# Analytic network process

Analytic network process |
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**Analytic Network Process** (ANP) is a decision-making technique used in management to model complex interdependencies and quantify the relative importance of multiple, disparate factors. It works by creating a network of elements that represent factors and their interdependencies, which can then be analyzed to determine the relative importance of each factor. ANP is an effective tool for structuring, ranking and measuring the relative importance of multiple, often conflicting objectives in a decision-making problem. It enables managers to make informed decisions based on a logical and quantitative analysis of the decision-making problem.

## Example of analytic network process

- Suppose a business must decide whether to launch a new product in the market. The factors to consider include the cost of production, potential sales revenue, customer feedback, competitive analysis, market research, and the company’s resources. In order to make an informed decision, an ANP model can be used to weigh the relative importance of each factor. The model can map out the relationships between the factors and assign weights to each based on the relative importance of each factor in the decision. This will help the business determine which factors are most important in the decision and make an informed decision based on the data provided.
- A hotel needs to decide which type of room amenities to offer. Factors that need to be considered include customer feedback, market trends, competitor offerings, cost of amenities, and the hotel’s resources. An ANP model can be used to weigh the relative importance of each factor and map out the relationships between them. This will help the hotel determine which amenities are most important to offer and make an informed decision.
- A company is considering investing in a new technology. Factors to consider include customer demand, cost of the technology, potential revenue, competitive analysis, and the company’s resources. An ANP model can be used to weigh the relative importance of each factor and map out the relationships between them. This will help the company determine which factors are most important in the decision and make an informed decision based on the data provided.

## Formula of analytic network process

The Analytic Network Process (ANP) is a decision-making technique used to model complex interdependencies and quantify the relative importance of multiple, disparate factors. The ANP model consists of two main elements: a network of elements that represent factors and their interdependencies, and a set of mathematical formulas to evaluate the relative importance of each factor.

The first element of the ANP model is the network of elements, which is a graphical representation of the various factors and their interdependencies. This network is represented by nodes, which represent the factors, and directed arcs, which represent the relationships between the factors. The directed arcs indicate the relative importance of each factor, with thicker arcs signifying a higher relative importance.

The second element of the ANP model is a set of mathematical formulas that are used to evaluate the relative importance of each factor. The formulas are based on the concept of supermatrix, which is a matrix of elements that represent the relative importance of each factor. The supermatrix can be calculated by a process known as supermatrix analysis.

The main formulas used in supermatrix analysis include the Supermatrix Weighting Formula (SWF), the Consistency Index Formula (CIF), the Relative Closeness Formula (RCF), and the Relative Betweenness Formula (RBF).

**The Supermatrix Weighting Formula**(SWF) is used to calculate the total weight of the network. This is done by multiplying the values of the elements in the supermatrix by the weights of the directed arcs connecting them. The result is a matrix of weights which represent the relative importance of each factor.**The Consistency Index Formula**(CIF) is used to measure the consistency of the network. This is done by calculating the sum of the squares of the elements in the supermatrix and dividing it by the sum of the elements in the supermatrix. The result is a value that ranges from 0 to 1, with 0 representing perfect consistency and 1 representing maximum inconsistency.**The Relative Closeness Formula**(RCF) is used to measure the closeness of each factor to each other. This is done by calculating the sum of the elements in the supermatrix that connect each factor to each other. The result is a matrix of values which represent the relative closeness of each factor to each other.**The Relative Betweenness Formula**(RBF) is used to measure the betweenness of each factor to each other. This is done by calculating the sum of the elements in the supermatrix that connect each factor to each other, divided by the number of elements that connect each factor to each other. The result is a matrix of values which represent the relative betweenness of each factor to each other.

The ANP model is used in decision-making to determine the relative importance of each factor in a given situation. The model can be used to identify key factors, prioritize objectives, and evaluate the relative importance of different objectives. By using the model, managers can make more informed decisions based on a logical and quantitative analysis of the decision-making problem.

