Science or fiction? ( 2)

Nolberto Munier

Estimated colleagues

In “science or fiction ( 1)”, I reported multiple dubious procedures, due to applying assumptions without any mathematical support, lacking rational explanations, and abundant personal beliefs, as they were created in the 70s. Now, in “science or fiction 2”, I am proposing to promote research to modify this situation. True, there has been advances in perhaps improving data reliability, but no action has been taken to improve the structure of these methods, and then, I wonder what is the purpose in continuing using them when everybody is aware that they are unable to model the characteristics of real problems?

Nowadays we are not solving real problems, but just consciously ignoring certain characteristics of projects, believing that they cannot be modelled, and then ‘solving’ not even proxies, but more relaxed versions that are only coarse simplifications of them. In my opinion I believe that we, researchers, should allocate our efforts in trying to model problems mathematically, with new structures, instead of wasting time in improving and justifying arbitrary pair-wise comparisons, weights, inconsistency, normalization, fuzzy, etc. in obsolete structures.

To be very clear, I am talking that we must consider some characteristics that appear in many projects, such as precedence between alternatives, inclusivity and exclusivity, multiple scenarios, real importance of criteria, not invented as we do now, resources and targets, not considering that they are infinite as present, use of binary variables (0-1), essential in many problems, marginal costs, enhance the fundamental participation of the DMs, that at present is more concerned to determining arbitrary weights, which are useless, because they cannot evaluate alternatives. Of course, normally not all criteria have the same importance, but the method has to determine it based on data, not from the DM mind or wishes.

We need the DM know-how, experience, research, not limited to applying a certain method, but by analyzing both internal and external or exogenous variables, or considering time as a variable to take into account, not as we do at present that real problems are static, and do not change during their execution.

I wonder why researchers don’t explore new avenues instead of clinging to inefficient and sometimes absurd techniques as pair-wise comparison, or assuming that the real world follows what they have in mind, or determining, by heart or intuition that a criterion is more important than another and putting a value to those preferences. Is there any nuance of reality and common sense? None.

What is amazing is that hundreds of MCDM problems are ‘solved’, not even respecting the structure of the method, and blatantly adapting them to their needs. A typical case is AHP, that everybody knows works only with independent criteria, as was created by Saaty, and even when himself warned in writing that this must be respected. Many people do not pay attention, and even knowing that, they don’t care, (I bear witness of this, it is not my invention), and use the method with criteria highly related, and then declare that an optimal solution is achieved. My question is: Why reviewers, not all of course, accept this flagrant violation? By ignorance or due to personal convenience, just to be able to add in their CV that he/she was a reviewer and his/her name published in Publons?

I guess that maybe 90% of the papers published using AHP, have this transgression. Did anybody complain? No, what for? “It is not my business”.

I am not precisely an AHP defender, quite the opposite, however, the method is not to be blamed by this violation, since it was created with a different structure and with another purpose.

Probably a reader will ask himself if what I say in this paper makes sense, when there are thousands of papers published using some of MCDM methods.

In many of those thousands of articles, the author/s proudly announce that the method used is efficient or that the problem was satisfactory solved. Nobody can assert this, because the result in any method, is product of an algorithm fed with real and subjective data. It only shows that the algorithm worked as designed, no more than that, inclusive giving a solution when the problem is unfeasible. No method can assert something like this, because nobody knows which is the real result.

Consequently, it is impossible to know the closeness of a result to reality, and thus, every result is acceptable. Maybe in our future, this uncertainty will disappear, and if so, we won’t be needing a MCDM method anymore. As Steve Percy said “What gets measured gets managed. What gets communicated gets understood”

I said before that actual methods cannot solve real-life problems, and at the same time, I will be describing a bunch of problems. It is not a contradiction or a mistake, because there is another approach, probably the grandad of decision-making methods. That procedure is Linear Programming (LP); technically, it is different in purpose to MCDM because LP aims to optimization of alternatives and balance of resources, when MCDM aims at balancing trade-offs.

The creator of LP was awarded the 1956 Nobel Prize in Economics because its development, and made accessible to everybody in 1948 by another researcher, using the Simplex algorithm. This algorithm is since 1993 part of Excel, and then free, and available in all personal computers. There are not pair-wise comparisons, no weights, no assumptions, no biases, no calculations from the user, no need to unify responses from different DMs, no unnecessary discussions about consistencies, which, by the way, are irrelevant.

LP is very easy to manage; the user just fills the initial decision matrix, establishes, if he has, and with the stakeholders, the target or goal they want to achieve for each criterion. If they do not have them, just do nothing. Next, the DM selects, using a drop-down menu, one of the three mathematical symbols needed. They correspond respectively to maximization or benefit (≤), minimization or cost (≥), and equalization (=) or equal to a budget, and press Start. He can choose step-by-step information or ask for the end result, and press the start key.

