Friday, October 23, 2015

An Analysis of Multi-Criteria Decision Making Methods

Mark Velasquez and Patrick T. Hester (2013)


This paper performs a literature review of common Multi-Criteria Decision Making methods, examines the advantages and disadvantages of the identified methods, and explains how their common applications relate to their relative strengths and weaknesses.

Multi-Attribute Utility Theory (MAUT)
MAUT is an expected utility theory that can decide the best course of action in a given problem by assigning a utility to every possible consequence and calculating the best possible utility. The major advantage of MAUT is that it takes uncertainty into account. It is comprehensive and can account for and incorporate the preferences of each consequence at every step of the method. This amount of accuracy is convenient, however it can lead to many possible disadvantages. An incredible amount of input is necessary at every step of the procedure in order to accurately record the decision maker’s preferences, making this method extremely data intensive. The preferences of the decision makers also need to be precise, giving specific weights to each of the consequences, which requires stronger assumptions at each level. MAUT has seen heavy application in economic, financial, actuarial, water management, energy management, and agricultural problems.

Analytic Hierarchy Process (AHP)
AHP is a theory of measurement through pairwise comparisons and relies on the judgments of experts to derive priority scales. One of its advantages is its ease of use. Its use of pairwise comparisons can allow decision makers to weight coefficients and compare alternatives with relative ease. It is scalable, and can easily adjust in size to accommodate decision making problems due to its hierarchical structure. Besides, it is not nearly as data intensive as MAUT. Due to the approach of pairwise comparisons, it can also be subject to inconsistencies in judgment and ranking criteria. One of its biggest criticisms is that the general form of AHP is susceptible to rank reversal. Due to the nature of comparisons for rankings, the addition of alternatives at the end of the process could cause the final rankings to flip or reverse. AHP has seen much use in performance-type problems, resource management, corporate policy and strategy, public policy, political strategy, and planning

Fuzzy Theory
Fuzzy set theory is an extension of classical set theory that allows solving a lot of problems related to dealing the imprecise and uncertain data. It has many advantages. Fuzzy logic “takes into account the insufficient information and the evolution of available knowledge. It allows imprecise input. It allows a few rules to encompass problems with great complexity. For disadvantages, fuzzy systems can sometimes be difficult to develop. In many cases, they can require numerous simulations before being able to be used in the real world. Fuzzy set theory is established and has been used in applications such as engineering, economic, environmental, social, medical, and management.

Case-Based Reasoning (CBR)
CBR is a MCDM method that retrieves cases similar to a problem from an existing database of cases, and proposes a solution to a decision-making problem based on the most similar cases. This provides the first of its advantages, which is that it requires little effort in terms of acquiring additional data. It also requires little maintenance as the database will already be existing and requires little upkeep. One major advantage that it has over most MCDM methods is that it can improve over time, especially as more cases are added to the database. It can also adapt to changes in environment with its database of cases. Its major drawback is its sensitivity to inconsistency in data. Previous cases could be invalid or special cases may results in invalid answers. Sometimes similar cases may not always be the most accurate in terms of solving the problem at hand. CBR is used in industries where a substantial number of previous cases already exist. This includes comparisons of businesses, vehicle insurance, medicine, and engineering designs.

Data Envelopment Analysis (DEA)
DEA uses a linear programming technique to measure the relative efficiencies of alternatives. It rates the efficiencies of alternatives against each other, with the most efficient alternative having a rating of 1.0, with all other alternatives being a fraction of 1.0. It has a number of advantages. It is capable of handling multiple inputs and outputs. Efficiency can be analyzed and quantified. It can uncover relationships that may be in hidden with other methods. An important disadvantage is that does not deal with imprecise data and assumes that all input and output data are exactly known. In real world situations, however, this assumption may not always be true. The results can be sensitive depending on the inputs and outputs. DEA is used wherever efficiencies need to be compared. This is commonly used in economic, medical, utilities, road safety, agriculture, retail, and business problems.

