Multiple Criteria Decision Analysis: State of the Art Surveys

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In these fields he cooperates with many researchers of different countries He received the Best Theoretical Paper Award, by the Decision Sciences Institute Athens, He is author of many articles published in important international. He studied mathematics, computer science and economics at the University of Kaiserslautern in Germany. In he was promoted to Senior Lecturer and in to Associate Professor. Matthias left the University of Auckland in to take up a professorship in the Department of Management Science at the University of Lancaster.


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JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Editors are three of the most prominent researchers in the field Prestigious group of contributors Will be the standard reference in a fast-growing field see more benefits.

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Buy eBook. Buy Hardcover. Buy Softcover. FAQ Policy. Part VI, on Multiobjective Optimization, contains chapters on recent developments of vector and set optimization, the state of the art in continuous multiobjective programming, multiobjective combinatorial optimization, fuzzy multicriteria optimization, a review of the field of goal programming, interactive methods for solving multiobjective optimization problems, and relationships between MCDA and evolutionary multiobjective optimization EMO. Part VII, on Applications, selects some of the most significant areas, including contributions of MCDA in finance, energy planning problems, telecommunication network planning and design, sustainable development, and portfolio analysis.

Show all. He is author of many articles published in important international journals and specialized books. This selection should optimize the benefit and respect the existing restrictions. Since there are limited resources in the decision context, it is natural that the decision-maker will be unable to carry out all the desired interventions; accordingly, a coherent process of prioritization should be followed to efficiently allocate the existing resources.

As a result, efficient portfolios can be determined, guaranteeing a maximization of the benefit obtained by the available resources Phillips and Bana e Costa, MACBETH is an approach that helps a decision-maker to quantify the attractiveness of different options based on qualitative judgments about differences of attractiveness Bana e Costa and Chagas, This approach uses an iterative questioning procedure that involves pairwise comparisons. At each comparison, a qualitative preference judgment is requested to the decision-maker. When the preferences are not consistent, the decision-maker is notified and modifications are suggested.

A numerical scale that is representative of the decision-makers judgments is generated and a similar process is followed to generate weighted scales for criteria. Value functions and weights are an essential part of additive values models. In this context, value functions are necessary to evaluate the performance of the possible options in each criterion partial evaluation , while weights transform partial scores into global scores global evaluation.


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Performance descriptors are defined according to the decision maker's objectives and provide a way to operationalize them. A discrete or continuous set of performance levels either quantitative or qualitative is associated with these descriptors to measure to what degree the objective has been reached. A comprehensive discussion on how to build performance descriptors can be found in Bana e Costa and Beinat Although it is not mandatory, the definition of these performance levels is important for the construction of quantitative interval scales because it provides an important reference for the decision-maker during the pairwise comparisons.

A reduction of the frequency of inconsistencies will result from the definition of these performance levels. These numeric functions result from qualitative judgments on the differences in attractiveness reported by the decision-maker. An arbitrary value of 0 and , respectively, should be assigned to these two performance levels.

The following sequence should then be considered to compare the attractiveness of the different performance levels using the qualitative judgments mentioned before:. During this process, the M-MACBETH software automatically verifies judgment consistency, pointing out all the detected inconsistencies and suggesting ways to solve it. The value functions should be validated by the decision-maker. Consequently, all funct ions should be discussed and adjusted until they reflect the opinion of the decision-maker. Weights determination aims to define weights that can convert local evaluations relative to each criterion into global evaluations relative to all criteria.

Since additive value models are compensatory, weights play an essential role because they reflect the importance of one criterion relative to others. The weights determination process is similar to that followed for the definition of value functions. To determine weights, the following sequence should be considered:.

As before, these questions are repeated until all the criteria have been compared to each other. During the weights determination process, as in the value functions definition, judgments consistency is automatically verified. In the end, the decision-maker should check and validate the obtained weights, to ensure that they reflect his opinion. This work follows a case-study design to demonstrate how the MACBETH approach can be used for pavement maintenance decision-making at the network level. The case-study refers to the definition of priorities for maintenance and rehabilitation interventions in pavements of the Portuguese road network, considering different criteria and budget constraints.

