Multiple-Criteria Decision Analysis for Better Decision Making

Multiple-criteria decision analysis is a systematic approach to decision-making that helps you weigh various factors to make informed choices. It's particularly useful when you have competing priorities or multiple stakeholders involved.

This approach involves identifying and evaluating multiple criteria, such as cost, quality, and time, to determine the best course of action. For instance, in a business setting, you might need to decide between two investment options, each with different risk levels, potential returns, and time frames.

By using multiple-criteria decision analysis, you can create a structured framework for evaluating these options and making a more informed decision. This approach can also help you identify potential trade-offs and opportunities for improvement.

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Multiple-criteria decision analysis (MCDA) is a method for solving complex decision problems involving multiple criteria. It's concerned with structuring and solving decision and planning problems involving multiple criteria, and the purpose is to support decision-makers facing such problems.

The difficulty of the problem originates from the presence of more than one criterion. There is no longer a unique optimal solution to an MCDA problem that can be obtained without incorporating preference information. The concept of an optimal solution is often replaced by the set of nondominated solutions.

MCDM has been an active area of research since the 1970s, and it draws upon knowledge in many fields including mathematics, decision analysis, economics, computer technology, software engineering, and information systems.

Here's a list of some of the fields that MCDM draws upon:

MCDM, or multiple-criteria decision-making, is a concept that's essential to understand in the world of decision analysis. MCDM is concerned with structuring and solving decision and planning problems involving multiple criteria.

The purpose of MCDM is to support decision-makers facing such problems. Typically, there doesn't exist a unique optimal solution for such problems, and it's necessary to use decision-makers' preferences to differentiate between solutions.

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Solving an MCDM problem can be interpreted in different ways. It could correspond to choosing the "best" alternative from a set of available alternatives, choosing a small set of good alternatives, or grouping alternatives into different preference sets.

The difficulty of the MCDM problem originates from the presence of more than one criterion. There is no longer a unique optimal solution to an MCDM problem that can be obtained without incorporating preference information.

The concept of an optimal solution is often replaced by the set of nondominated solutions. A solution is called nondominated if it's not possible to improve it in any criterion without sacrificing it in another.

Here are the main definitions related to MCDM:

These definitions are crucial to understanding the foundations of MCDM and how it can be applied in real-world decision-making situations.

MCDA can be combined with optimization methods to identify optimal or near-optimal solutions when dealing with complex decision problems with constraints or resource limitations.

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This integration can be particularly useful in situations where the decision problem involves dynamic or time-dependent factors, or when there is a need to evaluate the long-term consequences of different alternatives.

Combining MCDA with simulation techniques, such as Monte Carlo simulations or system dynamics models, can also be beneficial.

These approaches can help decision-makers evaluate the consequences of different alternatives over time, leading to more informed decisions.

Researchers are exploring the integration of MCDA with machine learning and artificial intelligence techniques, such as neural networks or evolutionary algorithms.

This integration can potentially automate certain aspects of the MCDA process, such as criteria weight determination or alternative evaluation, and improve the accuracy and efficiency of decision-making.

Incorporating spatial data and visualization can be achieved by combining MCDA with geographic information systems (GIS) and spatial analysis techniques.

This integration allows decision-makers to visualize the spatial distribution of alternatives or criteria, leading to more informed decisions.

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MCDM methods are numerous, with many implemented by specialized decision-making software. The Aggregated Indices Randomization Method (AIRM), Analytic Hierarchy Process (AHP), and Balance Beam process are just a few examples of the many methods available.

Some popular MCDM methods include outranking methods, value/utility-based methods, and fuzzy MCDA techniques. These methods can be chosen based on the problem characteristics and decision-maker preferences.

The choice of method depends on the problem and the decision-maker's preferences, and popular methods include ELECTRE, PROMETHEE, AHP, TOPSIS, VIKOR, and goal programming.

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MCDM methods are a crucial part of the decision-making process, and there are many different types to choose from.

Some popular MCDM methods include the Analytic Hierarchy Process (AHP), Analytic Network Process (ANP), and Balance Beam process.

The choice of method depends on the problem characteristics and decision-maker preferences.

Other methods, such as outranking methods like ELECTRA and Lexicographic methods, can also be used to support decision-making with multiple objectives or criteria.

