Bertrand Mareschal

How to select and how to rank projects: the Prométhée method

Abstract In this paper, we present the Promethee methods, a new class of outranking methods in multicriteria analysis. Their main features are simplicity, clearness and stability. The notion of generalized criterion is used to construct a valued outranking relation. All the parameters to be defined have an economic signification, so that the decision maker can easily fix them. Two ways of treatment are proposed: It is possible to obtain either a partial preorder ( Promethee I) or a complete one ( Promethee II), both on a finite set of feasible actions. A comparison is made with the Electre III method. The stability of the results given by the two methods is analysed. Numerical applications are given in order to illustrate the properties of the new methods and some further problems are discussed.

The PROMCALC & GAIA decision support system for multicriteria decision aid

PROMCALC & GAIA is the last development of the interactive decision support system based on the PROMETHEE and GAIA methodology. In the first section, the fundamental characteristics of multicriteria problems are recalled and requisites are formulated for an appropriate multicriteria decision aid methodology. Based on these requisites, the PROMETHEE methods are then introduced, including newer developments such as PROMETHEE V (multicriteria optimization under constraints) and the GAIA visual modelling method. The actual implementation of the proposed methodology in the PROMCALC & GAIA software is then detailed and a numerical example is developed to illustrate the possibilities of the system.

Weight stability intervals in multicriteria decision aid

Abstract In this paper we study the stability of the results given by a wide class of MCDA methods to changes of the weights of the criteria. Three aspects of stability are discussed. In each case we propose to construct stability intervals for the weights of either single criteria or groups of criteria. A necessary and sufficient condition for stability is also considered. The use of these instruments is demonstrated with a numerical example.

PROMETHEE V: MCDM problems with segmentation constraints

AbstractMulticriteria problems with a finite set of possible alternatives grouped in clusters or segments are considered. The problem is to select a subset of alternatives evaluated by several criteria and submitted to segmentation constraints between and within the clusters. The basic PROMETHEE-GAIA procedure for multicriteria problems is first briefly recalled. This procedure provides the decisionmaker with good compromises as well as an interesting visual descriptive view of the multicriteria problem; but, up to now, it doesn’t take the segmentation constraints into account. PROMETHEE V is combining the results obtained by the basic PROMETHEE-GAIA procedure and a partiaular (0–1) Linear Program in order to integrate these constraints. An application is described. An efficient microcomputer software is available from the authors.

Nuclear waste management: an application of the multicriteria PROMETHEE methods

Radioactive waste management is an important issue for every electronuclear programme. A particular problem is to know how to finance the waste disposal: indeed, the time span between the electricity production itself and the final disposal in geological formations can represent decades. The problem is made more complex by the choice of a time scenario and of a disposal site. Moreover, the decision-making process involves several points of view of different actors: electricity companies, consumers, public bodies, etc. A multicriteria analysis has therefore been applied, using the PROMETHEE methods and the geometrical representation GAIA. These methods are well adapted to this problem with many actions and few very conflicting criteria.

BANKADVISER: An industrial evaluation system

Abstract BANKADVISER is a multicriteria industrial evaluation system. It provides evaluations of individual items such as firms, industries, companies, industrial clients, …, within a set of similar ones. The evaluations take into account not only the own scores of the item but also those of the other ones in the set (positioning). The evaluation procedure is based on financial data from the Balance Sheet and the Income Statement of each item. BANKADVISER is particularly useful for decision-makers, financial analysts, banks, insurance companies, …, when they have to make decisions about their industrial clients. The system allows one to manage the data about the clients, to analyse their economic profile, to detect their strong and weak features, to evaluate any risk associated with them. Decisions such as whether or not to provide a loan, fix the loan modalities (interest, terms, …), offer guarantee for foreign activities, cover some deficits, …, can easily be finalized after the BANKADVISER evaluation. BANKADVISER is a visual interactive modelling system. It is interactive because for each item, the user has the opportunity to run through one part of the information to another, because he can ask for additional information on the strong or the weak features of the profile, because comparison with similar items can be given on request. It is a modelling system because an intricate multicriteria situation is modelled by using the extended PROMETHEE MCDM methodology. BANKADVISER has been implemented on a microcomputer. For the sake of an effective presentation the paper has been written according to the structure of the microcomputer software. It is illustrated by data of a Real-World application.

Novel types of sensitivity analysis for additive MCDM methods

Three novel types of sensitivity analysis are presented. They determine the following: 1) the sensitivity of a ranking to specific changes in the evaluations of all alternatives on certain criteria; 2) the influence of specific changes in certain criterion-scores of an alternative; 3) the minimum modification of the weights required to make an alternative ranked first. The use of these instruments is demonstrated by the results of a simulation experiment. Results show that the first and second type of sensitivity analysis enable to apply multiple criteria decision making (MCDM) methods in dynamic circumstances. The third type of sensitivity analysis is demonstrated to be a tool to analyze the total weight space.

The promethee VI PROCEDURE: How to differentiate hard from soft multicriteria problems

ABSTRACT The basic principles of the PROMETHEE and GAIA multicriteria decision aid methods are first recalled. An original procedure, called PROMETHEE VI, is then introduced to evaluate the degree of hardness of a multicriteria decision problem with respect to the weights given to the criteria. A classification between hard and soft multicriteria decision problems is then proposed. A numerical application is developed to demonstrate the procedure.

The PROMETHEE methods for MCDM: the PROMCALC, GAIA and BANK ADVISER software

The PROMETHEE Methods are particularly appropriate to treat multicriteria problems of the following type: