MADM (Multiple attribute decision-making)

Multiple attribute decision-making (MADM) is a technique used to make decisions based on multiple criteria or attributes. In many real-world situations, it is rare to have a single criterion or attribute to make a decision. In such cases, MADM techniques are useful to evaluate different options or alternatives based on multiple criteria.

MADM involves the use of mathematical models to evaluate and rank different alternatives based on a set of attributes or criteria. The aim is to find the best option or alternative that satisfies the decision maker's preferences. MADM techniques are used in a wide range of applications, including business, engineering, healthcare, and environmental management.

The process of MADM can be divided into four main steps: problem definition, identification of criteria, evaluation of alternatives, and selection of the best alternative.

1. Problem Definition: The first step in MADM is to define the problem. This involves identifying the decision to be made, the objective of the decision, and the constraints or limitations that may affect the decision. For example, if the decision is to select a supplier for a company, the objective may be to find the supplier that provides the best quality products at the lowest cost. Constraints may include the company's budget and the availability of suppliers.
2. Identification of Criteria: Once the problem has been defined, the next step is to identify the criteria that will be used to evaluate the alternatives. Criteria are the attributes or factors that are important to the decision maker in making the decision. Examples of criteria in supplier selection may include quality, cost, delivery time, and customer service.
3. Evaluation of Alternatives: The third step in MADM is to evaluate the alternatives based on the identified criteria. There are several methods for evaluating alternatives, including weighted sum models, analytic hierarchy process (AHP), and the technique for order preference by similarity to ideal solution (TOPSIS).

Weighted sum models involve assigning weights to each criterion based on its relative importance. The alternatives are then evaluated based on the weighted sum of their scores for each criterion. AHP involves a pairwise comparison of criteria and alternatives to determine their relative importance. TOPSIS is a technique that evaluates alternatives based on their distance from the ideal solution and their proximity to the worst solution.

Selection of the Best Alternative: The final step in MADM is to select the best alternative based on the evaluation of the alternatives. The best alternative is the one that satisfies the decision maker's preferences and objectives. The selection may be based on a single criterion or a combination of criteria.

There are several MADM techniques that can be used to evaluate alternatives. Some of the most commonly used techniques are discussed below.

Weighted Sum Model: The weighted sum model is a simple and widely used technique for MADM. The model involves assigning weights to each criterion based on its relative importance. The alternatives are then evaluated based on the weighted sum of their scores for each criterion. The formula for the weighted sum model is as follows:

WSi = w1Si1 + w2Si2 + ... + wnSin

where WSi is the weighted score of alternative i, wi is the weight of criterion i, and Si is the score of alternative i on criterion i.

1. Analytic Hierarchy Process (AHP): The analytic hierarchy process (AHP) is a popular MADM technique that was developed by Thomas Saaty. AHP involves a pairwise comparison of criteria and alternatives to determine their relative importance. The pairwise comparisons are done using a scale of 1 to 9, with 1 indicating equal importance and 9 indicating extreme importance. The comparisons are then used to generate a matrix of relative weights for the criteria and alternatives. The weights are then normalized to ensure that they sum to 1. The final decision is then made based on the weighted sum of the scores for each alternative.
2. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS): The technique for order preference by similarity to ideal solution (TOPSIS) is a widely used MADM technique that evaluates alternatives based on their distance from the ideal solution and their proximity to the worst solution. The ideal solution is the alternative that maximizes the benefit of the decision maker, while the worst solution is the alternative that minimizes the benefit. The TOPSIS method involves normalizing the criteria values and calculating the distance between each alternative and the ideal solution and the worst solution. The alternatives are then ranked based on their closeness to the ideal solution.
3. ELECTRE (Elimination and Choice Translating Reality): The ELECTRE method is a family of MADM techniques that involve ranking alternatives based on the outranking relationships between them. The method involves evaluating each alternative based on its performance on each criterion and comparing it to the other alternatives. The outranking relationships are based on the concept of concordance and discordance. Concordance is the degree to which an alternative is superior to another alternative on a criterion, while discordance is the degree to which an alternative is inferior to another alternative on a criterion. The final ranking of the alternatives is based on the concordance and discordance relationships.
4. Decision-making trial and evaluation laboratory (DEMATEL): The decision-making trial and evaluation laboratory (DEMATEL) is a method for MADM that involves constructing a network of causal relationships between criteria and alternatives. The method involves identifying the causal relationships between the criteria and evaluating the strength of the relationships. The method is useful for identifying the key criteria and their interrelationships.

In conclusion, MADM techniques are useful for making decisions based on multiple criteria or attributes. The techniques involve the use of mathematical models to evaluate and rank different alternatives based on a set of attributes or criteria. The process of MADM involves problem definition, identification of criteria, evaluation of alternatives, and selection of the best alternative. There are several MADM techniques that can be used, including weighted sum models, analytic hierarchy process (AHP), technique for order preference by similarity to ideal solution (TOPSIS), ELECTRE (Elimination and Choice Translating Reality), and decision-making trial and evaluation laboratory (DEMATEL). The selection of the appropriate technique depends on the problem being addressed and the preferences of the decision maker.