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Outranking methods have been developed for cases where one criteria may not necessarily be able to compensate for poor performance in another.

Some MCDM methods, such as the AHP, TOPSIS, and VIKOR, are value/utility-based methods.

Popular MCDA methods include outranking methods (ELECTRE, PROMETHEE), value/utility-based methods (AHP, TOPSIS, VIKOR), goal programming, and fuzzy MCDA techniques.

The choice of method(s) depends on the problem characteristics and decision-maker preferences.

Here are some of the most commonly used MCDM methods:

Mutual Preferential Independence is a crucial concept in MCDA, and it's essential to understand what it looks like in practice.

It's only valid in linear additive models, where the trade-off between criteria is independent of other factors.

Practitioners need to appreciate this concept, possibly even more than having a formal understanding of the term.

A lack of Mutual Preferential Independence is evident when stakeholders are reluctant to make preference judgements, citing that it depends on another criterion.

This can be a sign that the selection of objectives and criteria needs to be reviewed to eliminate the issue.

Eliminating Mutual Preferential Independence is usually simpler than adopting alternative forms of overall value function.

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A key part of multiple-criteria decision analysis (MCDA) is identifying the problem and organizing the relevant information. This involves understanding the type of recommendation desired by the user, which can be one of three main types: ranking, sorting, or choice.

The most common problem statement encountered in MCDA is ranking, which involves listing alternatives from best to worst. Sorting, on the other hand, involves assigning alternatives to pre-defined preference-ordered classes.

The type of recommendation desired can also be influenced by the dynamic character of the problem, particularly when the set of alternatives is evolving. In such cases, relative comparisons of alternatives become less stable, and models that focus on independent assessment of each alternative should be preferred.

Here are the main types of problem statements in MCDA, along with their characteristics:

Understanding the type of problem statement is crucial in MCDA, as it helps in selecting the appropriate method and criteria for analysis. For instance, ranking may require a cardinal type of recommendation, where the distance between each alternative is meaningful in quantitative terms.

The Value Model is a way of representing stakeholders' preferences in a quantifiable way, using an Overall Value Function that calculates the overall value or benefit of an option.

This function is often an implementation of a linear additive model, which takes into account the measures of Component Value or Preference Scores associated with each criterion.

The measures of Component Value or Preference Scores are on an interval scale with arbitrary limits, typically running from 0 to 100.

The Overall Value or Benefit is also on an interval scale with the same limits, making it easy to communicate the output of an MCDA to a wider audience.

Decision analysis recognizes both order-of-preference (ordinal value) and strength-of-preference (cardinal value), with MCDA based on strength-of-preference.

The weights of each criterion, represented by terms starting with "w", indicate the relative strength-of-preference of the criteria compared to each other.

These weights are normalized so they are in the range 0 to 1 and give a combined total of 1.

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Evaluating alternatives against the decision criteria involves determining their performance or score on each criterion, which can be based on quantitative data, qualitative assessments, or a combination of both.

Common scoring or rating methods include direct rating, pairwise comparisons, or value/utility functions.

Here are some common methods for evaluating alternatives:

Assessment and Weighting is a crucial step in Multiple-criteria decision analysis (MCDA). It's where you determine the relative importance of each criterion, which can significantly impact the overall output of an MCDA.

The weights must be elicited from the decision stakeholders in a valid manner, as the overall output is sensitive to the weights. Inexperienced practitioners often make the mistake of eliciting weightings based on the names or descriptions of the criteria, which can lead to inaccurate results.

There are various weighting techniques that can be used, such as pairwise comparisons, swing weighting, or direct rating methods. Swing weighting is a recommended approach that involves asking stakeholders to consider the swing from 'worst' to 'best' for each criterion.

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To use swing weighting, stakeholders are asked to consider the extremes of each criterion, which correspond to the "v=0" and "v=100" levels. One possible way to help stakeholders consider the swings is to assume a set of 'hypothetical options' where all criteria are set at their 'worst' levels, except for the 'corresponding criteria' which are set at their 'best' levels.

Here are some common criteria that are often rated as highly important:

These criteria are often rated high in various studies and publications, highlighting their importance in MCDA.

Determining strength of preference can be a challenging task, especially when dealing with a set of alternatives.

Asking people to directly provide ratings of their strength of preference can lead to limited repeatability of responses. This is why various techniques have been developed to address this issue.

