1977
A scaling method for priorities in hierarchical structures
Saaty, T.L. · Journal of Mathematical Psychology 15(3)
The founding paper: the eigenvector method, the 1–9 scale, and consistency measurement all appear here first.
AHP Resources
The AHP Library
Notable papers, books and videos related to the Analytic Hierarchy Process
We gather together a collection of influential papers, books and videos related to the Analytic Hierarchy Process. These capture the foundation of the method, and how it was refined and extended over time. The best “how to” content is also included, along with background reading on related topics such as linear algebra.
Classic AHP papers
Grouped by the major developments in each era: foundations, critiques and refinements, group aggregation, and modern surveys.
Foundations1977–1987
1986
Axiomatic foundation of the analytic hierarchy process
Saaty, T.L. · Management Science 32(7)
The formal footing: the axioms under which the AHP's ratio-scale priorities are justified.
1987
The analytic hierarchy process — what it is and how it is used
Saaty, T.L. · Mathematical Modelling 9(3–5)
The accessible overview in Saaty's own words, and still an excellent introduction for novices.
Critiques and refinements1983–1990
1983
On a short-coming of Saaty's method of analytic hierarchies
Belton, V. & Gear, T. · Omega 11(3)
The original rank-reversal critique: adding a copy of an alternative can change the ranking of the others. It started the longest-running argument in the field.
1990
Remarks on the analytic hierarchy process — and Saaty's reply
Dyer, J.S. · Management Science 36(3) · with Saaty's response in the same issue
The sharpest critique exchange in the literature: Dyer argues the method's rankings are arbitrary without utility-theoretic footing; Saaty answers in the same issue. Read both sides together.
DOIINFORMSGoogle ScholarResearchGate
Companion: Saaty, T.L., “An exposition of the AHP in reply to the paper ‘Remarks on the Analytic Hierarchy Process’”, Management Science 36(3).
Decisions and groups1983–1998
1983
Procedures for synthesizing ratio judgements
Aczél, J. & Saaty, T.L. · Journal of Mathematical Psychology 27(1)
The proof that the geometric mean is the only aggregation of group judgments consistent with unanimity and reciprocity. This explains why AIJ is the most common method for combining judgments.
1990
How to make a decision: the analytic hierarchy process
Saaty, T.L. · European Journal of Operational Research 48(1)
The most-cited tutorial introduction, with the worked examples most courses still teach from. The practical companion to the 1987 overview.
1998
Aggregating individual judgments and priorities with the AHP
Forman, E. & Peniwati, K. · European Journal of Operational Research 108(1)
Settles when a group should aggregate judgments (acting as one decision maker) versus priorities (acting as separate individuals).
Complementary methods1987–2008
1987
Incomplete pairwise comparisons in the analytic hierarchy process
Harker, P.T. · Mathematical Modelling 9(11)
How to derive priorities when not every pair has been compared, cutting respondent burden without abandoning the eigenvector method. The standard reference for incomplete matrices, and the method behind how missing comparisons are handled on our mathematics page.
1997
A Sensitivity Analysis Approach for Some Deterministic Multi-Criteria Decision-Making Methods
Triantaphyllou, E. & Sánchez, A. · Decision Sciences 28(1)
The systematic treatment of what “sensitive” should mean in a weighted decision: whether to count any rank swap or only a change at the top, and whether to measure weight changes in absolute points or relative to the weight itself. Their Percent-Top measure is the stability rating decisionpoint.io's Sensitivity page uses.
2006
Consistency in the analytic hierarchy process: a new approach
Alonso, J.A. & Lamata, M.T. · International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 14(4)
Re-estimates the random index from large-scale simulation and fits a simple closed-form rule to it, giving consistency thresholds that work at any matrix size. Their estimates appear in the consistency discussion on our mathematics page.
2008
A sensitivity analysis algorithm for hierarchical decision models
Chen, H. & Kocaoglu, D.F. · European Journal of Operational Research 185(1)
Extends sensitivity analysis from a single level to the whole hierarchy at once, including simultaneous changes to several weights.
Surveys and modern reviews2011–2018
2011
Review of the main developments in the analytic hierarchy process
Ishizaka, A. & Labib, A. · Expert Systems with Applications 38(11)
The standard methodological survey: judgment scales, priority-derivation methods, consistency indices and group aggregation, compared side by side.
2017
The state of the art development of AHP (1979–2017)
Emrouznejad, A. & Marra, M. · International Journal of Production Research 55(22)
A citation-network history of four decades of AHP research, identifying the seminal papers and how the field's themes evolved. The bibliometric companion to the methodological surveys.
2018
The state-of-the-art integrations and applications of the AHP
Ho, W. & Ma, X. · European Journal of Operational Research 267(2) · Invited Review
The standard post-2011 general review, covering how the AHP is combined with other methods and where it is applied. Start here for the current state of the field.
2018
Implementation of an online software tool for the AHP (AHP-OS)
Goepel, K.D. · International Journal of the Analytic Hierarchy Process 10(3)
The reference description of AHP-OS, a free online AHP tool widely used in academic studies. Useful both as documentation and as a record of the design choices a web implementation must make.
Books
From the non-technical introduction to the mathematics behind the method.
Decision Making for Leaders
Thomas L. Saaty · RWS Publications, New Edition 2001
Fundamentals of Decision Making and Priority Theory
Thomas L. Saaty · RWS Publications, 1994 (reprinted 2000, 2006)
Introduction to the Analytic Hierarchy Process
Matteo Brunelli · Springer, 2015
Models, Methods, Concepts & Applications of the AHP
Thomas L. Saaty & Luis G. Vargas · Springer, 2nd ed. 2012
Strategic Decision Making
Navneet Bhushan & Kanwal Rai · Springer, 2004
Linear Algebra with Applications (Alternate Edition)
Gareth Williams · Jones & Bartlett, 2012
An introductory text for the mathematics behind the AHP: vectors, matrices, eigenvalues and eigenvectors. Needed for studying AHP theory, not for applying the method. The alternate edition covers the AHP-relevant material earlier.
AHP Videos
Thomas L. Saaty explaining his own method in official Creative Decisions Foundation uploads, plus one applied walk-through by the author of AHP-OS.
Creative Decisions Foundation
The Origins of AHP
Why Saaty developed the method after his State Department work: “we needed a new way to measure things.”
Creative Decisions Foundation
How did the 1–9 scale come about?
The origin and rationale of the fundamental scale.
Creative Decisions Foundation
AHP Example: Selecting a School
The 1970s hierarchy Saaty and his son used to pick a high school — one of the first AHP applications.
Creative Decisions Foundation
AHP Example: Comparing Apples
A validation exercise: size ratios of apples in a pairwise comparison matrix.
Creative Decisions Foundation
AHP Example: Estimating Drink Consumption
The classic validation example: relative US beverage consumption from pairwise judgments alone.
Creative Decisions Foundation
Ratings Example: Salary Raises
Absolute measurement: rating employees one at a time against standards instead of each other.
Creative Decisions Foundation
AHP in Prediction and Forecasting
AHP used to predict elections, economic turnarounds and sports outcomes.