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Article On Sensitivity Analysis in the Analytic Hierarchy Process

Ca Dr. Gaurav Bhambri Thank you very much! On p. 66 of the paper I found the formula for calculating the total value for the alternative. When I transform the formula, I get the same formula that I have. However, strangely enough, when I calculate it at Goepel's online tool, I have different values than when I go through the sensitivity analysis by hand. What could be the reason for this?

Ca Dr. Gaurav Bhambri More specifically, I'm referring to the results you get here:

https://bpmsg.com/sensitivity-analysis-in-ahp/

As I understand it, the criterion "neighborhood" has to be reduced by 8 percent to make house A better than house B. If I apply the formula I showed above and plot the functions for house A and house B as a function of a criterion change in neighborhood, I get a result of almost exactly 7 percent... I don't understand what the reason for this is. I would be very happy if you or someone could help me there.

Probably you forgot to re-normalize the criteria to 100% after subtraction of 8% from the criterion Neighborhood. Divide all global weights by .92 to re normalize to 1. Then you will get your -7%. But for the sensitivity analysis I have to state, "that a change of -8% to the criterion Neighborhood will change the ranking of alternatives House A and B."

Dear Andreas

I consider that doing sensitivity analysis with AHP is a fallacy, for three reasons:

1- Selecting the criterion with the largest weight is incorrect. It can be easily demonstrated mathematically, that the largest weight is not synonymous with the most significant criterion; it even could be the less important. This applies when you want to determine the significance among criteria, BUT IT IS NOT RELATED WITH ALTERNATIVES SELECTION.

2. You gain nothing using for sensitivity analysis one criterion according to its weight (there is no mathematical basis for that!!!!); you have to select jointly the criteria that intervene in the selection of the best alternative.

3. Weights are only trade-offs, and thus, they are not suitable to evaluate alternatives, only useful to compare them.

These three aspects have since long been agreed upon by many researchers, it is not only my opinion.

I am aware of Klaus Goepel work, however, I don’t know his methods

If you decrease or increase C1 weight, then, C2 and C3 weights will change proportionally, since A HP is a compensatory method

Assume that C1 = 0.35, C2 = 0.42 and C3 = 0.23, an d then, their sum = 1

Therefore, if now C1 = 0.31, then C2+C3 must be 0.69. The differences 0.35-0.31 = 0.04 must be shared proportionally by C2 and C3

Then C1= 0.31, C2 = 0.446, C3= 0.244

The problem as I see it, is that weights have nothing to do with alternative evaluation.

It would be different if you use entropic weights because these are based on each criterion capacity to evaluate alternatives, based on the dispersion of its elements (Shannon Theorem).

If you use Linear Programming, the information you are looking for comes automatically when you solve a problem using it.

Nolberto Munier ad 1: please read the reference first, sensitivity analysis is not based on taking the criterion with the largest weight, but takes all criteria into account.

Klaus Goepel Nolberto Munier thank you very much!

I think I have now figured out how you, Mr. Goepel, calculated the values in your example table (see attachment). You simply subtract a value x from a criterion and then calculate the "new" values for each criterion, i.e. also for the criterion which has already been reduced. Thus, if a criterion is reduced from 60% to 50%, i.e., by -10%, this does not mean that the criterion yields 50%. Rather, one must calculate 0.5/1-x in a second step. I think I am correct with this. Please correct me if I have misunderstood this.

Dear Klaus Goepel

Thank you for your observation.

You are absolutely right, AHP does indeed take into account all criteria; the only problem is that it follows the OAT (One at A Time) procedure, i.e., varying only one criterion weight and keeping the other criteria constant, (ceteris paribus principle). I can name many researchers that agree with this. It should use AAT (All at A Time), but of course, AHP architecture is not able to do this.

Your definition of sensitivity analysis (SA), as determining the criticality of each criterion is, of course, correct, however, it denotes something that you don’t say, and it is that criticality is related with uncertainties in the criterion scope more than in the uncertainty of weight values.

I don’t think that knowing that a criterion value can vary between a low and an upper limit, as you say in your example, is as important as determining how stable or constant the solution is, and this depends not on the value of a criterion, but on how much it can be changed without altering the alternative selected.

Consequently, I believe that you can’t say, based on that argument, that the solution is stable, which, by the way, is not. I solved your problem using SIMUS and the result is quite the opposite, it is extremely sensitive because, considering the four criteria on which it depends, these do not have any leeway or zero scopes.

This translates that determining the uncertainty limits (and I don't know how you do that), of a criterion, is not good enough to determine the stability or strength of the solution.

In your example, the slightest variation in any of those criteria will most probably cause a change in the ranking. Of course, I can demonstrate this, and my calculations are at your disposal.