One technique is known as 'ranking/rating', which involves asking decision stakeholders to provide order-of-preference, or 'rankings', as a lead-in to strength-of-preference, or 'ratings' questions. Order-of-preference responses tend to be highly repeatable.

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Stakeholders can also use discrete pairwise comparison methods, where they select from a pre-defined set of comparative preference statements, such as 'equal preference', 'moderate preference', or 'strong preference'.

Here are some examples of comparative preference statements:

These statements can be used to derive the numerical strength of preference using an associated tool.

Swing weighting is another technique that asks stakeholders to consider which is the biggest 'swing' between best and worst performance for each criterion. This can be done by asking stakeholders to rank and rate the significance of the swings to determine weights.

Stakeholders can also be asked to rank and rate hypothetical options, where each option has all criteria set at their 'worst' levels, except for the 'corresponding criteria', which are set at their 'best' levels.

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Weighting is a crucial step in the MCDA process, and it's essential to get it right. The overall output of an MCDA is sensitive to the weights, so you must ensure they are determined in a valid manner.

Inexperienced practitioners often make the mistake of eliciting weightings from stakeholders simply based on the names or descriptions of the criteria and how they perceive their relative importance. This can lead to a criterion receiving a very high weight, simply because it is perceived as very important.

There are various weighting techniques that can be used, such as pairwise comparisons, swing weighting, and direct rating methods. The weights can be elicited from decision-makers or stakeholders and may involve group decision-making processes.

The most commonly used methods for weighting and scoring in MCDA models are simple additive weighting (five-point scale) and hierarchical point allocation. Three criteria are consistently rated as the most important: disease severity/burden, effectiveness/comparative effectiveness/therapeutic effect, and unmet medical need.

Here are some key points to consider when determining criteria weights:

In group decision-making scenarios, conflicts or disagreements among stakeholders are common due to differing preferences, priorities, or value systems.

Effective group decision-making often requires structured and facilitated discussions to ensure that all stakeholders have a voice and that the decision-making process is transparent and inclusive.

Facilitators can guide the discussion by encouraging participants to explain their reasoning, challenge assumptions, and explore alternative viewpoints.

By incorporating MCDA methods like the Analytic Network Process (ANP) or the Decision EXpert (DEX) method, group discussions can be facilitated to capture the complexities of real-world decision problems.

MCDA provides a framework for facilitating these discussions by clearly defining the decision criteria, alternatives, and evaluation methods, which can be used to communicate complex information and foster a shared understanding among group members.

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In group decision-making scenarios, conflicts or disagreements among stakeholders are common due to differing preferences, priorities, or value systems.

MCDA provides consensus-building approaches to facilitate the convergence of opinions and reach a compromise solution that is acceptable to all parties involved.

One widely used approach is the feedback mechanism, where individual judgments or evaluations are shared among the group members, allowing them to revise their assessments based on the opinions of others.

Facilitators can guide the discussion by encouraging participants to explain their reasoning, challenge assumptions, and explore alternative viewpoints.

This iterative process can lead to a gradual convergence of viewpoints and a consensus solution.

Another approach is the use of distance-based consensus measures, which quantify the level of disagreement or distance between individual preferences.

These measures can guide the group in identifying areas of significant disagreement and prioritizing efforts to reach a consensus.

Effective group decision-making often requires structured and facilitated discussions to ensure that all stakeholders have a voice and that the decision-making process is transparent and inclusive.

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Cognitive biases can significantly impact decision-making, leading to suboptimal or irrational choices. Anchoring bias, for example, causes decision-makers to place excessive emphasis on initial information.

Confirmation bias occurs when decision-makers selectively seek or interpret information that confirms their preexisting beliefs. This can lead to a narrow perspective and poor decision-making.

Researchers have explored ways to mitigate the impact of cognitive biases, including debiasing techniques and incorporating behavioral decision theory concepts into decision-making methods. One such concept is prospect theory, which accounts for decision-makers' risk attitudes and reference point dependencies.

Group decision-making approaches in multi-criteria decision analysis (MCDA) can help mitigate individual biases by aggregating multiple perspectives and facilitating discussions among decision-makers. However, group decision-making processes can also be susceptible to biases, such as groupthink or social influence biases.

