Improving consistency in AHP decision-making processes

Abstract Decision making in engineering is becoming increasingly complex due to the large number of alternatives and multiple conflicting goals. Powerful decision-support expert systems powered by suitable software are increasingly necessary. In this paper, the multiple attribute decision method known as analytical hierarchy process (AHP), which uses pairwise comparisons with numerical judgments, is considered. Since judgments may lack a minimum level of consistency, mechanisms to improve consistency are necessary. A method to achieve consistency through optimisation is described in this paper. This method has the major advantage of depending on just n decision variables – the number of compared elements – and so is less computationally expensive than other optimisation methods, and can be easily implemented in virtually any existing computer environment. The proposed approach is exemplified by considering a simplified version of one of the most important problems faced by water supply managers, namely, the minimisation of water loss.

[1]  María Teresa Lamata,et al.  Consistency in the Analytic Hierarchy Process: a New Approach , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[2]  R. Ewing,et al.  Comparing Land Use Forecasting Methods: Expert Panel Versus Spatial Interaction Model , 2009 .

[3]  J. Barzilai.  Deriving weights from pairwise comparison matrices , 1997 .

[4]  M. Brugarolas,et al.  A contingent valuation analysis to determine profitability of establishing local organic wine markets in Spain , 2009, Renewable Agriculture and Food Systems.

[5]  Kevin Kam Fung Yuen,et al.  Analytic hierarchy prioritization process in the AHP application development: A prioritization operator selection approach , 2010, Appl. Soft Comput..

[6]  Bruce L. Golden,et al.  Linear programming models for estimating weights in the analytic hierarchy process , 2005, Comput. Oper. Res..

[7]  Bojan Srdjevic,et al.  Linking analytic hierarchy process and social choice methods to support group decision-making in water management , 2007, Decis. Support Syst..

[8]  G. Crawford,et al.  A note on the analysis of subjective judgment matrices , 1985 .

[9]  H. Monsuur.  An intrinsic consistency threshold for reciprocal matrices , 1997 .

[10]  T. Saaty.  Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the analytic hierarchy/network process , 2008 .

[11]  Ludmil Mikhailov,et al.  A fuzzy programming method for deriving priorities in the analytic hierarchy process , 2000, J. Oper. Res. Soc..

[12]  Joaquín Izquierdo,et al.  An analytic hierarchy process for assessing externalities in water leakage management , 2010, Math. Comput. Model..

[13]  Jerónimo Aznar Bellver,et al.  Nuevos Métodos de Valoración. Modelos Multicriterio , 2012 .

[14]  Eng Ung Choo,et al.  A common framework for deriving preference values from pairwise comparison matrices , 2004, Comput. Oper. Res..

[15]  Joaquín Izquierdo,et al.  Balancing consistency and expert judgment in AHP , 2011, Math. Comput. Model..

[16]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[17]  Malcolm Farley,et al.  Developing a strategy for leakage management in water distribution systems , 2004 .

[18]  Yin-Feng Xu,et al.  A comparative study of the numerical scales and the prioritization methods in AHP , 2008, Eur. J. Oper. Res..

[19]  Heidi Kreibich,et al.  A Delphi Method Expert Survey to Derive Standards for Flood Damage Data Collection , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[20]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

[21]  J.S. Finan,et al.  The analytic hierarchy process: Does adjusting a pairwise comparison matrix to improve the consistency ratio help? , 1997, Comput. Oper. Res..

[22]  D. Galván,et al.  Aplicación del método de jerarquías analíticas (AHP) a la gestión de pérdidas de agua en redes de abastecimiento , 2011 .

[23]  Joaquín Izquierdo,et al.  Achieving matrix consistency in AHP through linearization , 2011 .

[24]  José María Moreno-Jiménez,et al.  The geometric consistency index: Approximated thresholds , 2003, Eur. J. Oper. Res..

[25]  Bruce L. Golden,et al.  Visualizing group decisions in the analytic hierarchy process , 2003, Comput. Oper. Res..

[26]  Zoran Kapelan,et al.  A review of methods for leakage management in pipe networks , 2010 .

[27]  Thomas L. Saaty,et al.  Decision-making with the AHP: Why is the principal eigenvector necessary , 2003, Eur. J. Oper. Res..

[28]  E. F. Lane,et al.  A CONSISTENCY TEST FOR AHP DECISION MAKERS , 1989 .

[29]  R. Kalaba,et al.  A comparison of two methods for determining the weights of belonging to fuzzy sets , 1979 .

[30]  T. L. Saaty.  A Scaling Method for Priorities in Hierarchical Structures , 1977 .

[31]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

[32]  Chang-Chun Lin,et al.  An enhanced goal programming method for generating priority vectors , 2006, J. Oper. Res. Soc..

[33]  William Ho,et al.  Integrated analytic hierarchy process and its applications - A literature review , 2008, Eur. J. Oper. Res..

[34]  Stefano Alvisi,et al.  Multiobjective Optimization of Rehabilitation and Leakage Detection Scheduling in Water Distribution Systems , 2009 .

[35]  Richard Burrows,et al.  An Integrated Model to Evaluate Losses in Water Distribution Systems , 2009 .

[36]  R. Jiang,et al.  Scale transitivity in the AHP , 2003, J. Oper. Res. Soc..

[37]  Kalyanmoy Deb,et al.  Calibration and Optimal Leakage Management for a Real Water Distribution Network , 2011 .