To my colleagues

In reality my question should have said ‘Do you think that there is a MCDM method than can solve this real-world problem?’

This is a problem similar to many that are solved and published by practitioners everyday using MCDM methods. However, there is a crucial difference: This problem reflects reality more accurately that other methods do.

Why?

Because it contemplates many aspects that belong to the scenario, THAT HAVE FORCEFULLY TO BE CONSIDERED, although MOST METHODS DON’T CARE about them.

Consequently, and answering my own question I understand that no present-day MCDM can solve the problem I proposed.

Why is that no method can solve it? Is it because it is a complicated problem?

Not really, the problem is simple. The reason is because as far as I know, none of them in their structure consider restrictions and conditions which are common in every project.

The example that I proposed illustrates those restrictions when it says as an example that if a certain alternative A is selected, alternative F can’t. This happens for instance, when it is necessary to select a certain methodology A instead of methodology F or vice versa. It is one or the other, that is, they are mutually exclusive. In this case, in addition to formulating this condition in the initial decision matrix, it is necessary to specify that the result must be in the binary format, that is (1) meaning YES, and (0) meaning NO.

Or when it states that if alternative B is selected, then alternative D has also to be selected, as in a case of two projects, one for building a housing complex and another for building the water line extension from the city main water trunk. Both are independent projects, both are inclusive, but both forcefully have to be built, because the housing complex is not habitable without water, and the water diversion does not make sense if there is no use for it.

Or when there are two projects A and B, and because technical reasons A must precede B, as in the case of building a rainwater drain in a street, and after that paving it. Obviously, the first must precede the second.

How many times have you seen in your city that a brand-new pavement is broken to install some underground utility, which should have been installed before paving?

Or that in a project there is clear evidence that correlation exist between criteria. For instance, between criteria maximum speed, safety and weather in a road, where it is obvious that maximum speed is strongly linked with safety and weather, and in truth depends on both. Heavy snowfall influences both speed and safety, and even can close the road, and also the higher the speed the lower the safety

In this case, and assuming that the correlation factors are known, how the DM introduces them in the model?

Of course, there are many more examples, on real situations, but I believe that they illustrate my point. I invite the reader to think about these elemental real circumstances and ask him/herself if he/she knows any MCDM that may cope with them, and if not, if it is correct ‘solving’ them by any MCDM method.

Or is it done because there is no choice?

I would indeed very much appreciate it, if somebody comes across and tell me that I am mistaken, and that methods XXX and YYY can do this.

Does anybody truly believe that solving a problem and reaching a result, without considering, if not all, at least most of the characteristics of the problem, is right?

That many aspects can be dismissed or ignored because they are difficult to model or because the method does not have the capacity to incorporate them, or because the DM decided not to consider them?

In the last case, on what grounds?

Well it is what is being done for decades now.

Is there any risk in this procedure?

No, because nobody knows if the result achieved is good or bad since the ‘ideal or true’ result is not known, however, we can see many papers where the author happily states that the problem was solved successfully. What he/she should say is that the method performed as expected, but that there is no guarantee that the result is correct

What it can be said for sure, is that the result does not reflect reality, and consequently, there are reasons to believe that it is not as good as it should.

I am not against any MCDM method, I don’t promote any, and I don’t want people be offended with my comments, it is not my intention. My aim is to alert, to make many practitioners and researchers realize that we have to find a new paradigm for MCDM, a paradigm that takes into account as many real aspects and characteristics as possible.

Much has been done in improving data quality, but nothing to model a scenario as faithful as possible. We are with the same modeling as developed 60 years ago.

I have been fighting in RG, Papers, Books, in Universities, in International Conferences and in Communications with other Researchers, about this same issue, that can be resumed as that nowadays MCDM methods don’t take into account the reality of a scenario.

They just work with approximations of the reality, and adapt it to their needs when it should be the opposite, since we have to adapt to reality.

My only aim is to promote research to correct this situation, which must be extended to sensitivity analysis, which at present-time, contributes very little to evaluate a solution.

I will be happy if we can initiate a technical discussion about this subject, with a lot of people participation and each one with his/her ideas. Maybe, just maybe, we can change the actual situation

I will be happy if we can initiate a technical discussion about this subject

To finish: The problem I proposed can be solved.

Guess which is the MCDM method that can do it.

Thank you for your patience

Nolberto Munier

Dear Nenad

Thank you for your answer.

You are right, there were no answers and probably never will. The simple reason is that AHP and ANP are indefensible.

Let me mention something that for me was very illustrative:

Two years ago, I prepared a paper where I mentioned 19 aspects related with real scenarios that in my humble opinion should be contemplated in MCDM, and sent it to about 40 scholars and researchers around the world. This paper is since then, in RG in my profile, under the number 265.

I only got two answers and to my great surprise and satisfaction, the first one was from the late Dr. Thomas Saaty, and the second from a known Chilean scholar, an expert and staunch defender of these methods and with a solid practice. He expressed his agreement with some suggestions and disagreement on others, but unfortunately without explanation or elaboration of his rebuttals.