The reader, with reason, will wonder why if LP is so good, it is rarely used.

Very simple, because LP is mono objective and does not work with qualitative criteria, and this is not realistic in nowadays projects that incorporate environment, economics, engineering, social issues, etc.

As designed, if gives optimal solutions which are Pareto efficient. To overcome these two drawbacks the SIMUS method was developed that can work up to 100 quantitative and qualitative criteria, in any mix. That is, it is a multi objective decision-making method. There is a software written in Visual Basic that very rapidly solves complex problems. It is grounded on LP and starts with an Excel matrix and uses the Solver algorithm that is a macro in Excel since 1993.

If interested, email your request for a software copy to:

[email protected]

It is free, and you can share it with as many persons as you want.

How to work with SIMUS and what can you get out of it

Upload the Solver algorithm, necessary for SIMUS work

Go to Excel, File, Options, Add-ins, select Solver add-in. The word ‘Solver’ will appear in all Excel spreadsheets in the top right corner of the screen. Therefore, when a user builds the decision matrix of a problem in Excel, Solver is already there, and SIMUS is able to start, this is done only once.

Now electronically transfer your problem to SIMUS

You have your matrix in Excel. Select the Simus v.1.3 icon, select DB and further Imsimus, paste and save

Delete every other Excel file you have open except that of the original matrix.

Access again Simus v.1.3, click in Load Simus, then Import and finally Recover.Y ou will be in the first screen of Simus. If you wish, in this screen you can access an extensive tutorial illustrated with real-life examples and their solution.

You will have your complete matrix there, and the only thing for you to do is inputting the targets- if you have them, if not, the software will input them for you. Last step, from a dropdown menu, indicate the corresponding mathematical symbols for maximizing, minimizing or equalizing. to each criterion, there can be any mix in the matrix, including binary (0-1) variables as well as fuzzy crisp values. Press the start key and you are done. You can select step-by-step or the final result. The result of your problem will be saved in an Excel library, to be accessed and reutilized at any time.

The final screen displays at left a complete look of the project data and its solution, in four matrices identified by colors as:

Red: Normalized decision matrix

Black: Original decision matrix

Blue: ERP Efficient Results matrix

Blue: Normalized efficient result matrix. This is the matrix that interest you the most. It shows:

§ Iin a solid blue row, the final scores for each alternative. The best alternative has the highest score

§ In red values, the ranking of alternatives, from the best at left to the worst at right

§ A blank row will indicate which criterion is not feasible

§ At right of the screen a table in green gives the marginal values or utility for each criterion

§ The same table informs about the basic criteria, i.e., the criteria that influence the best alternative

§ At bottom right of the screen a small table in dark green gives the period or interval in which each criterion is allowed to vary, fundamental for Sensitivity Analysis

§ Access to data for performing a reliable sensitivity analysis considering the different variations in max and min of all criteria simultaneously

§ The bottom part of the screen shows in brown the PDM or Project Dominance Matrix, with the result solving the problem, not by weighted sum, but using outranking. Notice the red values line that depicts the ranking, using outranking instead of weighted sum, and that both ranking coincides. There is no need to point out that reaching the same result using two different methods, gives a measure of high reliability of the method and internal consistency.

§ Allows by a simple comparison to compute in percent, the compliance of each criterion target

§ Consider exogenous variables with even daily variations

§ Contemplates working with fuzzy, fed by mathematically generated low and high values

§ Gives the DM the opportunity to analyze the final result, and introduce his weights, corrections and even rejection of the result, or add/delete alternatives and criteria with no effort

§ Work with DOE (Design of Experiment), using the same matrix modified in each case, without writing a new one

§ Defines when there are ties of alternatives selection

§ Saves the whole project and solution for further consultation

If you have a difficult problem and find it difficult to model it, please contact me; I will be more than happy to help

Some problems solved by SIMUS

1- In DOE (Design of Experiments), it is usual to run a software many times with different values in the initial matrix. The same original matrix structure can be used hundreds of times, i.e., no need to build a new one. Simply, delete the old values, which result has been automatically saved, and put the new ones, and press Start.

If the DM finds that new criteria and alternatives must be added, no problem. For that, when building the initial matrix in Excel add a couple of rows or alternatives and a couple of rows or criteria, and keep them blank. In a next run the DM can added alternatives and criteria in the blank columns and rows. However, if more criteria are added, remember to input the target and the symbols.

2- A normal problem involves working with its endogenous variables, but in more complex scenarios external or exogenous variables must also be considered simultaneously with the endogenous ones. These exogenous variables that do not depend on the problem examined and that nobody can control, like highly variable international prices for commodities such as crops, oil, cooper, etc. may influence the original scenario and even change the best solution found.