AHP should use the AAT (All at A Time) procedure, where all criteria are considered together, but of course, this is something that AHP can’t do, not only because its architecture is not built for that, but also because AHP considers independent criteria, and thus, the eventual relationship between criteria are ignored. I wonder how you solve an MCDM problem where there are criteria such as the number of sales and prices are related.

Dear Nolbert, as I remember, we had this discussion a while ago, no point to repeat here. Just for clarification: My example and the method I am using refers to "Triantaphyllou, E. (1997). A sensitivity analysis approach for some deterministic multi-criteria decision making methods. Decision Sciences, 28(1), 151–194." His paper is actually only mentioning AHP, and his proposed methodology applies to any weighted sum or weighted product method.

You state: "In your example, the slightest variation in any of those criteria will most probably cause a change in the ranking." No need to guess, just calculate and analyze the result.

Dear Klaus

Thank you for your answer, and yes, I remember we were in contact although I don’t remember if it was on this same subject. Instead, I am positive that our last contact was regarding one of the assumptions in ANP regarding feedback.

I believe have read all Triantaphyllou papers including the one you mention. In a very high percentage, I agree with this author, however, it is evident that he works with subjective criteria weights and considers that they are able to evaluate alternatives, concept with which I completely disagree.

Since they were arbitrarily computed, and due to the fact that they originate by pair-wise comparison without considering the alternatives the criteria are to evaluate, in my opinion, they are useless. Of course, the fact they they use the OAT approach, worsens t he situation. Considering these facts, I don’t think that they can be used for sensitivity analysis, and this is the reason of my disagreement.

What am I using? I use real values pertaining to the resources with which a criterion has forcefully to comply, and that AHP conveniently ignores, and in so doing, I work with criteria increases and decreases

After so many years in RG I have asked many times why subjective weights determined arbitrarily are considered suitable to evaluate alternatives. Needless to say, I NEVER received an answer or at least an explanation, or an intent of discussion, about which are the axioms, or theorem or rationality on which this assumption is based. Even Saaty recognized that they are not weights, but trade-offs, and thus, with very different functions. It strongly suggests that there is no answer to this question, and then, it is just an assumption.

Probably this was the object of the discussion you mention that we had years ago.

You said: No need to guess, just calculate and analyze the result.

Who is guessing? Not me, certainly, and I did exactly what you suggest. I analyzed the result as I told you, and from there I extracted my conclusions.

You asked for computation values and analysis, OK here they are, in your problem, only four criteria out of eight, are significant, the other four are irrelevant, in selecting the best alternative:

The same criterion is normally repeated because each may correspond to different objectives

• Please see Exel file attache

You can see that for criteria C3, C4, C5, and C6, there is no margin or allowances for increases (since we are maximizing), therefore, the solution is, as I said, extremely unstable since any variation in plus of any of those criteria may produce a Change in the best alternative, which Triantaphyllou calls AT)

The only exception is criterion C4 regarding objective O5, which allows an increase of 0.25, however, it has low participation (0.17), and thus, not very significant.

A valuable discussion between Goepel and Munier. It reminds me of what I always told my students. In sensitivity analysis of LP or MCDM, never forget, that stability of the solutions depends on criteria AND constraint set alike.

And, there is no "best" method, to solve a real world problem. Therefore, make different optimization models, if you can, and compare the answers. Someone

active in Operations Research should never be satisfied with " shut up and calculate." Operations Research is an art, that should be treasured, and it is certainly much more than applied mathematics.

Dear J.W.

Thank you for your comments

You are right: There is not the 'best method' in MCDM, but there is the best method to solve a certain problem, which brings to determining which is it.

Unfortunately, just reading the published papers in journals, at first sight, you realize that probably, in some of them, the author chose the wrong method, simply because it does not represent the scenario he/she has. The consequence is that most probably the results will represent the solution to a nonexistent problem, or to a gross simplification of the real one.

For instance, you can't use a linear hierarchy method to solve a problem that does not have this structure, because everything is connected. Apparently, this aspect is completely ignored by many practitioners, and what is WORSE, approved by some journal reviewers.

However, I disagree with you in the sense that solving the same problem by different methods, because that comparison adds nothing since we don't know which the 'true' solution is.

The best we can do, in my opinion, is to analyze which is the most adequate method for that particular problem. That is, it is easy to study the project, consult the stakeholders, users, and experts, and then, select a method that best models the scenario. This is not mathematics, only common sense, and expertise.

But the selection is, as you say, part art and part knowledge, because how many people can compare the characteristics of AHP, ANP, PROMETHEE, ELECTRE, TOPSIS, SIMUS, etc? And what is the gain in doing that?

Probably very few people. This is the problem.

