Multiple-criteria decision analysis
Multiple-criteria decision-making (MCDM) or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly evaluates multiple conflicting criteria in decision making (both in daily life and in settings such as business, government and medicine).
In their daily lives, people usually weigh multiple criteria implicitly and may be comfortable with the consequences of such decisions that are made based on only intuition.
[1] On the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria.
Structuring complex problems well and considering multiple criteria explicitly leads to more informed and better decisions.
A variety of approaches and methods, many implemented by specialized decision-making software,[3][4] have been developed for their application in an array of disciplines, ranging from politics and business to the environment and energy.
MCDM is concerned with structuring and solving decision and planning problems involving multiple criteria.
There is no longer a unique optimal solution to an MCDM problem that can be obtained without incorporating preference information.
There are several MCDM-related organizations including the International Society on Multi-criteria Decision Making,[6] Euro Working Group on MCDA,[7] and INFORMS Section on MCDM.
The solution methods for MCDM problems are commonly classified based on the timing of preference information obtained from the DM.
Methods based on estimating a value function or using the concept of "outranking relations", analytical hierarchy process, and some rule-based decision methods try to solve multiple criteria evaluation problems utilizing prior articulation of preferences.
Similarly, there are methods developed to solve multiple-criteria design problems using prior articulation of preferences by constructing a value function.
Once the value function is constructed, the resulting single objective mathematical program is solved to obtain a preferred solution.
These methods have been well-developed for both the multiple criteria evaluation (see for example, Geoffrion, Dyer and Feinberg, 1972,[11] and Köksalan and Sagala, 1995[12] ) and design problems (see Steuer, 1986[13]).
When the mathematical programming models contain integer variables, the design problems become harder to solve.
Multiobjective Combinatorial Optimization (MOCO) constitutes a special category of such problems posing substantial computational difficulty (see Ehrgott and Gandibleux,[15] 2002, for a review).
The dominated points of the weakly nondominated set are located either on vertical or horizontal planes (hyperplanes) in the criterion space.
The following two-variable MOLP problem in the decision variable space will help demonstrate some of the key concepts graphically.
The north-east region of the feasible space constitutes the set of nondominated points (for maximization problems).
Achievement scalarizing functions also combine multiple criteria into a single criterion by weighting them in a very special way.
Mathematically, we can represent the corresponding problem as The achievement scalarizing function can be used to project any point (feasible or infeasible) on the efficient frontier.
Different schools of thought have developed for solving MCDM problems (both of the design and evaluation type).
[18] Multiple objective mathematical programming school (1) Vector maximization: The purpose of vector maximization is to approximate the nondominated set; originally developed for Multiple Objective Linear Programming problems (Evans and Steuer, 1973;[19] Yu and Zeleny, 1975[20]).
Another approach is to elicit value functions indirectly by asking the decision-maker a series of pairwise ranking questions involving choosing between hypothetical alternatives (PAPRIKA method; Hansen and Ombler, 2008[28]).
Evolutionary multiobjective optimization school (EMO) EMO algorithms start with an initial population, and update it by using processes designed to mimic natural survival-of-the-fittest principles and genetic variation operators to improve the average population from one generation to the next.
The goal is to converge to a population of solutions which represent the nondominated set (Schaffer, 1984;[30] Srinivas and Deb, 1994[31]).
More recently, there are efforts to incorporate preference information into the solution process of EMO algorithms (see Deb and Köksalan, 2010[32]).
The AHP converts these evaluations to numerical values (weights or priorities), which are used to calculate a score for each alternative (Saaty, 1980[36]).
AHP is one of the more controversial techniques listed here, with some researchers in the MCDA community believing it to be flawed.
