References
The MACBETH approach: Basic ideas, software and an application
Bana e Costa C.A.; Vansnick J-C.
Advances in Decision Analysis, N. Meskens, M. Roubens (eds.), 1999, Kluwer Academic Publishers, Book Series: Mathematical Modelling: Theory and Applications, vol. 4, pp. 131-157
Abstract:
MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) is an interactive approach to guide the construction, on a set S of stimuli, of an interval scale which quantifies the attractiveness of the elements of S in the opinion of an evaluator. The aim of this paper is to present the main ideas on which this new decision-aid approach is based, and its software. macbeth has already been applied in several complex cases. One such case was in the first application of multicriteria analysis to the evaluation of a European structural programme, the Hainaut case, which is used to illustrate the presentation in this paper.
A career choice problem: an example of how to use MACBETH to build a quantitative value model based on qualitative value judgements
Bana e Costa C.A.; Chagas, M.P.
European Journal of Operational Research (accepted for publication). (Preprint: Working Paper LSEOR 02.55, 2002, London School of Economics).
Abstract:
MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) is a non-numerical approach developed to enable facilitators to avoid forcing their clients to rely upon numerical representations of their strength of preference. macbeth is an interactive approach that uses semantic judgments about the attractiveness of several stimuli to help a decision maker quantify the attractiveness of each. It employs an interactive questioning procedure that compares two elements at a time, requesting only a qualitative preference judgment. As the answers are entered into the software package (m-macbeth), it automatically verifies their consistency. It subsequently generates a numerical scale that is representative of the decision makerís judgments. Through a similar process, it permits the generation of weighting scales for criteria as well as a sensitivity analysis for each criterion. This paper makes use of the macbeth approach to help an individual select his future career from a number of self imposed possibilities. A comparison is made with the numerical technique SMART (Simple Multi-Attribute Rating Technique), previously used with the same intent.
Un Logiciel d'Exploitation d'Informations Préférentielles pour l'Aide à la Décision
De Corte, J.-M.
PhD Thesis, University of Mons-Hainaut, Belgium, 2002.
Introduction:
Il est courant, dans une étude d’aide à la décision, de devoir tenir compte de plusieurs points de vue pour comparer l’attractivité relative des différentes actions susceptibles de résoudre le problème de décision considéré. Ainsi par exemple, suite à un appel d’offres, il convient de comparer les réponses obtenues ( qui constituent dans ce cas les « actions » ) en tenant compte de tous les points de vue ( critères ) spécifiés dans l’appel d’offres. Une telle comparaison n’est pas facile pour le(s) décideur(s) car, comme l’ont montré les travaux de Miller (voir Miller, 1956), il est difficile pour l’esprit humain de traiter simultanément plus de sept informations. Or, la comparaison de deux actions selon quatre points de vue fait déjà intervenir huit informations. C’est la raison pour laquelle des procédures systématiques de comparaison des actions ont été imaginées. Bien que ces procédures puissent prendre des formes diverses, elles comprennent toutes :
- une phase d’acquisition, auprès du (des) décideur(s), d’information préférentielle
- une phase d’exploitation de cette information préférentielle ( phase d’agrégation ).
