A sensitivity analysis algorithm for hierarchical decision models

Hongyi Chen, Dundar F. Kocaoglu

Research output: Contribution to journalArticlepeer-review

82 Scopus citations


In this paper, a comprehensive algorithm is developed to analyze the sensitivity of hierarchical decision models (HDM), including the analytic hierarchy process and its variants, to single and multiple changes in the local contribution matrices at any level of the decision hierarchy. The algorithm is applicable to all HDM that use an additive function to derive the overall contribution vector. It is independent of pairwise comparison scales, judgment quantification techniques and group opinion combining methods. The allowable range/region of perturbations, contribution tolerance, operating point sensitivity coefficient, total sensitivity coefficient and the most critical decision element at a certain level are identified in the HDM SA algorithm. An example is given to demonstrate the application of the algorithm and show that HDM SA can reveal information more significant and useful than simply knowing the rank order of the decision alternatives.

Original languageEnglish (US)
Pages (from-to)266-288
Number of pages23
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - Feb 16 2008

Bibliographical note

Funding Information:
We gratefully acknowledge the financial support from Maseeh Fellowship awarded by Fariborz Maseeh College of Engineering and Computer Science at Portland State University. The valuable suggestions by Barry Anderson, Tim Anderson, Tugrul Daim, Hua Tang, Wayne Wakeland, EJOR anonymous reviewers, and the editorial team are highly appreciated.


  • Decision analysis
  • Multiple criteria analysis
  • Robustness and sensitivity analysis


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