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363 – Suggestion for choosing the most appropriate MCDM method to solve a certain problem

Author: Nolberto Munier

Dear colleagues

This is an old problem still unsolved, and probably it never will, if we continue using current MCDM methods. The present paper proposes a methodology to clarify this issue by following a procedure called ‘Analysis of the Main Objective’ (AMO).

AMO uses a principle, that as far as this author knowledge, has never be utilised before, and that can be enunciated as ‘Finding the objective that best reflects the purpose of the project’. That is, the criterion or objective that embodies or epitomizes what the project is aimed to. Alternatives are subject to a set of criteria of the most different nature related to economics, engineering, financing, environment, health, government, sustainability, transportation, food, social issues, manufacturing, mining, etc.

However, normally, among all criteria or objectives (both are equivalents), there is one most closely related with the purpose of the project, whatever it might be.

Examples:

· Minimize the investment objective, as in the case of a portfolio of different buildings construction project or in a mix of alternatives. The developer wants to invest as little as possible because his funds are limited, and thus, he wants to make the best use of his money. This is his priority

· Maximize the electricity demand objective, as in the case of deciding which type of installation or plant (Wind, PV, Biomass, etc.) to build. This is the basic objective

· Minimize the cost objective, as in the case of fabricating and exporting goods, subject to other criteria, like international prices volatility, competition, transportation delays, quality, etc. The result may guide a company to export or not, based on the results of the cost objective. All other criteria are directly or undirectedly, depend on it

· Minimize the contamination objective, as in the case of CO2 emissions from fossil fuel fired power plants, replacing contaminant plants with renewables. Nowadays this is the first concern world-wide. All criteria are important, but this is the most significant

· Maximize number of people objective, in the case of selecting transportation scenarios at national or regional level, selecting among air, private car, buses or trains, alternatives. This is a priority in all countries but especially in those with a very large population. This scenario looks for facilitating people movement. The most important aspect is for people to be able go to work, to schools, to hospitals, etc., the balance, is secondary. We can see it in some countries where people even travel in the roofs of overfilled railway cars; the objective is reaching the working place. Of course, the ideal would be people travelling comfortable seated, but if for whatever reasons this is not possible, people look for different, dangerous and bizarre means to reach a destination. All other criteria pale in comparison

· Maximize the enjoyment objective, in case of selecting a place for a vacation time, considering beaches, mountains, cruisers, cities, staying at home, visiting family, etc. This is perhaps the priority for everybody.

· Maximize probability of success objective, in case of selecting best health treatment for certain diseases. Very important when doctors with different opinions must agree on a treatment

· Minimize the risk objective in many different projects. Consider different risks like personnel, delays, material failure, dubious data, atmospheric conditions, strikes, etc. It is a fundamental objective in all projects; a severe transgression may produce serious problems

· In a plan to reduce poverty, maximize government help to poor family’s objective, according to different schemes (options or alternatives), like subsides, improving education, help to build their houses with affordable bank loans, etc. No need to emphasize its importance

· Maximize assisting people objective to communities affected by wars, natural phenomena (earthquakes floods, fires, etc.)., with different plans. This is prioritary as we have seen recently in some countries

It can be seen in the few cases mentioned that there is a main or primordial objective that is the essence of a project, and it is on which we are interested. It does not matter if it is weighted or not, or its relative value among the other objectives or criteria. We are not measuring its importance in numbers or in words, what we need is to establish a reachable target and select the MCDM that yield values as close as possible as the target.

Consequently, we are looking for a comparison not for absolute values. The degree of compliance with the established target, is a tangible measure that allows us to determine the best MCDM method for a particular scenario.

Suggested procedure

For starters, the DM needs to accept that criteria and objectives are equivalent - and this not an assumption, but linear algebra - and that both work with resources that can be money, people, number of equipment, percentages, contamination, etc. Each criteria/objective must have a goal, a target to achieve, they cannot be indefinite. That is, resources are the ‘material’ not necessarily physical, with what criteria work.

