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ANP Web App Information
This web application assists you in making decisions using the Analytic Network Process (ANP), an extension of AHP for complex problems with interdependencies.
It allows you to define a goal, create clusters of criteria and alternatives, specify influence relationships between these clusters, perform pairwise comparisons, and then calculates the global priorities of all elements by solving a Supermatrix.
** This web application is part of a research project by F F **
How to Use this Web App?
- Define your Goal: Enter the main objective of your decision (e.g., "Select the best IT project").
- Define Clusters & Elements: Create logical groupings (Clusters) of factors relevant to your decision (e.g., "Benefits", "Costs", "Alternatives"). Then, add specific items (Elements) within each cluster (e.g., for "Benefits": "Increased Revenue", "Improved Efficiency").
- Define Dependencies: Specify which clusters influence other clusters. For example, "Benefits influence Alternatives" or "Costs influence Benefits". This creates the network structure. (Note: This app simplifies by focusing on outer dependencies only, not inner-cluster dependencies).
- Perform Pairwise Comparisons:
- Cluster Comparisons: First, you'll compare all clusters to determine their overall importance for the network's weighting.
- Element Comparisons (based on dependencies): For each defined dependency (e.g., "Cluster A influences Cluster B") and for each element in the influencing Cluster A, you will compare the elements in the influenced Cluster B. This helps determine how important elements in Cluster B are *with respect to* that specific influencing element from Cluster A.
Use the Saaty scale (1-9 and reciprocals) for all comparisons.
- Calculate ANP: Once all comparisons are made, click "Calculate ANP". The app will construct and solve the Supermatrix to generate the final global priorities (weights) for all elements across all clusters. It will also display consistency ratios for all individual comparison matrices.
- Review Results: The global priorities show the overall importance of each element. Consistency ratios below 10% (0.10) indicate acceptable consistency; higher values suggest a review of your judgments.
What is AHP?
The Analytic Hierarchy Process (AHP) is a structured technique for organizing and analyzing complex decisions, developed by Prof. Thomas L. Saaty. It helps decision-makers find the best solution by breaking down the decision problem into a hierarchy of criteria and alternatives, then comparing them systematically.
How it's Used (in brief):
- Decomposition: The problem is structured hierarchically, starting with a goal at the top, followed by criteria, sub-criteria, and alternatives at lower levels.
- Pairwise Comparisons: Elements at each level (e.g., criteria) are compared against each other in terms of their relative importance with respect to the element directly above them in the hierarchy. This is done using a fundamental scale (Saaty scale of 1-9), where 1 means equal importance and 9 means extreme importance.
- Priority Calculation: From these pairwise comparisons, a matrix is formed, and the relative weights (priorities) of the elements are derived using mathematical methods (e.g., eigenvalue method or geometric mean method).
- Consistency Check: A key aspect of AHP is checking the consistency of the judgments. If the consistency ratio is too high (typically > 0.10), it indicates that the judgments are inconsistent and should be revised.
- Synthesis: The weights from different levels are combined to get overall priorities for the alternatives at the lowest level, indicating which alternative best achieves the goal.
Applications of AHP:
AHP is widely applied in various fields due to its ability to handle both qualitative and quantitative factors, and its structured approach to complex decision-making. Some common applications include:
- Resource Allocation: Deciding how to distribute limited resources among competing projects or departments.
- Supplier Selection: Choosing the best supplier based on multiple criteria like cost, quality, delivery, and service.
- Project Prioritization: Ranking projects based on strategic alignment, risk, and potential impact.
- Personnel Evaluation: Assessing candidates for a job or employees for promotion.
- Site Selection: Determining the optimal location for a new facility.
- Policy Making: Evaluating the impact of different policies and choosing the most effective one.
- Investment Decisions: Selecting investment portfolios based on risk, return, and other factors.
- Conflict Resolution: Providing a structured way to analyze and resolve disputes by finding common ground.
What is ANP?
The Analytic Network Process (ANP), also developed by Prof. Thomas L. Saaty, is a more generalized and advanced form of AHP. While AHP uses a hierarchical structure (top-down, one-way influence), ANP allows for complex relationships, including dependencies and feedback among elements within and between clusters. It is designed to model real-world problems where decision factors are not independent.
How it's Used (in brief):
- Network Structuring: The problem is modeled as a network (or a "hierarchy with dependencies"). It consists of:
- Clusters: Groups of related elements (e.g., Criteria, Benefits, Costs, Alternatives).
- Elements: Individual decision factors within each cluster.
- Dependencies: Arrows indicating influence or feedback loops between elements and/or clusters. These can be inner (within a cluster) or outer (between clusters).
- Pairwise Comparisons: Similar to AHP, pairwise comparisons are performed. However, in ANP, elements are compared not just for their importance, but for their importance with respect to the influence of other elements or clusters. This generates local priority vectors.
- Supermatrix Formulation: The local priority vectors from all pairwise comparisons are assembled into a "Supermatrix". This is a partitioned matrix where each block represents the influence of one cluster on another.
- Unweighted Supermatrix: Contains the local priorities.
- Weighted Supermatrix: The blocks of the unweighted supermatrix are then weighted by the importance of the clusters themselves (derived from a separate set of cluster-level comparisons).
- Limit Supermatrix (Solving the Network): The weighted Supermatrix is raised to sufficiently large powers until it converges to a stable matrix. The columns of this converged matrix (the "limit supermatrix") will become identical, and this stable vector represents the global priorities of all elements in the network.
- Consistency Checks: Each individual pairwise comparison matrix within the ANP structure is checked for consistency, similar to AHP.
When to use ANP (vs. AHP):
ANP is typically used for more complex decision problems where:
- There are interdependencies or feedback relationships between criteria, alternatives, or other decision factors.
- A simple top-down hierarchy cannot fully capture the real-world complexity.
- The influence flows in multiple directions.
Common applications include strategic planning, resource allocation with complex interdependencies, risk assessment, and policy analysis where factors influence each other in intricate ways.