The decision-maker is an expert in Pavement Engineering with enough technical knowledge and experience to hold decision-making responsibilities regarding the interventions to be carried out on a national road network. Considering the steps of the decision analysis process, the following sections detail the assessment of the decision maker's objectives, the modeling process using the MACBETH approach, and the prioritization and selection of maintenance and rehabilitation interventions. The decision situation is described by a decision maker whose primary responsibility is to manage a road network so that it satisfies the needs of society.

In the context of a decision analysis process, it is necessary to understand how the decision maker intends to do so. Thus, the first step is to understand the decision maker's objectives, by asking him to express his objectives assuming no economic and financial restrictions. The mentioned objectives are recorded. When necessary, additional questions are made to gather more information and to ensure that the objectives are essential, comprehensible, operational, succinct, concise and preferably independent Franco and Montibeller, The following list of objectives resulted from the interaction with the decision-maker:.

Table 1 shows the performance descriptors defined for this study. The rationale behind each performance descriptor is given in the following sub-sections. In order to benefit the largest number of people, goods, and services, the decision-maker considered that it was important to have a criterion related to the actual use of the road, that is, a traffic-related criterion. The AADT is the total volume of vehicle traffic on a road for a year divided by days. As suggested by the decision-maker, the performance levels of this descriptor were defined based on the specifications presented by the [ Portuguese Road Administration JAE , ].

Table 2 shows, in descending order of attractiveness, the different performance levels of the interventions. The construction of quantitative interval scales requires the definition of two reference points to which values are assigned Belton and Stewart, It is usual to consider the friction coefficient value Henry, as a measure of how safe the circulation of vehicles on that road is as it translates to the skid resistance characteristics of the pavement.

Lower values of the friction coefficient correspond to a lower skid resistance unsafe pavements. The regulation defined by the Portuguese road authorities imposes minimal values for the friction coefficient. Thus, the decision-maker defined a performance scale based on this information. The decision-maker was then invited to add any other performance levels that were plausible and necessary.

Consequently, two other levels were included, corresponding to friction values of 20 and Table 3 presents the resulting performance scale. The different performance levels are presented in descending order of attractiveness. Table 3. Performance scale of the interventions relative to friction coefficient.

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To ensure adequate pavement condition, it is necessary to take into account two aspects:. This index is based on the work developed by Ferreira et al.

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Since the decision-maker decided to use the QI as a descriptor of pavement condition. It was defined that pavements in very bad condition would have value 0. Also, it was established that pavements in very good condition would have value 5. Table 4 presents the different performance levels in descending order of attractiveness. Since the decision-maker intends to keep the network at least at reasonable levels QI equal to or greater than 2.


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Maintenance and rehabilitation interventions aim to restore or improve pavement condition. Since these interventions imply significant construction works, it is not desirable that roads are repaired repeatedly.

Multiple Criteria Decision Analysis State Of The Art Surveys 2004

Furthermore, in a national road network, an equal distribution of interventions over the network is expected to promote a feeling of social equity. Considering this, the number of maintenance and rehabilitation interventions in the last 10 years was considered as a performance descriptor of the interventions. The length of time considered was chosen by the decision-maker. The construction of the performance scales followed the same procedure as before. When asked about the need for other performance levels, the decision-maker decided to add a performance level for the two interventions scenario.

Table 5 shows the performance levels described in descending order of attractiveness. Table 5. Performance scale of the interventions relative to the number of interventions in the last 10 years. The case study illustrates a decision analysis process that works for scenarios in which, due to budget limitations, only a set of maintenance and rehabilitation interventions can be performed.

In this context, it is necessary to prioritize and select the interventions that should be done. From the set of selected interventions, the maximum benefit, in terms of the preferences of the decision-maker, should be derived. In order to provide a practical demonstration of the approach proposed in this study, a portfolio of possible interventions in the road network was created through a simulation process. The simulation process was based on existing records and previous interventions made in the road network.

Average network conditions were considered to allow the comparison of intervention options. Table 6 presents the portfolio of possible intervention options considered in this case study.

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This road had no interventions in the last 10 years. A simple additive value model was used to evaluate each intervention option. Equation 1 defines the simple additive value model. Following the procedures described in sections Performance descriptors and Value functions definition, a total of four value functions and weights were determined one per each criterion.