Some researchers as well as myself, have produced a guide to performing this analysis, in different formats. Mine is an interactive matrix, with 10 different methods (SAW, AHP, TOPSIS, VIKOR, PROMETHEE, MOORA, ELECTRE, ANP, LINEAR PROGRAMMING, SIMUS), arranged in order of solving capacity for complex scenarios, and 54 conditions or characteristics, including sensitivity analysis.

It is in RG in my profile since 2017, under the numbers 300a and 300b.

The practitioner has only to select in the rows which are the characteristics of his/her protect and will get which are the best methods to tackle the problem

Thank you for all the comments!

Klaus Goepel Nolberto Munier

I see that the sensitivity analysis is more difficult than one might think. Also, I have read the paper by Triantaphyllou, E. (1997). A sensitivity analysis approach for some deterministic multi-criteria decision making methods. Regardless, I do not see in any papers how sensitivity analysis can be done for a two-step or multi-step problem. In the appendix I have shown such a problem. Here there is stage 1 with criteria CX and CY and stage 2 with subcriteria C1-C5. I would assume that one would then calculate the value for alternative 1 as a function of a change in criterion C1 by x as I have shown. I have also used Mr. Goepel's tool, but unfortunately I do not get the values that the tool calculates. Therefore, I would like to know if the formula is "correct".

Thank you in advance!

Dear Andreas

Sensitivity Analysis is not difficult if you use the correct procedure

You insist in using AHP weights for SA and this is incorrect, and I gave you the reasons.

Your own question reflects these reasons. You can't make an agreement with what Klaus states, which I don't discuss here, because you are assuming something that is wrong, and again it is using subjective weights in SA. I told you before, and curiously, I did not get any answer from you

By the way, since you don't give information, could you tell us at least, if criteria and sub criteria are independent?

I only ask you that

Nolberto Munier Klaus Goepel

Dear Mr. Munier, dear Mr. Goepel,

the criteria C1-C5 are independent, as are CX and CY. I know that in AHP the criteria should be independent, that's why I chose them that way.

As part of a larger project work, me and my project group are doing research on emissions from transportation and the AHP is structured so that CX= reduce emissions, CY= avoid emissions. The criteria C1-C5 include fuel consumption or the load factor etc.... I must confess that it is not very clear when doing the evaluation of this problem. Because we have not 3 but 7 alternatives. I left that out for clarity. So we have 2 criteria, 5 subcriteria (as in the figure) and 7 alternatives.

I admit that it is not always clear how a meaningful evaluation is to come about with such a quantity of pairwise comparisons. This is very "subjective". But if no objective facts are (or can be) taken into account, I ask myself why one takes the trouble to conduct an AHP at all (we were given the AHP by the university), if one can simply say in advance that alternative 1 or alternative 3 is probably the best alternative. I don't understand why you have to make such a fuss about subjective impressions.

Regardless of this, I find Mr. Goepel's tool very detailed. You can quickly calculate the results without much Excel effort. However, I see the problem in this, because if you want to recalculate the values once, you get different values depending on the method. So far, I have only been able to reconstruct the values for a single-stage problem (example table from Mr. Goepel). I ask precisely because I do not know how exactly the final value for an alternative is calculated for a two- or multi-stage problem.

Thank you very much!

Dear Andreas

Thank you for your answer

I am perplexed by your first paragraph, where you say that you chose the criteria to be independent. Sincerely, in all my years in MCDM this is the first time to hear it. Given a problem, you rationally, can’t select the criteria all being independent; IT IS A CHARACTERISTIC OF A PROBLEM.

YOU CAN’T MODIFY A REAL PROBLEM TO FIT YOUR NEEDS, IT IS JUST THE OPPOSITE

If you were given that method by the university, fine, but they surely did not know what your project is.

You still do not share with us what your problem is, therefore, I am sorry, but I can’t continue advising you if I don’t know which the problem is, and working on assumptions; you asked for our help, thus, please be open with us.

You mention that in criteria C1-C5 one of them is fuel consumption, and another is ‘the load factor’.

Load factor of what? There are many, the main being on electricity generation.

If you are talking about fuels, most probably they and load factors are strongly related. I don’t know about the sub-criteria, are they also unrelated according to you?

Your second paragraph illustrates you very well your doubts. The AHP method is too subjective, and real-life projects are very real. Well, usually you can’t say in advance that alternative 1 is better than alternative 3 because A1 may have very good values for a set of criteria, while A3 normally has quite different and better for another alternative. This is the essence of MCDM. Alternatives SUBJECT TO a set of criteria

Klaus Goepel did a very good job with his way of rapidly calculating the weights, and I myself used it once or two.

Of course, you can get different values according to the method, but in most of them they depend on the DM, which for me is another inconsistency, because DM1 may get a result, DM2 another, and so on. This is the reason that I claim that MCDM values should be done WITHOUT human interference on DATA, this has to be completely objective, using reliable values, or statistics, in the case of uncertainty, but the DM must have a very strong implication in analyzing results, and even rejecting them, according to his experience and know-how. To do that, he must use reasoning, something absent in AHP, and knowledge, not intuitions as in AHP.