For instance, in a common problem like determining location and size to install an oil refinery, aspects as historical oil price series that varies almost continuously, and then the demand, may influence the original result found, must be mandatorily considered

SIMUS allows to compute the added risk to the project due to these external variables. For that, it works with marginal criteria or marginal utility values, automatically computed based on time series of alternatives published in the Web. In here, the labor of the DM is invaluable and no software can compete with him, because it involves research, interpretation, reasoning, vision and AI. It is a symbiosis between man and machine

3- As said, resources are not unlimited. For this reason, it is possible to mathematically compute the interval of variation. The software will work with that interval that is also useful in a fuzzy approach, using for instance a triangular membership

4- Considering dynamical scenarios, that is, when time counts, a typical problem is the very actual transition to convert by 2050 all electricity generation to zero CO2. Two years ago, a paper was published using SIMUS to determine the best selection of oil-fired power plant to be decommissioned between 202 3and 2050. At the beginning of 2025 another paper was published using SIMUS and AI to determine the compliance in years to come for demands of critical minerals like cooper and lithium, related to established targets fixed by United Nations for each one of its 17 SDG (Sustainable Development Goals)

These are problems with some complexity, but that present-day MCDM methods are unable to grasp.

For instance, at present, in a portfolio of several projects, all of them are considered to start and finish at the same time, something clearly unreal, and considering that aspects like yearly advance of each project is considered constant, when in reality is follows a logistic curve. This case was solved by SIMUS and published 2019.

MCDM methods cannot consider even a simple problem like determining the amount of water to be provided in a new housing development, that is, the daily water amount has two limits, the minimum one established by the WHO (World Health Organization to satisfy minimum requirements per person and per day, and the maximum, to avoid waste. They can’t either determine is the project is feasible, that is, there could be not enough water volume for the total development, according to the criteria requirements

5- Present-day methods are unable to give information about on what percentage a criterion was satisfied.

6- They cannot determine realistically which is the most important criterion, something fundamental for the stakeholders to analyze if a project is or not convenient. For instance, it is established that the Internal Rate of Return, (IRR), one of the most important financial indicators in a project, is say 9.5%, will be achieved or not. In most projects the author/s proudly announce that the solution found is optimal. Is there any proof of this? None, because he does not know what is the real IRR from computation.

7- However, probably the worst drawback of these methods is that they ignore that a matrix represents a system, and as that, there is high interconnectivity between criteria. A criterion may influence other and in turn, another, in a chain. What does this mean?

That the actual procedure of adding up results of all criteria is erroneous because then, the interrelationships are not considered.

The correct way is to work with intersections or multiplications. Even many aspects of life and physics show that the final result is not necessarily equal to the sum of the parts. A typical example is the very well-known Venn diagram where the three legs of sustainability are Economics, Social and Environment that interact in one space shared by them. Needless to say, intersection is the core of LP

8- At a world-wide scale countries are trying to improve poor people living conditions by building hundreds of modest houses in an area, with all infrastructure services, pavement, sewerage, water, electricity, etc. Generally, more than one development is built along a certain time. The objective is to evict people living in shanty houses, generally in a large city, and transferring them to the new dwellings, normally sponsored by development banks. It is then necessary to coordinate which emptying slums and transferring people to the new development. This is a complex problem linked to many variables like funding, construction time, payment capacity for dwellers, cashflows, etc.

SIMUS was used years ago i n a similar scenario involving several Ghana villages without basic infrastructure, financed by the World Bank. The SIMUS study was made by a private firm, and the United Nations Development Agency in Nairobi nominated the work proposed by SIMUS for the Africa Prize. This project was also published.

9- Sometimes alternatives in a project are implicit but not explicit. As an example, there is a need to build a highway between a city downtown and its international airport located 25 km away. Early, years before, the connection was done by using existing avenues, streets and junctions between the city boundary and the airport, with three important medium size cities in between. The government decided to build a high-speed highway between the city and the airport, using some of the existent roads and avenues in the rural area outside the city border, indicating that cities A, B and C between the two ends must have a rapid and safe access to the highway through cloverleaves interchanges.

Therefore, there were a large inventory of alternatives according the routes selected by a user, but not defined alternatives. Consequently, unique route should be generated. To complicate the scenario, there were exclusive between roads related to the cities A, B and C, because for instance three existing routes were already in use between the airport and city A, but only one of them should be chosen. The matrix was formed including the nominal criteria regarding cost, speed, time, ancillary structures, etc., and in he same matrix was another smaller pertaining the exclusivity and inclusivity.

SIMUS designed a continuous path from the airport that connected the three cities A, B and C and being the shortest rout between the airport and the city. This study was published.

10- Determination of sources of contamination in the Niger River, Nigeria, also published

As can be seen there is a large variety of projects and different degrees of complexity that can be solved using the adequate MOO (Multi Objective Optimization) method, SIMUS or others.

Thank you for your reading

Nolberto Munier

[email protected]