Ethics and decision

Real World situations can be faced by qualitative and by quantitative approaches, by perceptions and by measurements, by feelings and by models. In this paper we first compare the management of Natural Real World situations and the management of Human Real World situations. Although there are strong similarities, there are also major differences. “GOD” is keeping the laws of Nature unchanged and therefore it is not to be included in the models of Physics, while the “MIND” of the Decision-maker has to be taken into account in Operational Research (OR). Decision-making for Human processes requires also to take into account three poles of influence: the Rational, the Subjective and the Ethical one. Most of the basic models of OR are only considering the Rational Pole. No freedom is left to the Decision-maker, no Ethical aspects are considered. It is shown that, if well adapted, the Multicriteria Decision Aid (MCDA) PROMETHEE–GAIA procedure can provide well-balanced solutions between Rationality, Subjectivity and Ethics. Both the Mind of the Decision-maker and the “Ethical Conscience” of Mankind can be represented and included in the model.     

Model choice in multicriteria decision aid

The purpose of this paper is to illustrate, using a real case study, one of the points stressed in the “Manifesto of the new Multi Criteria Decision Aid (MCDA) era” (Bouyssou et al., 1993) regarding the application of the basic theory of MCDA procedures. Although the great diversity of MCDA procedures may be seen as a strong point, it can be a weakness, and a systematic analysis of decision procedures if one method makes more sense than another for a specific problem is necessary. The problem of selecting the most appropriate (MCDA) technique for a particular application is in itself a MCDA problem since the decision making criteria used for the selection are different and conflicting in nature. In this paper three selection models are implemented to assist the system analyst, when confronted with a multi-objective decision problem, to select the most appropriate MCDA technique for application to the problem of optimal ranking of water development projects in an arid country. These models are developed by Deason (1984), Gershon (1981), and Tecle (1988). Results indicated that PROMETHEE was the most preferred method for this problem.     

PROMETHEE: A comprehensive literature review on methodologies and applications

In recent decades, several Multi-Criteria Decision Aid (MCDA) methods have been proposed to help in selecting the best compromise alternatives. In the meantime, the PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) family of outranking methods and their applications has attracted much attention from academics and practitioners. In this paper, a classification scheme and a comprehensive literature review are presented in order to uncover, classify, and interpret the current research on PROMETHEE methodologies and applications. Based on the scheme, 217 scholarly papers from 100 journals are categorized into application areas and non-application papers. The application areas include the papers on the topics of Environment Management, Hydrology and Water Management, Business and Financial Management, Chemistry, Logistics and Transportation, Manufacturing and Assembly, Energy Management, Social, and Other Topics. The last area covers the papers published in several fields: Medicine, Agriculture, Education, Design, Government and Sports. The scholarly papers are also classified by (1) year of publication, (2) journal of publication, (3) authors’ nationality, (4) PROMETHEE as applied with other MCDA methods, and (5) PROMETHEE as applied with GAIA (Geometrical Analysis for Interactive Aid) plane. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of PROMETHEE methodologies and applications, and hence promote the future of PROMETHEE research.     

Assessing the performance of biogas plants with multi-criteria and data envelopment analysis

This paper performs an assessment of 41 agricultural biogas plants located in Austria to determine their relative performance in terms of economic, environmental, and social criteria and corresponding indicators. The comparison of these renewable energy conversion plants is based on two complementary analyses. Data envelopment analysis (DEA) was conducted to provide measures of radial efficiency relative to the observed frontier of production possibilities. Multi-criteria decision analysis (MCDA), using the IRIS/ELECTRE TRI methodology, was conducted to obtain a different perspective on the results, and as a tool that would enable to incorporate managerial preferences easily. To be able to use IRIS while keeping the spirit behind DEA, the evaluation criteria were defined as different output/input efficiency ratios, and no information about criteria weights was introduced at the outset. The results suggest that MCDA, and the use of IRIS in particular, constitutes a useful approach that can be applied in a complementary way to DEA.     