Andreas, one does not need to be a mathematician to understand why AHP can’t work with related criteria. If according to a pair-wise comparison if A= 3B and they are independent, the AHP procedure is correct, even considering the absurdity of pair-wise comparison, however, if they are not; just think that B is also related to A, and thus, affecting it. Now, and this is the question, how do you know what part of A is affected by B, and then, perhaps it is no longer certain that A = 3B.

It is strange that the university is asking using a particular method, without knowing which your problem is unless it is a general one for every group, but this is not my business. If this is the case, and the university demands to be solved by AHP, well…..I prefer not to judge it

You have, as it should be, your own doubts about the method. I would suggest talking with your professor or advisor and making him aware of your doubts about using AHP. If I were that professor, I would be happy that a student of mine reasons, and I would tell him to use any other MCDM methods; there are more than 100.

Then, the problem seems to be emissions from transportation, and apparently, you have 7 alternatives, which is not a problem, you most probably are working with trucks with engines burning gas oil, natural gas, liquid natural gas, hybrid, hydrogen cells, or trains, or even ships or barges using fuel oil. You can also have transhipments to different modes such as trucks to rail, rails to barges, etc., and then, these are also alternatives to consider, as well as restrictions to consider that involve working with binary values.

Believe me, none of these options are subject to independent criteria. Years ago, I performed a similar project in Europe using long-distance trucks burning oil or gas (the actual trend is gas).

I would strongly suggest that you speak with your group, and then, contact your university professor or advisor and tell him/her why you can’t use AHP

Andreas K. I don't really understand the diagram and formula. Usually, when I have a hierarchy, I am used to differentiate local and global priorities. If your Cn and Cx,y are local, then Cx+Cy=1, C1+C2+C3=1 and C4+C5=1. Global priorities are Cx*C1, Cx*C2 ... Cy*C5. Triantaphyllou refers to global priorities. Once you know the critical global value, you can calculate back in the hierarchy to find the corresponding local priorities.

Nolberto Munier Klaus Goepel

thanks for the answers!

In the attachment I have run the problem with numbers. It is about the emissions in truck traffic. The goal is to reduce emissions with digitalization measures and if this is possible, to avoid them completely. Accordingly, alternatives 1-7 represent digitization measures. The criteria from level 2 (subcriteria) refer to the 2 criteria from level 1. I have already written the respective values for the criteria or subcriteria below. On the right side you see the alternatives 1-7. They refer to each subcriterion from level 2. You can simplify the left part, that is level 1 and 2. For example, if you multiply "reduce emissions" by "load factor" you get 0.752*0.485=0.365. The remaining values are in the table as "Global Priority". If I want to calculate the final value for alternative 1, I simply calculate 0.173*0.454+...+0.365*0.445=27.1%. If I do the same for the other alternatives, I see that alternative 1 has the highest value, followed by alternative 3 with 21%.

In the second table, I now change the weighting of the "load factor", which was previously 0.485. I want to reduce it by the amount x. However, since the sum of "indirect fuel saving", "direct fuel saving" and "load factor" is now no longer 1, I must first divide the value 0.485-x by 1-x to get the new weighting for the "load factor". I also normalize "indirect fuel saving" and "direct fuel saving". I have said here as an example that x=0.1, i.e. I decrease the "load factor" and reduce it by x=0.1. With this I then get the new "global priorities", which are shown in bold in the table. If I now calculate the final alternative values, I get the value 25.4% for alternative 1 and the value 19.7% for alternative 3.

But what I'm really interested in is how strong this x has to be so that alternative 1 is no longer the alternative with the largest value. This was also the aim of my formula from the last article. That is, I leave x variable. The online tool from Goepel tells me that the "percent-top" critical criterion is the "load factor", since a change from 36.5% by absolute -34.4% will change the ranking between alternative 1 and alternative 5. I'll try to recalculate this by hand (Appendix 2) exactly as I just showed. Graphically you can do it with Geogebra. I get for x=0.362. Therefore I wonder if my calculation can be correct.

I thank you both in advance for further answers!

Dear Andreas

Thank you for the material you sen t, now, the problrma is is more understandable.

However, you use criteria terms, which meanning is unknown for us.For instance:

1-How does it mean that alternative 1-7 represent digitalization measures? Does it mean the if an alternative A5 is selected no other alternative can't be selected? If this is the meanning, it is incorrect, because you can have not one, but several alternatives witrh the same scores, and this is very common, and called 'tie'.