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MCDA techniques have been widely applied across various domains to support complex decision-making processes involving multiple, often conflicting criteria.

In finance and investment, MCDA methods like TOPSIS and PROMETHEE assist in identifying investment opportunities that align with an investor’s preferences and risk profile.

By considering criteria like expected return, risk, liquidity, and environmental, social, and governance (ESG) factors, MCDA enables decision-makers to systematically evaluate alternatives based on multiple criteria, understand trade-offs, and make well-informed choices that balance competing objectives.

Multi-Criteria Decision Analysis (MCDA) has been widely applied across various domains to support complex decision-making processes involving multiple, often conflicting criteria.

Energy planning decisions, including energy source selection, power plant siting, and renewable energy investment, necessitate the consideration of multiple factors like cost, environmental impact, reliability, and social acceptance.

MCDA techniques, such as the Analytic Hierarchy Process (AHP) and TOPSIS, have been employed to evaluate and prioritize energy alternatives based on these conflicting criteria.

Healthcare decisions, such as treatment selection, resource allocation, and technology assessment, often involve trade-offs between clinical outcomes, cost-effectiveness, and patient preferences.

Multi-attribute utility theory (MAUT) and outranking methods provide a structured framework for evaluating healthcare alternatives based on multiple criteria.

In finance and investment, MCDA techniques are used for portfolio optimization, project selection, and risk management.

By considering criteria like expected return, risk, liquidity, and environmental, social, and governance (ESG) factors, MCDA methods like TOPSIS and PROMETHEE assist in identifying investment opportunities that align with an investor’s preferences and risk profile.

MCDA offers a comprehensive and transparent approach to decision-making, enabling decision-makers to systematically evaluate alternatives based on multiple criteria, understand trade-offs, and make well-informed choices that balance competing objectives.

MCDA techniques have been employed in various domains, including energy, healthcare, and finance, to facilitate informed decision-making and support complex decision-making processes involving multiple, often conflicting criteria.

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Transportation and logistics is a crucial area where MCDA shines. By integrating criteria like travel time, cost, environmental impact, and safety, MCDA methods help identify optimal transportation solutions.

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MCDA methods like VIKOR and goal programming are particularly useful in route planning, allowing for the evaluation of multiple factors to find the best route.

Transportation hubs can be analyzed using MCDA to determine the best location, taking into account factors such as accessibility, safety, and environmental impact.

Evaluating transportation policies is another key application of MCDA, enabling policymakers to assess the effectiveness of different policies in balancing competing objectives like cost, safety, and environmental impact.

MCDA can also help with mode selection, considering factors like travel time, cost, and environmental impact to choose the most suitable mode of transportation.

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Integrating MCDA with GIS and other systems can be a game-changer for decision-makers. By combining MCDA methods with GIS, decision-makers can incorporate spatial criteria and constraints into the decision-making process.

ArcGIS and QGIS offer extensions or plugins that enable the integration of MCDA methods, allowing users to perform spatial multi-criteria analyses and create suitability maps.

This integration can be particularly useful in applications such as land-use planning, site selection, environmental management, and natural resource allocation. Decision-makers can leverage these tools to more effectively apply MCDA techniques and gain valuable insights to support their decision-making processes.

Various software tools and decision support systems are available to facilitate the implementation of MCDA methods, ranging from commercial packages to open-source alternatives. These tools offer different levels of functionality, customization, and integration capabilities.

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Software and tools play a crucial role in facilitating the implementation of multiple-criteria decision analysis (MCDA) methods. They can greatly simplify the process of applying MCDA methods, performing calculations, and visualizing results.

These tools can help manage complex decision problems involving multiple stakeholders and large datasets. Commercial software packages, such as Hiview, Decision Lens, and Criterium Decision Plus, offer a wide range of features and capabilities.

Some popular commercial software packages include Hiview, Decision Lens, and Criterium Decision Plus. These packages often provide user-friendly interfaces, extensive documentation, and technical support.

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However, they can be costly, especially for individual users or small organizations. Open-source tools, on the other hand, are typically free to use and allow users to modify the source code as needed.

Some popular open-source MCDA tools include MCDA-Py, MDCA, and MCDA-RES. These tools are particularly useful for researchers, students, and developers who want to explore and modify the underlying algorithms or integrate MCDA capabilities into their applications.

