ford Motor Company, site selection for infrastructures managed by Bechtel and Fluor Corporation, and health-care prioritization in programs by World Health Organization and Centers for Disease Control and Prevention. Academic case studies involve collaborations with researchers at Imperial College London, University of Melbourne, National University of Singapore, and Tsinghua University addressing energy planning for projects involving BP, TotalEnergies, ExxonMobil, and municipal transportation planning in cities like New York City, London, Singapore, and Tokyo.

Criticisms and Limitations

Critiques from scholars at University of Chicago, University of Pennsylvania, University of Michigan, and University of California, Los Angeles emphasize sensitivity to scale, rank reversal concerns noted by researchers at Cornell University and University of Texas at Austin, and challenges in aggregating group judgments debated in forums hosted by American Statistical Association and Royal Statistical Society. Alternative multi-criteria methods such as those developed at University of Pittsburgh and University of Twente (including outranking methods and multi-attribute utility theory used by analysts at RAND Corporation) are often compared to highlight scenarios where AHP’s assumptions limit robustness.

Software Tools and Implementation

Numerous software packages implement the method, including commercial tools from vendors used alongside systems at SAP SE, Oracle Corporation, and Microsoft Corporation, as well as specialized programs developed at Georgia Institute of Technology, University of Toronto, and Delft University of Technology. Open-source implementations originate from projects associated with R Project for Statistical Computing, Python Software Foundation, and repositories maintained by contributors at GitHub and research groups at National Institute of Standards and Technology, facilitating integration with decision support systems in enterprises like Accenture, IBM, and Capgemini.

Category:Decision analysis