Hoever, you can digitalize indeed if needed; you can say: if A5 is selected, alternatives A1 and A7 can't be selected (this is called 'exc,usive condition'), but for that, you need to use binary criteria.You can do that with a new criterion where there is a 1 beneath A5, A1 and A7 and then indicating that their sum must be 1. In this way only one of them will be selected. But I understand than this is beyond AHP modelling capabilities.

2- How is the differences between 'Avoid" and 'Reduction'. Does 'avoid' mean to do nothing or keep the status quo?

3- what are indirect fuel savings and direct fuel savings?

4 - There are aspects that I don't understand. Normally in a transport system there is certasin amount of merchandise or load to be transporterd; how can you decrease them,

or how can you shorten the routes, or the routes length? Aren't they fixed?

5- When you use as a criterion 'Load fuel factor', it seems to me that the more the load the larger the fuel consumption, that is, these two or criteria are related, which was my suspition, and therefore, you can't use AHP.

6- I understand that when you use the word 'digitization', you refer to the factothat there are only two main criteria, i.e., to 'avoid' or ' to reduce'. Both are EXCLUSIVE. It is one or the other. Is this correct?

I don't thimk that you performed a sensitivity analysis, because, if it is true that you considered tha AAT procedure instead of OAT procedure, which for me is correct, you simple increased the values obtained forTable 1 and then by multiplying the three criteria by the same amount

I agree with Klaus. in the sense that I don't understand either the diagram.

I run this problem, using thr values from Table 1, and using another MCDM method.

I got as a reasult A4 =A6 > A2 > A3 >A1

Your ranking is: A1>A3 > A4 = A5 > A6 > A7 > A2

In my result, A4 has only a lithe margin in one of the criteria; that measnd that it is not very stable.

I hope thisd analysis can help you

Andreas K. When I take your numbers and do the analysis according Triantaphyllou (see https://bpmsg.com/sensitivity-analysis-in-ahp/, eq.3), there is no way to change one of the global priorities to get a change in ranking between Alt1 and Alt3. See the table attached. You can have a change between A1 and A4 or A1 and A5, but only when you decrease criterion 5 by 35.1% resp 34.4%. The most critical criterion is criterion 2, a change by +0.8% will change the ranking between Alt2 and Alt7 (second table, marked in red).

Nolberto Munier this is regardless by what method the criteria weights are determined, i.e. with or without AHP.

Dear Klaus

Thank you for your message

For Sensitivity Analysis (SA), and once the best solution has been reached, the right term in any inequation can be used as a parameter, and normally in MCDM, it represents resources as well as criteria limits.

Since it is part of the inequation, any change may produce a change or not, in the best alternative position in the ranking. As you know, this change implies a parallel displacement of the line, plane, or hyperplane defined by the inequation.

This movement will certainly change the value or score of the best alternative, however, it does not necessarily mean that it will change its position as the best, but it will, when the change is larger than the allowable range for the criterion is changed.

You cited George Dantzig.

For those who are not familiar with this name, he was an American Mathematical Scientist, that developed the Simplex algorithm for optimization in Linear Programming (LP), used in thousands of projects since 1947, and selected as one of the best mathematical algorithms in the XX Century. LP was possibly the first MCDM method. This is the same algorithm that constitutes the core of the SIMUS method, with which I solved the problem posted by Andreas, and using his data.

Your page reproduced possibly one of the best and most concise definitions of SA, due to Dantzig.

Sensitivity analysis is a fundamental concept in the effective use and implementation of quantitative decision models, whose purpose is to assess the stability of an optimal solution under changes in the parameters. (Dantzig)

The two keywords here are ‘stability’ and ‘parameters’, the first refers to the strength of the solution found, the second to parametrization. These equations are not parametric, however, they will, when in SA, you use the right hand of the inequation as a parametric variable, and thus, the values of the left hand are a function of it.

This is the problem with weights: They can’t be used as parameters because they don’t have ANY link with the criteria values. As a matter of fact, they were computed without considering the alternatives.

Consequently, how can you use subjective weights to evaluate criteria, which are assumed to evaluate alternatives, if there is nothing in common? Compare them with objective weights from entropy and statistics, which are derived considering the discrimination existent among a criterion value. In AHP, the so-called weights, are only a measure of the relative importance among criteria, no more than that.

Answering your comment that any weight follows your procedure, I believe that it is correct, but on what purpose, if they are not suitable to evaluate alternatives?

https://iopscience.iop.org/article/10.1088/1742-6596/1028/1/012069/pdf

Dear Deep

Thank you for sharing the article.

Do you really believe that an engineering problem like this can be solved by pair-wise comparisons and based on preferences?

In addition, did the authors realize that their criteria are independent, and thus, they can't use this method?

Klaus Goepel Nolberto Munier

Thank you for your responses!

Due to time constraints, I can only answer you now.