Here's a brief overview of some popular MCDA software packages:

GIS software packages, such as ArcGIS and QGIS, also offer extensions or plugins that enable the integration of MCDA methods. These tools allow users to perform spatial multi-criteria analyses and create suitability maps.

MCDA is an active area of research, with ongoing developments and emerging trends.

One notable trend is the increasing focus on group decision-making and collaborative decision-support systems, which is driven by the need for MCDA methods and tools that facilitate group decision-making processes, consensus building, and conflict resolution.

The integration of multi-criteria decision analysis with big data analytics and data-driven decision-making is another emerging area, which has the potential to lead to more accurate and informed decisions.

Sustainability and environmental decision-making are also driving new research in MCDA, as concerns about climate change, resource depletion, and environmental degradation continue to grow.

Researchers are exploring the application of MCDA in emerging domains, such as smart cities, Industry 4.0, and the Internet of Things (IoT), which present new challenges and opportunities for multi-criteria decision analysis.

These domains require decision-makers to consider a wide range of interconnected factors, including technological, social, and economic aspects.

The field of MCDA continues to evolve, driven by theoretical advancements, practical applications, and the integration of new technologies and data sources.

The demand for robust and flexible MCDA methodologies is likely to grow, fostering further research and development in this area.

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The methodology used in this research involved exploring the existing literature on MCDA, with a focus on the conduct of the MCDA process, comparison of MCDA methods, and recommendation of a relevant method. This was done by conducting two searches, one using a combination of keywords in the Web of Science and Scopus databases, and another manual search.

The searches yielded 948 publications, which were then screened and included in the analyzed dataset if they provided an overview and/or a set of steps to lead the MCDA process. The studies were identified in the peer-reviewed literature, specifically in the Web of Science and Scopus databases.

The taxonomy of the MCDA process characteristics has a hierarchical structure, composed of three main phases and ten main characteristics. Its structure is available in Figs. 2, 3, 4, and 5, and the complete taxonomy is summarized in Table 1.

The taxonomy is a useful tool for understanding the MCDA process, with each characteristic and sub-characteristic labeled using a "c." and "c.x." nomenclature, respectively.

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Study and Evaluation is a critical step in Multiple-criteria decision analysis (MCDA). Each alternative is evaluated against the decision criteria to determine its performance or score on each criterion.

The evaluation can be based on quantitative data, qualitative assessments, or a combination of both. Various scoring or rating methods can be used, such as direct rating, pairwise comparisons, or value/utility functions.

The complexity of the evaluation process can vary depending on the method used. For example, MAVT involves weights as trade-offs and value functions, while ELECTRE methods require weights as importance coefficients and comparison preference and majority thresholds.

The time required for interaction with decision-makers (DMs) to explain the method and/or obtain preference information can also impact the evaluation process. This can be affected by the simplicity of structuring sensitivity analysis, which can vary according to the type of preference model.

In some cases, the evaluation process can be subjective, driven by the type of analyst and the DMs/stakeholders involved. The understandability of the method is a key consideration, as it can affect the time required for interaction with DMs and the level of input required from stakeholders.

The processing time and effort needed to compile the data required for the method can also be significant. This can vary considerably according to the selected method, with some methods requiring more comprehensive judgments on a set of reference alternatives.

The number of alternatives and criteria the method can deal with is another important consideration. This can vary according to the type of method, with some methods being more suitable for complex problems with many criteria and alternatives.

The extent of use of the method in the specific context/area can also be a factor. While it may seem logical that a method used in a certain area is the correct method, this assumption can be risky, as the structure of the problem and preferences may be different.

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The current design of MCDA models is unclear and results are difficult to interpret, which warrants a simplification of current designs.

MCDA models often have too many domains and overlapping criteria, making them hard to work with.

Simplifying the design of MCDA models with fewer and well-defined domains could improve their clarity and usefulness.

A strict separation of value from costs in MCDA models would increase their flexibility and transferability of results.

This separation would also aid in the implementation of MCDA models in healthcare HTA.

Further research and model improvement are necessary to bring about consensus and fulfill the potential of MCDA in healthcare HTA.

Multi-stakeholder discussion is also crucial to ensure that MCDA models meet the needs of various stakeholders.

Practical application of MCDA models is essential to validate their effectiveness and make them more useful in real-world scenarios.

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