## Tuesday, March 13, 2012

### Comparison of "Closest to the Ideal" MCDM Approaches

Summary: Pourcavad and Shirouyehzad attempted to address a major criticism of MCDM- that different techniques may yield different results when applied to the same problem. They evaluate the utility of three MCDM methods, TOPSIS, ELECTRE, and VIKOR, which all look for the solution that is “closest to the ideal.” This study is a comparison analysis of these methods applied to eight parallel production lines from a factory.

TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution)
In this technique the chosen solution must have the shortest distance from the ideal solution and the farthest distance from the negative-ideal solution. The process for the TOPSIS procedure is as follows:
1.  Compute the normalized decision matrix
2.  Calculate the weighted normalized decision matrix
3.  Determine the ideal and negative-ideal solution
4.  Calculate the separation measures, using the n-dimensional Euclidean distance
5.  Calculate the relative closeness to the ideal solution
6.  Rank the preference order (mathematical formulas concerning these steps may be found in the original document)

ELECTRE (Elimination and Et Choice Translating REality)
This technique is based on a Multi-Attribute Utility Theory that sequentially decreases the number of alternatives the decision maker is faced within a set of non-dominated alternatives. The goal of this method is to find the best alternative, that which simultaneously trumps all others and is not trumped by any others. With this method, it is important to accurately weight all possible options. The process for ELECTRE is as follows:
1. Obtain the normalized values of all the criteria
2. Construct the outranking relations and develop a graph representing the domination relations among the alternatives
3. Acquire a minimum dominating subset by using the minimum concordance and maximum discordance indices
4. Select the last decision or repeat steps 2-4 until a single element remains (mathematical formulas concerning these steps may be found in the original document)

VIKOR (Compromise Ranking Method)
This technique was developed as a multi attribute decision making method to solve a problem that contains different units and opposing criteria. The method is meant to find a compromise solution among the opposing criteria by comparing the measure of closeness to the ideal alternative. The process for VIKOR is as follows:
1. Determine the best and worst function and use them to formulate ranking measure
2. Use the algorithm (mathematical formulas concerning these steps may be found in the original document) to rank the alternatives
3. Propose as a compromise solution the alternative which is ranked best by the algorithm and which satisfies both acceptable advantage and acceptable stability

Findings: In order to compare the techniques, the study ranked parallel production lines in different areas of the Chadormalu Mining and Industrial Company, considering fourteen criteria with each method. Each method yielded different results. The authors then ranked the production lines using aggregate methods. However, the results of the MCDM methods are not similar to the aggregate method, and the study cannot conclusively state which method yielded the correct answer. (Pourjavad & Shirouyehzad, 2011)

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