L’objet de cette thèse est l’étude de problèmes mathématiques apparaissant au cours de ces deux phases ainsi que la présentation d’un logiciel mettant en pratique les solutions que nous y avons apportés dans le cadre d’une méthodologie particulière d’aide à la décision : l’approche MACBETH ( Measuring Attractiveness by a Categorical Based Evaluation TecHnique ). Elle comporte deux grands chapitres correspondant aux deux grandes phases évoquées ci-dessus. Le premier chapitre consiste en l’étude, pour chaque mode de questionnement introduit dans l’approche MACBETH, des structures mathématiques permettant de représenter numériquement, sur base de règles de mesurage, l’information préférentielle obtenue. Cette étude nous a conduit à concevoir d’une part, des algorithmes de détection des « inconsistances » pouvant apparaître dans les réponses du (des) décideur(s) d’autre part, des algorithmes de recherche de suggestions de modification des jugements initiaux à soumettre au(x) décideur(s). Nous présentons également dans ce chapitre quelques outils graphiques que nous avons mis au point en vue de faciliter la discussion avec le(s) décideur(s) concernant une représentation numérique particulière ( échelle MACBETH ) de l’information préférentielle disponible. Le deuxième chapitre concerne ce qu’on appelle, dans le domaine de la décision, la phase d’agrégation de l’information préférentielle. C’est dans cette phase que sont spécifiées les règles selon lesquelles la comparaison globale ( c’est-à-dire en tenant compte de tous les points de vue ) des actions est effectuée. Il s’agit là d’une phase délicate car des problèmes de signifiance mathématique ( des résultats des comparaisons globales ) peuvent apparaître si la non-unicité des représentations numériques de l’information préférentielle n’est pas correctement prise en charge. Après avoir explicité les grandes phases de la méthodologie MACBETH, nous présentons, dans ce deuxième chapitre, le cadre mathématique dans lequel nous nous sommes placés pour garantir la correction des résultats des comparaisons globales des actions. Les divers algorithmes que nous avons mis au point sont expliqués et nous décrivons aussi la manière dont nous avons intégré ces idées nouvelles dans le logiciel que nous avons réalisé en vue de pouvoir appliquer, en pratique, l’approche MACBETH. Notre travail se termine par une brève conclusion dans laquelle nous citons notamment quelques applications réelles d’aide à la décision qui ont déjà pu être réalisées grâce à ce logiciel.
Behind MACBETH
Bana e Costa J.
Nato Advanced Research on Risk, Uncertainty and Decision Analysis for Environmental Security and Nonchemical Stressors, Lisbon, Portugal
MACBETH
Bana e Costa CA, De Corte JM, Vansnick JC: MACBETH. Int J Inf Tech Decis 2012, 11:359-387.
Abstract:
This paper presents an up-to-date comprehensive overview of the MACBETH approach to multicriteria decision-aid. It requires only qualitative judgements about differences of attractiveness to help a decision maker, or a decision-advisory group, quantify the relative value of options. The approach, based on the additive value model, aims to support interactive learning about evaluation problems and the elaboration of recommendations to prioritize and select options in individual or group decision making processes. A case study based on a real-world application of MACBETH for multicriteria value measurement of IT solutions is presented. It shows how the M-MACBETH decision support system can be used in practice to construct an additive evaluation model. The paper addresses key issues related to structuring the model, building value scales, weighting criteria and sensitivity and robustness analyzes. Reference is also made to applications of MACBETH reported in the scientific literature.
Other references : Applications
Facilitating bid evaluation in public call for tenders: a socio-technical approach
Bana e Costa C.A.; Corrêa E.C.; De Corte J.-M.; Vansnick J.-C.
OMEGA The International Journal of Management Science, 2002, vol. 30, no. 3, pp. 227-242
Abstract:
A specific multicriteria socio-technical approach to facilitating bid evaluation processes is presented and several issues that warrant its use are discussed. Some real-world interventions in international public call for tenders illustrate practical aspects of structuring criteria and creating a computer-based additive value model in direct interaction with Evaluation Committees responsible for bid evaluation, supported by the macbeth approach.
Qualitative modelling of credit scoring: a case study in banking
Bana e Costa C.A.; Barroso, L.; Soares, J.O.
Journal of European Research Studies, 2002, vol. V, no. 1-2, pp. 37-51
Abstract:
Several modelling procedures have been suggested in the literature that aim to help credit granting decisions. Most of these utilize statistical, operational research and artificial intelligence techniques to identify patterns among past applications, in order to enable a more well-informed assessment of risk as well as the automation of credit scoring. For some types of loans, we find that the modelling procedure must permit the consideration of qualitative expert judgements concerning the performance attractiveness of the applications. In this paper, we describe in detail the various steps taken to build such a model in the context of the banking sector, using the macbeth interactive approach. The model addresses the scoring of medium and long term loans to firms, to enable the multicriteria assignment of each application to a category which may range from rejection to acceptance with different spreads.
Multicriteria approach for strategic town panning: the case of Barcelos
Bana e Costa C.A.; Costa-Lobo M.L.; Ramos I.A.J.; Vansnick J.-C.
in Aiding Decisions with Multiple Criteria: Essays in Honour of Bernard Roy, D. Bouyssou, E. Jacquet-Lagrèze, P. Perny, R. Slowinsky, D. Vanderpooten, P. Vincke (eds.), 2002, Kluwer Academic Publishers, Book Series: International Series in Operations Research & Management Science, vol. 44, pp. 429-456.
Abstract:
Barcelos was one of the medium sized Portuguese towns selected to be included in a governmental program aiming at restructuring the country urban network. Each town had to prepare a “City Strategic Plan” as a previous condition to get financial support for the implementation of its strategy. This paper describes how a multicriteria methodology, enhanced with problem structuring techniques, supported the construction of a strategy for Barcelos in direct interaction with planners and the local elected politicians in a decision-conferencing framework. This was a socio-technical and learning process that successfully implemented, in a strategic town-planning context, what Bernard Roy defined as “decision aiding”.
Assigning priorities for maintenance, repair, refurbishment in managing a municipal housing stock
Bana e Costa C.A.; Oliveira R.C.
European Journal of Operational Research, 2002, vol. 138, no. 2, pp. 380-391
Abstract:
The municipality of Lisbon owns a large housing stock that requires maintenance, repair and refurbishment. Taken together, these activities imply a financial effort each year that clearly exceeds the available budget, and therefore it is critical that the decisions on which sub-set of potential activities should be carried out in each coming year are based on sound analysis and evaluation. The design and construction process of a model to assist the Lisbon Municipality to assign priorities to these activities is described. The macbeth approach was extensively used, in an interactive and constructive process, to derive the value functions associated with each criterion and their respective weights, reflecting municipal policies and their officials preferences and attitudes. The paper also presents the procedure used to determine multidimensional reference-profiles that define urgency categories, enabling to assign each potential action to one of these categories. Finally, a specific model was defined to aggregate elemental building jobs in ”packages”, when there are arguments (in terms of cost reduction, action coherence, urban environment impact synergies, etc.) that favour their joint execution under a single contract.
The use of multi-criteria decision analysis to support the search for less conflicting policy options in a multi-actor context: case study
Bana e Costa C.A.
Journal of Multi-Criteria Decision Analysis, 2001, vol. 10, Issue 2, pp. 111-125
Abstract:
Public resource allocation often requires the management of conflicting objectives of multiple policy actors at different spatial levels. An example is the case study on which this paper is based: the definition of an investment policy in new inter-municipal road-links in the Lisbon Metropolitan Region (LMR) for the period 1999-2004. The key regional (inter-municipal) objective is to choose the sub-set of proposed road projects that maximizes the quality of LMR’s road network for a fixed available budget. Conflict arises, however, if environmental, social and economic impacts at the level of the 18 municipalities involved are significantly unbalanced. This paper describes how multi-criteria decision analysis’ concepts, techniques and software tools were used to analyse spatial conflicts in the LMR case. The study provided the decision-making body formed by all the municipal mayors with useful information about how much it is necessary to negotiate to reach an agreement on a specific investment policy option.
Conflict dissolution in the public sector: A case-sudy
Bana e Costa C.A.; Nunes da Silva F.; Vansnick J.-C.
European Journal of Operational Research, 2001, vol. 130, no. 2, pp. 388-401
Abstract:
The construction of a new railway link to the port of Lisbon has been postponed many times as a result of a conflict of different viewpoints held by various public stakeholders, namely between the municipality of Lisbon and the Lisbon Railway Node Bureau, while the Portuguese Railway Company has assumed a more flexible attitude. Over recent years, three groups of solutions, totalling nine alternative projects, have been proposed by each of these three actors, but none has been simultaneously accepted by all the three. The development of the urbanisation plan for Alc‚ntara (the zone of the city where the railway line links to the port) has presented an opportunity to try to dissolve the conflict. This paper describes the multicriteria approach followed to support the creation of a new ”good” (win-win) compromise solution by the planning team based on the study of the consequences of the existing alternatives. In particular, we describe the structuring phase of the study and the use of a disaggregation-aggregation approach to take into account the different value systems of the stakeholders.
Decision Support Systems in action: Integrated application in a multicriteria decision aid process
Bana e Costa C.A.; Ensslin L.; CorrÃa E.C.; Vansnick J.-C.
European Journal of Operational Research, 1999, vol. 113, no. 2, pp. 315-335
Abstract:
We describe a real application of Multi-Criteria Decision Analysis (MCDA) in which several Decision Support Systems (DSSs) were harmoniously integrated in the interactive learning process of tackling the complex strategic problematic situation faced by the Santa Catarina textile industry, in the south of Brazil. We feel that two significant conclusions can be drawn from our conjoint use of Graphics COPE, macbeth, V.I.S.A, and EQUITY in building a model of values: (1) Providing decision-support is much more than merely applying a technical tool to solve a well-defined decision problem; it is, at least it was in our case, a complex (but exciting) activity of someone (the facilitator) who, with the support of adequate methodological and technical tools, progressively tried to shed light on an initially ill-structured decision-making process. (2) Under a constructive attitude in decision-aid, DSSs became effective tools for helping the facilitators to help the decision-actors, both in the structuring and evaluation phases of the process, and in creating new decision opportunities. In particular, visual man-machine interaction greatly contributed to the actors’ learning about their problem and values. Moreover, visually appealing sensitivity analyses increased the problem-owners’ trust in the recommendations elaborated from the model.
Applications of the macbeth approach in the framework of an additive aggregation model
Bana e Costa C.A.; Stewart T.J.; Vansnick J.-C.
Journal of Multi-Criteria Decision Analysis, 1997, vol. 6, Issue 2, pp. 107-114
Abstract:
In measurement theory terminology, macbeth is an interactive approach for mapping into a real scale the various degrees to which the elements of a finite set possess a property P. The originality of macbeth’s questioning procedure is the possibility of establishing a constructive path towards cardinal measurement in both quantitative and substantive meaningful terms, avoiding the operational problems recognized as a weakness of other procedures. The use of the notion of semantic absolute judgements plays a key role here and the simplicity, interactivity and constructiveness of our approach insert it in the modern paradigms of decision aid. This article illustrates the usefulness of macbeth as a tool to facilitate decision support, by describing its application in two real public decision situations where we acted as facilitators. Although the cases correspond to quite different decision contexts and problematics and our interventions have addressed diverse issues, they have in common the fact that we conducted both evaluation processes in the framework of an additive multicriteria aggregation procedure. In the first case macbeth has been used to support the construction of (local) cardinal value functions, while the second illustrates how our approach can serve as a weighting procedure to determine the scaling constants of an additive aggregation model.
Other references : Theory
Cardinal value measurement with MACBETH
Bana e Costa C.A.; Vansnick J-C.
in Decision Making: Recent Developments and Worldwide Applications, S.H. Zanakis, G. Doukidis, C. Zapounidis (eds.), 2000, Kluwer Academic Publishers, Book Series: Applied Optimization, vol. 45, pp. 317-329.
Abstract:
Decision-making is above all a human activity in which value judgments about the attractiveness of options play a key role. The integration of technology and human decisions by means of the design and use of tools for the representation of value judgments that are simultaneously semantically meaningful, practically operational (user-friendly) and theoretically well founded is therefore an important research challenge. The MACBETH approach (Measuring Attractiveness by a Categorical Based Evaluation Technique) overviewed in this paper is a contribution in that direction. macbeth is an approach designed for building a cardinal scale measuring the attractiveness of options, throughout a learning process supported by a visual interactive software. This is interesting for decision-making when one wants to measure by how much an option is better than another one. Moreover, cardinal preference information is required to meaningfully perform operations with numerical scales, such as comparison of average sums, as required by multi-attribute value theory.