Dear Mr. Goepel:

Thank you for doing the calculation. Attached you will find the result from your website. Criterion 4 (direct fuel saving) is given there as a percent-any critical criterion. Then the order of alternative 4 and 5 changes, but you say that the percen-any critical criterion is criterion 5, is that right? This confuses me...

Dear Mr. Munier:

1. we just want to generate a ranking. We do not (yet) derive recommendations for action.

2. "avoid" means to give up 100% of the (additional) emission output. "Reduce" means you have an emission output, but you can't avoid it 100%, so you have to look to reduce it.

3. indirect here means that fuel is only saved when someone reacts to an electronic display, for example. That is, nothing is done automatically.

4. we make a simplified assumption

5. by bundling loads on one vehicle the trips of other trucks can be prevented

6. I still do not fully understand this question. Could you elaborate on this?

Thank you both!

Translated with www.DeepL.com/Translator (free version)

Dear Klaus and Andreas

Thank you for answering my questions.

If I don't remember wrong your scenario deals with environmental contamination. If this is correct, I have some observations to your explanations

1. If you only want a ranking this must be feasible, in the sense that it must consider how strong the best alternative is. Therefore, you must take action, and it is not a matter of recommendation.

2. I don't think that it is normally feasible to eliminate contamination in 100 %, and of course, if it exceeds established limits, you need to reduce it. However, avoid and reduce do not have any sense if you don't establish limits. For instance, reduce SO2 to what limit? Maybe you can reduce say by 10%, but how is it related to the maximum limit allowed for SO2?. Is that enough? This is the problem in MCDM methods that don't work with resources values, and they assume that they are infinite, which of course, is no-sense

3. Sorry I don't understand your explanation of 'indirect'. What does it mean 'someone reacts to an electronic display, for example. That is, nothing is done automatically'.

If your software is properly designed, it can do some things automatically. It is simply a matter of comparing an established value with the obtained value.

4. What is your simplified assumption, because in AHP all are assumptions?

5. It does not mean that you can supply in time all destinations

6. I don't remember what was my question. Kindly, repeat it to me.

Andreas K. The website result is correct. percent any critical criterion is criterion 4 changing A4-A5. You can actually download the complete sensitivity tables via csv.

Klaus

Please open the attached file.. It is regarding a question you posed on February

Hope it can help you

Nolberto

Nolberto Munier Dear Nolberto Munier,

thank you very much for the detailed file! We got a very good grade, also thanks to your help. I will probably use an AHP for my master thesis as well and will refer to the sensitivity analysis. Maybe I will write to you then. Until then!

Dear Andreas

Congratulations. I am happy that I could collaborate to your success

Nolberto Munier Hi Nolberto, thanks for the detailed answer! I am moving forward and implemented a group consensus cluster algorithm in my AHP-OS software. Paper in preparation.

https://bpmsg.com/ahp/

Dear Klaus

Thank you for your acknowledgment and for the material attached.

I read it, and reckon that it is a very good introduction for beginners. My praise for your intention or objective aimed at helping people, certainly not for the method itself that you enthusiastically support.

It is indeed very refreshing to know that you have - if I remember right - about 14,000 followers; it has to be complimented because you are disinterestedly assisting them, but you are not doing them a favor if you don’t let them know, at least in your presentation, the pros and cons of AHP, when declaring that it is a tool to solve complex scenarios, when in reality, it only can solve some type of problems, following a certain structure, because Saaty created AHP for that.

It is not his fault if AHP was adopted by enterprises assuming that it could solve their problems, due to the fact that they also had used during centuries the hierarchical structure.

You know that the structure of problems or scenarios changed, when environmentalists and social groups, demanded that the traditional cost-benefit analysis for selecting and analyzing projects, was no longer valid since there should be room for criteria related to these disciplines, and thus, considering many more aspects, and paving the way for ELECTRE, PROMETHEE, SAW and many other methods, with a more flexible structure. However, the original structure of AHP did not change, and it appears that there was no interest in disturbing the demand for AHP.

Saaty said that “The AHP is the only and rigorous mathematical way for the measurement of intangibles. It is not going to get old for a long time”

I had the privilege of corresponding with him in February/March 2017 interchanging ideas, and with respect to his memory, I will refrain from making comments about this sentence.

In my opinion, it does not matter if a mathematical method is considered obsolete. If it were, Einstein’s General Theory of Relativity, revealed in 1915, shouldn’t be used, and after 107 years it is today as valid as it was at that time because our universe did not change.

However, with AHP it is not the same, because most possibly it was a good method in the 70s. to address certain kinds of problems, but at present, it is NOT used for the purpose for which it was designed, and in addition, in a completely different scenario. This is the quid of the question, and something many AHP supporters refuse to see. Therefore, advising practitioners about this circumstance is a task for us, who have many years of experience and practice in MCDM, and this is the reason I am criticizing your presentation.

