A teaching and research model for ranking alternatives against many criteria - ten evaluation methods, six weighting schemes and five robustness analyses, one verified engine, developed 1995-2026.
What MCEWR does
MCEWR ranks a finite set of alternatives - projects, sites, technologies, management options - against several criteria with weights, organised as a flat list or as a hierarchy. It was developed for the Ph.D. dissertation of Mohamed Rami Mahmoud (Colorado State University, 1995) and applied in four published studies. In 2026 the author rebuilt it in Python and extended it: the five original methods are reproduced exactly - 5,980 paired runs, identical to the 1995 program to the last digit - and five further evaluation methods, five weighting schemes (equal, Best-Worst, entropy, CRITIC, MEREC) and the comparison, sensitivity and rank-reversal analyses were added beside them.
Evaluate
A guided workflow of eleven steps: open one of the example files, your own file or a new problem; enter alternatives, criteria and values; choose the weights (given, equal, Best-Worst, entropy, CRITIC, MEREC) and the method; run it; compare all methods, test the sensitivity to the weights, the values and the settings, the Monte Carlo robustness and the rank reversal; download the reports. The evaluation runs on the MCEWR server: the problem is computed and discarded, nothing is stored.
Open the evaluatorWorked examples
One example per method with the exact settings and the expected results - the verification examples of the dissertation and the published articles.
See the examplesLearn the methods
Each of the ten methods, the weighting schemes (including the Best-Worst Method) and the analyses explained with a solved example computed by hand, plus the equations, the tutorial and the user guide of the website.
The methods DocumentsThe ten methods
Five methods of the 1995 program, audited against the dissertation and the original output files:
- Weighted Average Method (WAM) - additive value (Einhorn & McCoach (1977); Nijkamp, Rietveld & Voogd (1990))
- PROMETHEE II - outranking (PROMETHEE family) (Brans, Vincke & Mareschal (1986), European Journal of Operational Research 24(2), 228-238)
- Compromise Programming (CP) - distance to the ideal (Zeleny (1973); Duckstein & Opricovic (1980), Water Resources Research 16(1), 14-20)
- ELECTRE II - outranking (ELECTRE family) (Roy & Bertier (1973); Goicoechea, Hansen & Duckstein (1982), Multiobjective Decision Analysis with Engineering and Business Applications, Wiley)
- Analytic Hierarchy Process (AHP) - pairwise hierarchy (Saaty (1980), The Analytic Hierarchy Process, McGraw-Hill; Harker (1988))
Five methods added in version 2.0, provisional - their formulation follows the primary literature and is verified against closed forms, independent implementations and hand-computed examples, while a published worked example is still to be reproduced:
- Expected Value (EV) - ordinal / expected values (Rietveld (1980); Nijkamp, Rietveld & Voogd (1990); expected weights: Barron & Barrett (1996), Management Science 42(11))
- Regime Analysis (RA) - ordinal / outranking (regime method) (Hinloopen, Nijkamp & Rietveld (1983), Regional Science and Urban Economics 13; Nijkamp, Rietveld & Voogd (1990))
- TOPSIS - distance to the ideal and the anti-ideal (Hwang & Yoon (1981), Multiple Attribute Decision Making, Springer)
- VIKOR - compromise ranking (group utility and individual regret) (Opricovic (1998); Opricovic & Tzeng (2004), European Journal of Operational Research 156(2), 445-455)
- ELECTRE III - outranking on pseudo-criteria (credibility and distillations) (Roy (1978), Cahiers du CERO 20(1); Roy & Bouyssou (1993); Figueira, Mousseau & Roy (2005))
Plus the SPOTIS identity (Compromise Programming with the provided limits and s = 1 - rank-reversal free), five weighting schemes besides the given weights (equal, the Best-Worst Method of Rezaei solved by linear programming, and the objective schemes entropy, CRITIC, MEREC), and the analyses of versions 2.0 and 2.1: comparison of methods, sensitivity of the ranking to the weights, to the decision values and to the settings of the method, Monte Carlo robustness under uncertain data and weights, and rank-reversal diagnostics.
The author
Prof. Mohamed Rami Mahmoud, Ph.D., P.E.
Research Professor Emeritus, National Water Research Center, Cairo, Egypt
Email: rami@m-rami.org · Web: www.m-rami.org and rami.mrami.org
ORCID: 0000-0002-3393-987X · LinkedIn
Publications - the model and its published applications
- Mahmoud, M.R., December 1995, "Multi-criteria Location and Sizing of Water Resources Projects by GIS and Dynamic Programming", Ph.D. dissertation, Water Resources Planning and Management, Civil Engineering, Colorado State University, Fort Collins, Colorado, USA (the model; Appendix 2 verification examples).
- Mahmoud, M.R., and Garcia, L.A., 1995, "MultiCriteria Decision Support System Implementation and Application", presented at the First International Conference on Multiple Objective Decision Support Systems for Land, Water, and Environmental Management: Concepts, Approaches, and Applications, Honolulu, Hawaii, July 23-29, 1995.
- Mahmoud, M.R., April 1999, "Integrated Mathematical Models for Evaluating Desalination Technology", Water Science Journal, National Water Research Center, Cairo, Egypt, Issue 25, pp. 21-32 (Regime Analysis and Expected Value applied).
- Mahmoud, M.R., and Garcia, L.A., May 2000, "Comparison of Different Multi-Criteria Evaluation Methods for the Red Bluff Diversion Dam", Environmental Modelling & Software, Elsevier, Vol. 15, Issue 5, pp. 471-478. https://doi.org/10.1016/S1364-8152(00)00025-6
- Mahmoud, M.R., Fahmy, H., and Labadie, J.W., March 2002, "Multicriteria Siting and Sizing of Desalination Facilities with Geographic Information System", Journal of Water Resources Planning and Management, ASCE, Vol. 128, Issue 2, pp. 113-120. https://doi.org/10.1061/(ASCE)0733-9496(2002)128:2(113)