## When to use analytic network process

Analytic Network Process (ANP) is an effective tool for making decisions when there are multiple, often conflicting objectives present. It is useful in a variety of decision-making situations, such as the following:

**Strategic planning**: ANP can be used to develop and prioritize strategic objectives, as well as to measure success.**Risk management**: ANP can be used to identify and quantify the risks associated with a decision and how to best manage or mitigate them.**Resource allocation**: ANP can be used to identify the most efficient and effective use of resources in order to meet objectives.**Multi-criteria decision-making**: ANP can be used to identify and prioritize multiple objectives and to determine the most appropriate decision based on those objectives.**Multi-stakeholder decision-making**: ANP can be used to identify and prioritize multiple objectives from multiple stakeholders and then to determine the most appropriate decision based on those objectives.**Portfolio management**: ANP can be used to develop and prioritize portfolios of projects and to determine the optimal mix of projects to maximize returns.

## Types of analytic network process

A one-sentence introduction to the types of Analytic Network Process (ANP) is: ANP is a powerful decision-making tool that can model complex interdependencies and quantify the relative importance of multiple, disparate factors. There are several types of ANP, including:

**Hierarchical ANP**: Hierarchical ANP is used to rank and assign weights to different elements in a hierarchical structure. It is often used to quantify the relative importance of objectives in a decision-making problem.**Super-Matrix ANP**: This type of ANP is used to analyze and measure the relative importance of multiple objectives in a decision-making problem. It works by creating a super-matrix which can be used to calculate relative importance for each objective.**Structured ANP**: Structured ANP is used to evaluate the relative importance of multiple elements in a decision-making problem. It works by creating a network of elements and their interdependencies. The network can then be analyzed to determine the relative importance of each factor.**Probabilistic ANP**: Probabilistic ANP is used to quantify the relative importance of multiple objectives in a decision-making problem. It works by creating a probabilistic network which can be used to calculate the probability of each objective.**Fuzzy ANP**: Fuzzy ANP is used to quantify the relative importance of multiple objectives in a decision-making problem. It works by creating a fuzzy network which can be used to calculate the relative importance of each objective based on a range of criteria.

## Advantages of analytic network process

Analytic Network Process (ANP) is a powerful decision-making technique that helps managers to structure, rank, and measure the relative importance of multiple, often conflicting objectives. There are many advantages to using ANP, including:

- ANP allows managers to visualize the structure of a decision-making problem and identify the relationships between different elements. This helps managers to gain better insight into the problem and make more informed decisions.
- ANP enables managers to quantify the relative importance of the different objectives in a decision-making problem. This helps managers to prioritize objectives and focus on the most important ones.
- ANP is flexible and can be used to analyze almost any type of decision-making problem.
- ANP provides a logical and quantitative approach to decision-making, which helps managers to make more informed and accurate decisions.
- ANP is relatively easy to understand and use, making it accessible to a wide range of users.

## Limitations of analytic network process

Analytic Network Process (ANP) is a popular decision-making technique in management. However, there are several limitations to consider when implementing ANP. These include:

- Complexity – ANP can become quite complicated as the number of elements and interdependencies increase. This can make it difficult to understand the results and can lead to incorrect decision making.
- High Resource Requirements – ANP requires a significant amount of time and resources to create and analyze the network.
- Subjectivity – ANP relies heavily on subjective input from decision-makers, which can lead to biased results.
- Limited Flexibility – ANP is limited to analyzing the elements of a decision-making problem within the framework of the network. It cannot account for other factors that could affect the decision.

One-sentence introduction: There are several related approaches to Analytic Network Process (ANP).

**Multi-attribute Decision Making (MADM)**: MADM is a decision-making technique that is used to evaluate and compare multiple, conflicting objectives and determine the best option. It involves the use of various criteria and weights to identify the most desirable outcome.**Multi-criteria Decision Analysis (MCDA)**: MCDA is a decision-making technique that uses mathematical models to evaluate multiple criteria and determine the best option. It involves the use of various objective and subjective factors to identify the most desirable outcome.**Analytic Hierarchy Process (AHP)**: AHP is a decision-making technique that uses a hierarchical model to evaluate multiple criteria and determine the best option. It involves the use of various criteria and weights to identify the most desirable outcome.**Decision Trees**: Decision Trees are graphical representation of a decision-making process. They provide a visual representation of the decision-making process and allow users to identify the most desirable outcome by analyzing the various branches of the tree.

## Suggested literature

- Saaty, T. L., Vargas, L. G., Saaty, T. L., & Vargas, L. G. (2013).
*The analytic network process*. pp. 1-40. Springer US. - Saaty, T. L., & Vargas, L. G. (2006).
*Decision making with the analytic network process*. vol. 282. Berlin, Germany: Springer Science+ Business Media, LLC.