As you probably know, I am addressing this issue in RG since I joined it, about six or seven years ago. Unfortunately, there is no proof that I succeed, since, after 130,700 readings of my comments, nobody refuted them, which, as a colleague said a time ago, means that there are no logical answers.

Since you ask for feedback, here it is:

1- You use some old clichés that have been proved to be not credible; I am surprised that they come from a widely recognized expert in AHP like you.

It is true that AHP is easy to understand, widely used and with thousands of applications, but it is not true that it can solve complex problems, for different reasons, one of them is that its structure is tied to a lineal hierarchy, which is inexistent at present in complex real-life problems.

There is no doubt that a project like selecting a route for the construction of a high-speed train for instance, can’t be represented as a rigorous top-down hierarchy.

Do you believe that a complex project, like the selection of sites on a river for the construction of large hydropower plants, considering many criteria and sub-criteria (certainly more than 9!), can be solved assuming that it is linear, without precedence between alternatives, and thus, assuming for instance, that the discharge flow of a plant does not affect the capacity of the second, as it happens in reality?

Can you imagine determining the output of an oil refinery, with several products, that are subject to crude oil supply, the storage capacity of final products, and demand, can be solved by intuition?

By the way, part of this problem, the number of different products, was solved in the 50s. using Linear Programming, and at present, there is not an MCDM method that can even approximate it.

I could continue but I don’t think it is necessary. I believe that you understand my point. Neither AHP nor ANP can solve problems even considerably less complicated. Just think, how can you analyze a problem if you don’t take into account the resources needed for each one of the different criteria? AHP is not the only one since most MCDM methods assume that resources are infinite……………

2- By the way, why don’t you mention that AHP establishes that all criteria MUST be independent? That is a serious restriction, and even Saaty warned about it, back in the 80s, however, practitioners apparently ignore it or prefer to ignore it, as I was answered by one recognized professor.

However, don’t believe me, just verify it by yourself; go to Scopus and read some abstracts of thousands of papers published using AHP. Obviously, reviewers often have a blind eye to that…., or maybe ignore it…..

3-Your sentence: “Rational Decision Making Made Easy”

Dictionary definition of ‘rational’: Based on or in accordance with reason or logic.

Please illustrate to me where reason and logic are present in AHP?

You say that it allows making decisions in a more rational way. You know that there is no rationality, no research, no logic in AHP unless you consider that determining weights using intuition is the output of research, reasoning, knowledge, and experience.

4- You say that the hierarchy makes a problem better understandable, and this is normally true, for it helps to understand the nature of a problem. Ironically, it is precisely that knowledge about the true nature and characteristics of a scenario, that makes AHP not able to solve complex problems, because the method can’t model these requirements.

5- You say “As you need to structure the problem as a hierarchy’’

Yes, you can do that in AHP, provided that there is a linear hierarchy. What happens if the problem requires for instance that in order to start activity D you need to have completed activity B?

For instance, in selecting between several construction alternatives on an island, there is a mandatory alternative that must precede all of them: the necessity to first build a bridge to supply personnel and materials. If you don’t consider this precedence, the result can indicate to build first the buildings, leaving the bridge as the last undertaking. This is not mathematics, but common sense and knowledge.

I have detected in many, if not in most projects published solved using MCDM methods, that authors use a method blindly, without considering the real problem. That is, to solve a problem in MCDM it is necessary to have practical and theoretical experience. For instance, the engineering department gives the different alternatives, but it is the DM who has to ask questions about a project, and with their answers, he is able to build a representative decision matrix.

6- You rightly say: “consider possible decision criteria and select the most significant criteria with respect to the decision objective”

What happens, as is normal, when there is more than one objective?

As a bottom line, I believe that you did a good job illustrating people, but unfortunately, the method does not match your goodwill. In my opinion, your presentation should instruct practitioners about the advantages (very few), and disadvantages (very many) of AHP, using your experience and taking advantage of your influence and prestige,

AHP is a method that probably was good in the 70s.` when companies followed the lineal structure, but that changed, and it is inadmissible that it is still being used at this time.

Sorry, Klaus, it is not my intention to belittle your work, far from it, but I am puzzled that you believe in this method can be used to solve complex scenarios.

Regards

Nolberto

Dear Nolberto Munier,

thanks for your feedback, always appreciated.

Just a short answer today, as we had this discussion before, and I don't want to repeat myself. Yes, of course, AHP can not be used for everything, and for sure, there are many complex (or even less complex) scenarios, where AHP is not suitable and would be the wrong approach to use. (I assume, this was also the reason that Saaty extended the method and introduced ANP, though in my opinion it is very difficult to model a decision problem in ANP, I personally gave up on it.)