Mi greatest surprise with Dr. Saaty’s answer is because most of my suggestions are absent in AHP and ANP, and possibly they can’t be implemented in these methods because their structure. However, this scholar had the honesty, the candor and the decency to accept them, acknowledging, against his own work, that they were in reality needed, and expressing his desire to collaborate, as I requested.

Further, I was privileged enough to interchange some correspondence with Dr. Saaty - who always answered me - on the same subject, and especially about some weakness of AHP that I had pointed out, however, I did not receive answers from him substantiating his methods.

Unfortunately, his passing away in August 2017, interrupted this healthy interchange of opinions.

I was and still am in disagreement with his methods, but I think that he deserved among other aspects, to be known for his integrity.

Now, if the same creator of these two methods implicitly acknowledged their drawbacks, and did not haves answer for me, I believe that the chance that we receive response form other scholars is very slim.

In my opinion, the reason is that there are no logical and mathematical justifications to support these systems. The idea of working with preferences is good, however, it is not applicable to the problems most of practitioners face every today.

Regarding to your conclusion that there are issues in my letter that are also general ones and then not only applicable to AHP and ANP, I wholly agree with you, since this is something I have been fighting for years in RG, in international fora, and in discussions with colleagues, when I maintain that at present NO MCDM heuristic method is able to represent reality even approximately.

As a matter of fact, two colleagues and I found the necessity of diffusing our ideas and suggestions, and to that effect we wrote a book where we extensively address this issue, examining the actual MCDM status, followed by enumeration and discussions using examples, of the main drawbacks of present-day methods, without pointing out any of them in particular. This is followed by our opinion about what should be done, and ending with a set of very complex and actual examples solved. The book, was just on the bookstore’s shelves about a week ago, and published by Springer NY. Of course, it is also as ebook.

In it, we don’t work with formulas or assumptions. Every theme both as a drawback and as a suggestion, is analyzed considering common sense and using solid arguments, with also reference to the opinion of other scholars. It finishes with the development and solution of six complex scenarios.

Therefore, your liking to turn this discussion in another way, is more than welcome.

Now, you request answers for several important questions that I am happy to comply.

* Which methods can consider complex problems, that involve a very large number of criteria/alternatives?

I am not sure that we can consider complex problems those with a large number of alternatives and criteria. In my opinion, complex problems involve more than that, such as including many restrictions on both alternatives as well as correlation among criteria, or involving especial circumstances, as for instance a portfolio of projects that do not start and finish at the same time and wit changing performance values

Some time ago, I challenge in RG to sdolve a problem that I propose, under the title of

‘Can you model and solve this real-world scenario with a MCDM method?

Answers: Not even one

Coming back to your question I believe that methods such as ELECTRE, PROMETHEE, TOPSIS, VIKOR, etc. are very well suited to address projects with a large number of criteria and alternatives. Even if they use assumptions, these are based on sound reasoning such as the preference statistic functions in PROMETHEE, or the selection of type of distance in TOPSIS. They are subjective, but not arbitrary, and the same applies to other current methods.

However, unfortunately, most of them work with weights derived from AHP, which of course are completely subjective and which, in addition, are not fit to evaluate alternatives. Of course, there is always the option of using objective weights as in methods ‘STEP-WISE WEIGHT ASSESSMENT RATIO ANALYSIS’ (SWARA), or ‘PREFERENCE SELECTION INDEX’ (PSI), or using entropy derived or statistic s derived weights.

Your second question: ‘* Which methods take into account interdependence and/or correlation between criteria/alternatives?’

I understand that your word is ‘interdependence’ and not ‘interrelationships’

If it is the first the answer is: No method, as far as I know, consider that there can be dependencies among alternatives and dependencies among criteria, or correlation, and this is exactly my point when I said that these features may appears in real-world scenarios, and that no MCDM method can tackle them. However, LP and SIMUS, and without a doubt, can tackle them, and of course, I can prove it.

If you mean ‘interrelationships’ between criteria, yes, many methods can handle it, including ANP, but as far as I know none method can handle interrelationships among alternatives. Again. LP and SIMUS can handle them without problems.

Your third question: ‘* Which methods have weights or some other means for determining importance of criteria that are flexible to change based on specificity of alternatives that are compared?’

LP, as you know, as well as SIMUS do not use weights. However, it does not mean that they do not consider relative criteria importance. As a matter of fact, examining the LP Simplex algorithm it can be seen that in each iteration the selection of which criteria is the most important, when selecting an alternative, but most especially when determining which alternative must be eliminated from the former solution, to keep the dimension of the problem constant. If you wish I can explain this in detail using the Simplex algebra, and as did some time ago in RG when a researcher asked why LP is immune to rank reversal.

The last part of you question is exactly what LP and SIMUS do at each iteration where a new set of criteria importance are computed based on the just selected alternative. Alternatives are selected in each iteration using the economic concept of opportunity costs, and compared each other.

As mentioned above some other methods use objective weights which are legitimate for alternatives selection.

Thank you again for your questions, and please continue with them since they benefit us all.

Nolberto