Preference relations and MCDM
Bana e Costa C.A.; Vansnick J-C.
in Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory and Applications, T. Gal, T. Stewart, T. Hanne (eds.), 1999, Kluwer Academic Publishers, Book Series: International Series in Operations Research & Management Science, vol. 21, pp. 4-14-23
Abstract:
Multicriteria decision aid is above all a human activity in which value judgements of involved actors play a crucial role. Therefore, “how to represent such judgements?” is a key question in MCDM. This chapter is devoted to this subject. Depending on the particular paradigm adopted for preference modelling, different questioning procedures can be conceived which lead to different preference structures. We present a few questioning procedures related to three basic paradigms, together with some preference structures that are useful for MCDM. First, the classical preference-indifference structure is discussed, followed by the introduction of the ideas of “incomparability” and “hesitation”. Finally, we present some complementary questioning procedures particularly relevant for cardinal modelling of value judgements.
A theoretical framework for Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH)
Bana e Costa C.A.; Vansnick J-C.
in Multicriteria Analysis, J. Climaco (ed.), 1997, Springer-Verlag, pp. 15-24
Abstract:
This paper presents a theoretical framework for the MACBETH approach. Taking as a starting point the measurement rules used for numerically representing the qualitative (categorical) preference information assessed by the questioning procedure of macbeth, we study the existence of a solution for our particular representation problem and we briefly discuss its unicity.
General overview of the MACBETH approach
Bana e Costa C.A.; Vansnick J-C.
in Advances in Multicriteria Analysis, P.M. Pardalos, Y. Siskos, C. Zopounidis (eds.), 1995, Kluwer Academic Publishers, Book Series: Nonconvex Optimization and its Applications, pp. 93-100
Introduction:
MACBETH is an interactive approach for cardinal measurement of judgments about the degrees to which the elements of a finite set A possess a property P. The name MACBETH, Measuring Attractiveness by a Categorical Based Evaluation Technique, comes from the fact that we conceived our approach with the aim of facilitating the measurement of (degrees of) attractiveness in decision processes. Nevertheless, macbeth can also be applied to measure other properties in domains of knowledge others than Decision Sciences, such as in Psychophysics or in Social Sciences. In this article we offer a general overview of macbeth where we introduce some modifications improving the initial technical formulation of [Bana e Costa and Vansnick, 1993 and 1994a], although the basic conceptual ideas remain the same.
MACBETH - An interactive path towards the construction of cardinal value functions
Bana e Costa C.A.; Vansnick J-C.
International Transactions in Operational Research, 1994, vol. 1, no. 4, pp. 489-500
Abstract:
The application of classical models and techniques for cardinal measurement of values usually requires a person (D) to answer very difficult questions. The MACBETH approach, presented in this paper, proposes a simple questioning procedure to ‘drive’ the interactive quantification of values through pairwise verbal judgements of difference of attractiveness between valuable elements of a set A. Technically, MACBETH uses a chain of four linear programs for assigning numbers to the elements of set A based upon the qualitative judgements expressed by D and to reveal possible sources of incoherence. In practice, this information is to be used as a basis for discussion and learning. MACBETH stands for Measuring Atrractiveness by a Categorical Based Evaluation TecHnique.
On the Mathematical Foundations of MACBETH
Bana e Costa CA, De Corte J-M, Vansnick J-C: On the Mathematical Foundations of MACBETH.
in Multiple Criteria Decision Analysis: State of the Art Surveys. Edited by Greco S, Ehrgott M, Figueira RJ. New York, NY: Springer; 2016: 421-463
Abstract:
MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) is a multicriteria decision analysis approach that requires only qualitative judgements about differences of value to help an individual or a group quantify the relative attractiveness of options. This chapter presents a new up-to-date survey of the mathematical foundations of MACBETH. Reference is also made to real-world applications and an extensive bibliography, spanning back to the early 1990s, is provided.