Other Methods

SMART: SMART is one of the simplest forms of MAUT. It requires two assumptions, namely utility independence and preferential independence. This method conveniently converts importance weights into actual numbers. Major advantages of SMART, in addition to those described in MAUT, are that it is simple to use and it actually allows for any type of weight assignment techniques. It requires less effort by decision makers than MAUT. It also handles data well under each criterion. Like MAUT, a disadvantage is that the procedure for determining work is not convenient considering the complicated framework.
Goal Programming: Goal Programming is a pragmatic programming method that is able to choose from an infinite number of alternatives. One of its advantages is that it has the capacity to handle large-scale problems. Its ability to produce infinite alternatives provides a significant advantage over some methods, depending on the situation. A major disadvantage is its inability to weight coefficients. Many applications find it necessary to use other methods, such as AHP, to properly weight the coefficients. Goal programming has seen applications in production planning, scheduling, health care, portfolio selection, distribution system design, energy planning, water reservoir management, timber harvest scheduling, and wildlife management problems.
ELECTRE: ELECTRE, along with its many iterations, is an outranking method based on concordance analysis. Its major advantage is that it takes into account uncertainty and vagueness. One disadvantage is that its process and outcomes can be hard to explain. Further, due to the way preferences are incorporated, the lowest performances under certain criteria are not displayed. The outranking method causes the strengths and weaknesses of the alternatives to not be directly identified, nor results and impacts to be verified. ELECTRE has been used in energy, economics, environmental, water management, and transportation problems.
PROMETHEE: PROMETHEE is similar to ELECTRE in that it also has several iterations and is also an outranking method. Its advantage is that it is easy to use. It does not require the assumption that the criteria are proportionate. The disadvantages are that it does not provide a clear method by which to assign weights and it requires the assignment of values but does not provide a clear method by which to assign those values. PROMETHEE has seen much use in environmental management, hydrology and water management, business and financial management, chemistry, logistics and transportation, manufacturing and assembly, energy management, and agriculture
SAW: SAW is a value function is established based on a simple addition of scores that represent the goal achievement under each criterion, multiplied by the particular weights. It has the ability to compensate among criteria. It is also intuitive to decision makers. The calculation is simple and can be performed without the help of complex computer programs. It has specific disadvantages: All the values of the criteria should be maximizing. Minimizing criteria should be transformed to maximizing ones before being used in the analysis. All the values of the criteria should be positive and the estimates yielded by SAW do not always reflect the real situation. SAW has had applications in water management, business, and financial management.
TOPSIS: TOPSIS is an approach to identify an alternative which is closest to the ideal solution and farthest to the negative ideal solution in a multi-dimensional computing space. It has numerous advantages. It has a simple process. It is easy to use and programmable. The number of steps remains the same regardless of the number of attributes. A disadvantage is that its use of Euclidean Distance does not consider the correlation of attributes. It is difficult to weight attributes and keep consistency of judgment, especially with additional attributes. TOPSIS has been used in supply chain management and logistics, design, engineering and manufacturing systems, business and marketing management, environmental management, human resources management, and water resources management.


This paper assesses the more common methods of MCDM in order to benefit practitioners to choose a method for solving a specific problem. Identification of common MCDM methods and identification of strengths and weaknesses is very useful however; this article solely itself is not enough to determine a method of MCDM. It only gives a general idea and helps researchers during the method choosing process.


Velasquez, M., & Hester, P. T. (2013). An analysis of multi-criteria decision making methods. International Journal of Operations Research, 10(2), 56-66. Retrieved From:


  1. Having read through most of the techniques you have listed and others available on MCDM, I think the AHP is the most practical and easiest method for the intelligence community to employ because it involves the least amount of math. Likewise, the AHP is especially useful when dealing with qualitative elements like politics or regional disputes. In your opinion, which MCDM method or methods do you think is the overall best option in the intelligence community?

    1. Oleg, I agree with you. AHP is very common due to its ease of use. However, I think Fuzzy Theory can also be useful for the intelligence community because it allows solving a lot of problems related to dealing the imprecise and uncertain data and it takes into account the insufficient information and the evolution of available knowledge.

  2. I think this article is useful in just getting a grasp on the range of varients that are out there. Most of the articles I had looked at utilized AHP, and it is good to at least have some information about what else is out there. The only question I would ask has already been posed by Oleg.