Dear Hamed Taherdoost, Mitra Madanchian

I have read your paper

Analytic Network Process (ANP) Method: A Comprehensive Review of Applications, Advantages, and Limitation

These are my comments

1- in the abstract you say “The analytic network process (ANP) method is one of the most widely used MCDM methods”

I am afraid that is incorrect. The most widely used are AHP, TOPSIS and PROMETHEE. It is rare to see an article with a project solved by ANP.

2- In page 2 you say “As a result, the procedure for selecting decision-makers has developed into a more explicit form. In this setting, the decision-maker is no longer able to depend just on an approximation or intuition of an analysis of the options”

This is true, an it is one of the reasons by which ANP is not widely used. Nobody can solve complex problems using intuition.

3- ANP is not new as you say. It was developed in the late 80s.

4- AHP is not multi objective as you say. It has an objective, or goal as you call it, and adjusts everything to its compliance.

5- The feedback that you mention repeatedly does not exist in MCDM. It was a Saaty’s assumption that is only assumed, as others.

ANP does not work with dependencies but only with links expressed as arrows between nodes. Dependency is when an activity cannot start until the precedence is complete has been completed. This concept was apparently drawn from the Critical Path Method methodology. Just think, how do you express mathematically in ANP that activity A3 must be done in order to start activity A9? You can’t.

6- In page 3 “In ANP, linear top-to-bottom hierarchy structures are replaced with a feedback approach”

Interesting. Which is the source of that? Is there any demonstration? I can’t imagine a network where each link is the consequence of feedback

7- “To sum up, in ANP, a network is used to represent a system with feedback”

Could you be more explicit?

In despite of your abundant comments on how good ANP can treat complex problems, please explain me how do you manage in aspects that are common in complex problems like:

a) Say alternative A8 must precede A3, A7, and A21.

b) How ANP can manage problems where there are inclusive and exclusive alternatives, that is, you have to establish that if A8 is chosen then A2 cannot be chosen?

c) How ANP can model that a resource must be 1.5 times greater than anther resource?

d) Or that in a portfolio of projects not all of them start at the same time, and have different performance values as a function of time.

e) AHP and ANP, assume that resources are infinite, obviously, something that is false.

f) How do you establish limits for day investments?

g) What if a criterion may oscillate between a minimum and a maximum?

These are real-life problems not blackboard examples.

AHP have the same drawbacks as AHP. The only advantage is that it works with networks instead with linear hierarchies, and then criteria are interconnected in every sense, but the non-sense of arbitrarily quantifying criteria is the same as in AHP.

Curiously, you say nothing about sensitivity analysis in ANP. Why? Because it is cumbersome and very difficult to understand, and, the same as AHP, based on the assumption that the criterion with the highest weight is the more important, which does not have any mathematical support.

I hope these brief comments can help you

Nolberto Munier