Interactive outranking approaches for multicriteria decision-making problems with imprecise information

PROMETHEE is a powerful method, which can solve many multiple criteria decision making (MCDM) problems. It involves sophisticated preference modelling techniques but requires too much a priori precise information about parameter values (such as criterion weights and thresholds). In this paper, we consider a MCDM problem where alternatives are evaluated on several conflicting criteria, and the criterion weights and/or thresholds are imprecise or unknown to the decision maker (DM). We build robust outranking relations among the alternatives in order to help the DM to rank the alternatives and select the best alternative. We propose interactive approaches based on PROMETHEE method. We develop a decision aid tool called INTOUR, which implements the developed approaches.     

Stochastic multicriteria acceptability analysis using the data envelopment model

Data envelopment analysis (DEA) and stochastic multicriteria acceptability analysis (SMAA-2) are methods for evaluating alternatives based on multiple criteria. While DEA is mainly an ex-post tool used for classifying alternatives into efficient and inefficient ones, SMAA-2 is an ex-ante tool for supporting multiple criteria decision-making. Both methods use a kind of value function where the importance of criteria is modeled using weights. Unlike many other methods, neither DEA nor SMAA-2 requires decision-makers’ weights as input. Instead, these so-called non-parametric methods explore the weight space in order to identify weights favorable for each alternative. This paper introduces the SMAA-D method, which is a combination of DEA and SMAA-2. SMAA-D can be characterized as an extension of DEA to handle uncertain or imprecise data to provide stochastic efficiency measures. Alternatively, the combined method can be seen as a variant of SMAA-2 with a DEA-type value function.     

Additive DEA based on MCDA with imprecise information

This work exploits links between Data Envelopment Analysis (DEA) and multicriteria decision analysis (MCDA), with decision making units (DMUs) playing the role of decision alternatives. A novel perspective is suggested on the use of the additive DEA model in order to overcome some of its shortcomings, using concepts from multiattribute utility models with imprecise information. The underlying idea is to convert input and output factors into utility functions that are aggregated using a weighted sum (additive model of multiattribute utility theory), and then let each DMU choose the weights associated with these functions that minimize the difference of utility to the best DMU. The resulting additive DEA model with oriented projections has a clear rationale for its efficiency measures, and allows meaningful introduction of constraints on factor weights.     

An interval version of PROMETHEE for the comparison of building products' design with ill-defined data on environmental quality

Life Cycle Assessment (LCA) is a powerful technique used to calculate total input and output flows of materials and energy from and to the environment during every step of a product life. A measure of a product Environmental Quality (EQ) can then be derived and help in the selection and in the design of more environmentally friendly design alternatives. EQ is a multicriteria measurement. In the construction field, LCA flows cannot be known with precision without loss of realism. Hence intervals have been introduced to model them. Thus, different designs are characterized by interval multicriteria measures. Manipulation of such environmental performances calls for a MCDA method which (1) does not allow for trade-offs between criteria, (2) preserves as much information as possible and (3) is simple enough to be understood by non-specialist users. PROMETHEE was identified as a suitable method according to the previous criteria, but it is not able to handle interval performances so far. We discuss the necessary changes to devise an interval version, called “PROMETHEE I”.     

The SMAA-PROMETHEE method

PROMETHEE methods are widely used in Multiple Criteria Decision Aiding (MCDA) to deal with real world decision making problems. In this paper, we propose to apply the Stochastic Multicriteria Acceptability Analysis (SMAA) to the family of PROMETHEE methods in order to explore the whole set of parameters compatible with some preference information provided by the Decision Maker (DM). The application of the presented methodology is described in a didactic example.     

A careful look at the importance of criteria and weights

We investigate the connection between weights, scales, and the importance of criteria, when a linear value function is assumed to be a suitable representation of a decision maker’s preferences. Our considerations are based on a simple two-criteria experiment, where the participants were asked to indicate which of the criteria was more important, and to pairwise compare a number of alternatives. We use the participants’ pairwise choices to estimate the weights for the criteria in such a way that the linear value function explains the choices to the extent possible. More specifically, we study two research questions: (1) is it possible to find a general scaling principle that makes the rank order of the importance of criteria consistent with the rank order of the magnitudes of the weights, and (2) how good is a simple, direct method of asking the decision maker to “provide” weights for the criteria compared to our estimation procedure. Our results imply that there is reason to question two common beliefs, namely that the values of the weights would reflect the importance of criteria, and that people could reliably “provide” such weights without estimation.     

