Dear Susmita Bandyopadhyay

Reference is made to your paper

A novel multi-criteria decision analysis technique incorporating demanding essential characteristics of existing MCDA techniques

Here are my comments

1- In the abstract you say “However, no single research study has considered the prime characteristics of these techniques through a single algorithm”

I am afraid that you are mistaken. The Simplex algorithm, accessible through the Solver add-in (Excel spreadsheet), and in your computer, contemplates all the issues which you correctly call ‘prime characteristics’, that is:

The relation among alternatives (precedence, inclusivity, exclusivity, time of execution, etc.)

The relationships among criteria

The relationships between alternatives and criteria.

In addition, it can make simultaneous comparisons between an alternative and many others, and use a same criterion calling for maximization and minimization, that is, establishing lower and upper limits.

What it does not consider is entropy and criteria weights, because the Simplex algorithm does not use them. It evaluates alternatives using the economics ‘Opportunity cost’ concept of each alternative (that makes the method immune to rank reversal), and generates its own ‘criteria ratios’, that quantify criteria importance in EACH iteration (and there could be hundreds or thousands), and which are extensively used even in a single problem.

Thus, the importance of a certain criteria changes according to the alternatives to evaluate.

2- “The proposed method has also been compared with four different types of already existing MCDA techniques, AHP,……’

Since covariance is a measure of the joint variability of two random variables, I don’t think that you can use covariances among criteria in AHP, because this method works only with independent criteria.

3- In page 1 “shows techniques which endeavored to establish relations among the alternatives and the relationships among the criteria (such as AHP, ANP)’

Again, you can establish those relations in ANP (because its matrix structure), but not in AHP (due to its lineal hierarchy structure, i.e., with not transversal connections)

4- “Unbiased assignment of the weights to the criteria”

The essence of subjective weights generated in AHP is intuition. Do you think that they are unbiased?

Well, they are, only if you use entropy. However, using entropy in AHP? How?

5- In page 2 your question “Is it possible to find a MCDA technique which incorporates the most essential characteristics of MCDA techniques?”

Yes, there exists that technique since 1948: Linear Programming, and its Simplex algorithm, which earned the Nobel Prize in 1958 to its creator.

Your paper makes very useful comments about the different techniques which in some way explains the gap you talk about. In my humble opinion, you forget perhaps the main reason.

Real-life scenario can’t be solved as a bunch of different entities and the add them up. A MCDM is a system, and as such, the modification of one component may or may not have effects and impacts on a another.

It is like a car. It is a system composed by the engine, the body, the electronics, transmissions, etc. You can’t study the engine alone, independently from all the other components, because if you change for instance the aerodynamics of the body, you are altering the amount of power needed to move the car, and that power depends on the engine. This is what engineers do using models to scale of a car, a train or an airplane in a wind tunnel, and adding or modifying in some way the body and at the same time, reading the necessary power in each condition. As an analogy, in MCDM the model is the initial decision matrix and the software the wind tunnel. When you change a value, it could or not affect the result.

6 “The use of rank correlations and some other methods to compare among the MCDA techniques only establishes the associations and thus is unable to identify the most appropriate MCDA technique for the problem”

Absolutely correct, and this is the reason by which it is a waste of time to solve a problem by different methods.

7 “The reason lies in the fact that any change in criteria or alternatives or decision matrix is definitely going to have influence on the final ranking. Therefore, the concept of robustness is not applicable to the ranking obtained from MCDA techniques.”

The first part of your paragraph should not be absolute. In reality, a criterion may change a lot without altering the ranking, while in others, a little change will produce a ranking modification.

This is because each binding criterion, that is, a criterion that influence the best alternative, may have a certain allowed margin for variation without altering the ranking. This range is due to its relationships with other criteria

An alternative may also change without altering the ranking, the same for performance values.

Robustness of the best solution is how stable the best solution is when subject to variations of binding criteria, considered simultaneously. That is, not only one, but varying several criteria at the same time

As you can see, the problem is much more complex.

8- “Based on the requirements of the MCDA techniques, the best MCDA ranking for a particular problem is required to be found, but before the application of such a technique to verify the effectiveness of the proposed MCDA technique in a later section, this section applies traditional sensitivity analysis in the form of rank reversal in order to establish the validity of the proposed technique”.

Rank reversal has two meanings:

a) Change in the ranking of alternatives when an alternative is added or deleted

b) Change in the ranking of alternatives when a binding criterion is added or subtracted.

I guess you refer to the second, since you are talking about sensitivity analysis.

You are contradicting yourself here, first you say that you need to determine the ranking, and later that you apply sensitivity analysis before it!!

9-Rank reversal is not a method as you say, but an occurrence or result, normally negative.

I hope that these comments may be useful to you

Nolberto Munier