Thus, we can say in a housing development, that criterion ‘Water supply’, must be at least the minimum value by household, according to HWO (Health World Organization), for instance about 150 litres/day-person. This value is a target, a goal, limit, or reference, and expressed in the same units as the respective criterion, whatever they might be.

If the project is to purchase a car, there must be a criterion ‘Investment’, that puts a limit, and specifying for instance, do not spend more than 5,500 Euros, because this is the amount that the purchaser has in mind. This value is the target

If the problem refers to the selection of an electricity generation equipment, the criterion ‘Demand” says that as a minimum it must deliver 200 MWh, i.e., a minimum limit. This value is the target.

If the scenario deals with environment, there must be a value, that can be a percentage, establishing a limit, for instance, that the maximum allowable noxious emissions of NOx is 25 ppm (parts for million). This value is a target.

These four completely different cases in type and complexity have a common factor: It is that in each one there is a single criterion that dominates the rest. Dominance not in value, but in the sense that without it the project does not exist.

Just think:

A developer cannot sell a house without enough supply of water

A person cannot purchase a car if he/she does not have the money

To generate electricity, it is necessary to know the demand

A metallurgical company might be violating the law, if its emissions surpass a certain limit, which of course must be known

Observe that these anthropometric or natural limits govern our existence as in maximum car speed, water usage, sleeping hours, high and low temperatures, heavy snow, date to pay taxes, closing times in a supermarket, number of years to graduate in a university, metric system, etc.

Example

Using the energy generation case, with options or alternatives A1, A2 and A3, and four criteria (C1, C2, C3, C4), and results from MCDM methods X, Y and Z, the proposed procedure can be summarized in these steps:

1- Identify the most important criterion or objective in the project, for instance (C4) (Demand)

2- Solve the problem using the X MCDM method

3- The result may show for instance that the ranking is

A2 > A1 > A3. Therefore, A2 f is the best alternative

4- Now, for A2 observe the value for the wished objective ‘Demand’ which is 250 MWh, and compare to the same for C4, that is for instance 265 MWh, according to the X computation. As seen, the out put is higher than the wished value of 250 MWh. Consequently, A2 surpasses the demand in 15 MWh

5- Run the project data again using the Y method witch that yields this ranking: A1 > A3 > A2

In this case, assume that objective C4 is exactly satisfied with 250 MWh

6- Replicate the process with the Z method which yields this ranking: A3 > A1 > A2, and verify that C4 is now 240 MWh, t hat is, short in 10 MWh to satisfy the estimates demand of 250 MWh

7- It appears evident that the X method produces the best solution since it yields the best value for C4, the main objective

Conclusion

As can be seen the proposed procedure is simple. It does not matter which MCDM methods are used, it is irrelevant if they employ subjective or objective weights, and it is immaterial the correlation value between them, that in reality does not make any useful contribution. No personal opinions and assumptions are needed and it can be performed very easily, since it only requires to run the same problem on the chosen method, and analyze the main objective.

Naturally, the reader can say ‘Yes, it can help, but how do we use it if our MCDM methods do not use resources or limits’?

Well, that is the problem, which is not attributable to the procedure but to the methods themselves, and it is due to the algebraic process of most of them, with the exception of PROMETHEE/GAIA and SIMUS, that do take resources into account, deeming criteria as objectives with a target, not as simple restrictions as other methods do.

Non considering resources indicate that out of these two methods, the balance of MCDM methods assume that resources are bottomless, limits do not exist, and that there is no need to determine how a criterion performs. All is reduced to find the best alternative, when it is fundamental to see how each criterion/objective performs.

This information allows the DM to make the correction in data he considers necessary according to the nature of the problem and on what the stakeholders say.

Some readers may think that sensitivity analysis is the response to this problem

No, definitely it is not, and it addresses another different problem, that is finding if the alternative selected is strong or not.

If this author’s opinion it appears that in MCDM it is enough to find the best alternative, yes, it is extremelly important but it is not enough.

We need to know in what extent each criterion has been satisfied. This is the information that the DM needs

Your comments will be very welcome

Nolberto Munier