It is also not about "believing" in a method: I see AHP as one tool in a big toolbox, and as such it is a good thing to have and there is nothing wrong with it. As I told you before, I was able to use it in practical business applications successfully. (Yes, I know, It depends on what you define as 'complex' and as ' success'.)

I respect the many users of my AHP-OS. It is their decision and depends on their evaluation, whether AHP is the right tool for their projects, and whether they want to use or not to use the method. No need to argue for or against it.

Regards,

Klaus

P.S. I remember my young brother, trying to repair his bicycle by putting in a screw using a hammer ...

Dear Klaus

Thank you for your answer

Yes, I remember that in the past we discussed some points, but I don’t remember if we agree in most of them or at least partially, or reached or not some constructive conclusion.

It is important your second paragraph where you assert, with reason, that ‘AHP can not be used for everything, and for sure, there are many complex (or even less complex) scenarios, where AHP is not suitable and would be the wrong approach to use’

I think that even the staunchest AHP supporter recognizes it, and I have been told the same thing by different colleagues, opinion that I share, and that is applicable to all MCDM methods, not only to AHP. I also share your opinion that Saaty developed ANP when he realized that the largest AHP limitation was its lineal hierarchy.

As I expressed, AHP was a great tool and probably still is, for the purpose it was created; that is military problems, because of its lineal structure, and was also suitable for personal and trivial problems, because they generally follow the lineal structure. It seems that it is useful in those scenarios related with some social issues, health care and personal decisions, all of them with a large degree of subjectivity, and where rational decisions are often absent.

Even for those cases, I criticize AHP for its nebulous structure, where everything is assumed and accepted, like establishing comparisons of things that perhaps can’t be compared, like non - measurable issues, for instance, that happiness is two times more important than friendship, and on what there may be many different answers, and depending on different circumstances and environments, that is, even for an assumption, it is very naïve and simplistic.

Or assuming that what the DM estimates is transferable to the real world, (this is not even a credible hypothesis), or that this is transitive (when the real world generally is not), or that trade-offs can be used as weights, (which is not acceptable, since both are different things) etc. What confidence can you have on a method where nothing is explained, and where rationality does not exist?

It is funny to read sometimes, that AHP is based as ‘a rigorous mathematical method’

Many years ago, when I learnt AHP, and from the very first reading of the method, what really impacted and impressed me, was that all of these assumptions were not justified, and however, they were freely accepted by people without thinking or wondering about their genesis, when obviously, they defy common sense.

The only exception is the use of the Eigen Value (which could be replaced by the geometric mean).

You have used the toolbox analogy, and it is very good. In real life, you look for the tool that is appropriate for the job, and in multi criteria, given a problem, you look for the tool that can do the job.

However, it appears, because the overwhelming use of AHP in comparison with other methods, that it is a one thousand uses tool, from selecting a restaurant for dinner to decide which is the best rocket to put a satellite in orbit.

It seems that people do not think if they can apply a tool with so many unexplained assumptions, perhaps acceptable in trivial problems but not for complex ones

AHP looks like a kitchen receipt. ‘Mix 200 gr of flour, 6 eggs, two cups of cold water…….’ Voila, you get your cookies. The cook does not care if the procedure makes sense, she believes that who wrote the receipt knows what to do.

The similarity with In AHP, is that the DM selects 2 criteria and decides, just by intuition, that C1 is greater than C2 (she does not care if it realistic or not, the method says nothing about it), then goes to a table and finds that an adequate number is 5, why? it does not matter, the method say so, and repeats the process with other pairs it, then mix them all and get the answer, but a formula says that that is incorrect and that she must correct it. She thinks, well, I did something wrong, but I don’t have a hint where is the error, and then, she continues because the model says so, and so on…. She may ask herself why she has to do things that she does not understand, gives up and says, well, I do what I am told to do…Very professional, indeed…….

You say that you have been able to use AHP successfully in practical business applications, and I don’t have any reason to doubt your words, but as you honestly say, all depends on what you call success. Maybe the success was in using the algorithm and getting results.

And I think that your use of the word ‘business’ is relevant, because in many of them there is a good deal of personal decisions. But when I read that AHP has been used for determining railways performances, or for selecting site locations, or for determining environmental indicators, or for GIS applications, I think that something is utterly wrong.

Of course, you must respect the many users of your AHP-OS, and if you are in this business is because you believe in the method, even if you know its structural drawbacks, and for me, that is puzzling.

However, as far as I know, you limit your explanation to the mathematical part of the method, i.e., the EV and the analysis of weights, and honestly, you are doing a great job on it, clarifying many doubts, helping people, and using reasoning and research, and you wisely avoid areas of AHP that I am sure are black holes for you and for me

Maybe it is I, who does not understand these unknown characteristics of AHP, and if it so, I will be grateful if you or somebody else can explain them to me.

Thank you, Klaus, for your interest

Best regards

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