#124

Dear Renzo C. Bertuzzi , Sajid Sirajb, , Ludmil Mikhailovd , John A. KeaneDear

I read your paper

Sensitivity Analysis Techniques for Enhancing a Decision Support Tool

My comments:

1-In page 3 you say “discussed trends in MCDM and declared AHP to be the most active area of research in decision making”

I am afraid that |I do not concur with this, AHP is an elemental MCDM model, probably useful for prosomal decisions and trivial scenarios, but not for medium and complex projects. They need more than the simple hierarchical assumption of AHP. Scientists at this moment are not interested in AHP but in more advanced issues. I do not think that there is research on AHP, it is not worth to try to improve something that was born flawed

2- In page 3 “In AHP, the relative importance of the alternatives and criteria is assessed by using the Pairwise Comparison (PC) method”

True, and using pair-wise comparisons is probably the most negative aspect of the method, because real-life problems do not follow what the DM wants but what it should be. It produces invented criteria values that are useless, at least in the real-world. These values are the product of following a descriptive process based on personal wishes, instead of using a normative process where the reality is important, norms must be followed, independently of what a person thinks or wishes.

3. In my opinion it is wrong to assume that SA is necessary because uncertain values. SA, as you correctly defined before, is aiming at to determine the strength of the best solution found when certain criteria change. Many times, the change does not come from the DM.

An example, consider when you export an article that heavily depends on the international prices for said product; variation in plus and minus are due to the market; what you try to learn with SA is in what range these changes do not affect the best solution. There is uncertainty, not because the DM but to global markets.

4- One-at – At -Time analysis or ‘ceteris paribus’ in economic language, is not adequate and rejected by most economists. You cannot select a criterion, increase it while holding the others constant. That is not real. Why? Because there could be other criteria that are related to the former, that also contribute to its value. This is also the reason b y which Saaty, the creator of AHP, said very clearly, that AHP cannot be used in a system where criteria are interrelated.

5- In page 4 “When comparing elements Ei and Ej , Ei is said to be aij times more important than Ej , and the reciprocal value of the judgment is used to score the inverse comparison”

On what basis? Intuition? Please consider this question” How can you compare two intangibles as love and tenderness?” Would you dare to put a value of superiority?

6- “The self-comparison aii is therefore considered to be equal to 1. All the judgments for a given criterion are organized in a PC matrix”

That is, you get a useless matrix. What if the DM has second thoughts? He has to start all over again, very practical indeed!

7-In page 5 “The two judgments a12 = 2 and a23 = 3 suggest a13 to be equal to a12a23 = 2 × 3 = 6. However, the DM has judged a13 to be equal to 5 that turns out to be an inconsistent judgment. There exist two types of consistency: cardinal consistency (CC) and ordinal consistency (OC). For a matrix to be cardinally consistent, the condition aij = aikakj must hold true for all i, j and k. OC however, refers to the order of preferences i.e. if Ei is preferred over Ej , and Ej is preferred over Ek, then Ei should be preferred over Ek. When this condition is not met, the matrix is said to be ordinally inconsistent”.

Good analysis! First time I see it. My question is” Why the DM must be consistent? Saaty, did not mention any reason for that. The only reason is that if it is not consistent, you cannot apply the Eigen Value method.

Now, a second question; Is there an axiom or a theorem that says that what is in the mind of the DM can be applied to the real world? It is only a hypothesis with no foundation neither in mathematics nor from the common-sense point of view. Thus, what is its wort? ZERO

There is another question: Consistency equals to transitivity, a very useful axiom, but who told the DM that the real-world is transitive? Therefore, what does the DM get with this matrix and corresponding trade-offs? NOTHING

8- In Table 2, how do you measure Aptitude and Flexibility? You can certainly consider that one of them is more important than the other, but it does not mean that you can put a number to that importance.

It appears that you considered that all criteria must me maximized, but that is incorrect, since expenditure should be minimized, and you did not consider it.

How do you manage in AHP to mix these two opposite objectives? In this case, dentistry should be the best in both counts, because it has the largest market value and the minimum tuition. It is followed by computers with the second market value (something that I doubt), and with the second minimum cost, that could be.

9- In page 7 “In addition, the visual representation is not possible when more than three criteria are simultaneously considered”

And who decides which criteria to consider? In a MCDM problems all criteria must be considered for the valuation, no matter their number, may them be 4, 25 or 200. However, only a few criteria are mandatory for SA; if you have 4 criteria, maybe only 2 are relevant, the other two are irrelevant, at least for the alternative analyzed.

My question: How AHP determines which are the criteria to be considered and which are discarded?

My answer: It cannot. What it does is to select for variation the criterion with the maximum trade-off and consider the others constant, as you know. Intuitively this is correct, but it is not. It is easily proved, using entropy, that the criterion with the highest trade-off may or may not be the most important. I suggest doing this analysis, it is simple.

10- In page 7 “The algorithm can easily detect the rank-reversal points whenever the order of rankings gets changed during this incremental process”

Therefore, for AHP the DM can increment or decrement as much as he wants?

NEGATIVE

Because each criterion can change, without altering the selected alternative, in a certain range that can be null, small or large. How do you know in AHP which is that range?

You do not know, but believe me that it can be easily found, not using AHP of course, but other MCDM methods. If you want more information, please contact me, I be happy to oblige

11- In page 8 “For large problems with several criteria and alternatives, analysing only one element at a time may not provide enough information for making a decision.”

Absolutely right, therefore, this is one of the reasons for the lack of realism or “advantages” of AHP and others MCDM methods, that use AHP to ‘compute’ weights. By the way, AHP assumes that trade-offs are equivalent to weights, however, they are completely different

12- In page 14 “As the output of the algorithms are considerably different and cannot be compared directly, the analysis has focused on finding how many alternatives may be the most preferred according to each algorithm. Under this analysis, the most effective algorithm is the one that finds the highest number of rank reversals that causes the top-ranked alternative to change. Rank reversals between other alternatives are ignored”

Good approach, but unfortunately useless, since the weight of each criterion must be based on data not on simulation. If you have quantitative and qualitative data, you must work with a method that computes the relative weights for criteria based on data.

Is there any MCDM method that can do that?

Yes, very easily, and ironically the oldest method in MCDM. Linear Programming, developed in 1940 and that earned in 1956 the Nobel Prize in Economics to its creator (L. Kantoarovich). Its Solver algorithm is in your computer. Look for Solver in Excel, under ‘Data’. Very simple, straightforward and mathematically exact.

It also will tell you which are the significant criteria and which are irrelevant and why. After so many years, this is still and by far the best MCDM method ever developed, although it also has some drawbacks

I hope these comments may help you

Nolberto Munier