Weight determination for consistently ranking alternatives in multiple criteria decision analysis

One of the most difficult tasks in multiple criteria decision analysis (MCDA) is determining the weights of individual criteria so that all alternatives can be compared based on the aggregate performance of all criteria. This problem can be transformed into the compromise programming of seeking alternatives with a shorter distance to the ideal or a longer distance to the anti-ideal despite the rankings based on the two distance measures possibly not being the same. In order to obtain consistent rankings, this paper proposes a measure of relative distance, which involves the calculation of the relative position of an alternative between the anti-ideal and the ideal for ranking. In this case, minimizing the distance to the ideal is equivalent to maximizing the distance to the anti-ideal, so the rankings obtained from the two criteria are the same. An example is used to discuss the advantages and disadvantages of the proposed method, and the results are compared with those obtained from the TOPSIS method.     

An estimate of the objective function optimum for the network Steiner problem

The study area is La Colacha sub-basins from Arroyos Menores basins, natural areas at West and South of Río Cuarto in Province of Córdoba of Argentina, fertile with loess soils and monsoon temperate climate, but with soil erosions including regressive gullies that degrade them progressively. Cultivated gently since some hundred 60 years coordinated action planning has become necessary to conserve lands while keeping good agro-production. Some of the authors were engineers trained here and other had former experience in Salta, Argentina, using a set of Decision Theory Methods, (DTM), to consider the possible systems of soil uses and actions to be recommended. After having improved data on soils and on hydrology for the study area, they have adapted as academic study these DTM for Arroyos Menores areas where gully erosions are severe, also intending to offer better view for the necessary planning to have policies of actions and uses, done by the local society decision and services, and in part by land owners. This paper concentrates on the application of a set of discrete multi-criteria models (MCDM), where alternatives were global, considering soil conservation and hydrologic management actions, and main types of use of soil, and where criteria were about the diverse consequences, grouped as environmental, economic, and social. As methods they have used for the sub areas PROMETHEE with sets of weights, comparing results with ELECTRE with same data and weights, and with AHP method needing comparisons of criteria by authors, getting somehow compatible results, but finding that the “weighted PROMETHEE II” was the more adapted for the present study. The system and results are very global, and are offered as indications for planning, that will require using detailed engineering and administration aspects for series of local singular actions or for management pursued in time.     

A general decomposition approach for multi-criteria decision trees

In this paper, we address the dynamic and multi-criteria decision-making problems under uncertainty, generally represented by multi-criteria decision trees. Decision-making consists of choosing, at each period, a decision that maximizes the decision-maker outcomes. These outcomes should often be measured against a set of heterogeneous and conflicting criteria. Generating the set of non-dominated solutions is a common approach considered in the literature to solve the multi-criteria decision trees, but it becomes very challenging for large problems. We propose a new approach to solve multi-criteria decision trees without generating the set of all non-dominated solutions, which should reduce the computation time and the cardinality of the solution set. In particular, the proposed approach combines the advantages of decomposition with the application of multi-criteria decision aid (MCDA) methods at each decision node. A generalization of the Bellman’s principle of decomposition to the multi-criteria context is put forward. A decomposition theorem is therefore proposed. Under the sufficient conditions stated by the theorem, the principle of decomposition will generate the set of best compromise strategies. Seven MCDA methods are then characterized (lexicographic, weighted sum, multi-attribute value theory, TOPSIS, ELECTRE III, and PROMETHEE II) against the conditions of the theorem of decomposition and against other properties (neutrality, anonymous, fidelity, dominance, independency), in order to confirm or infirm their applicability with the proposed decomposition principle. Moreover, the relationship between independency and temporal consistence is discussed as well as the effects of incomparableness, rank reversals, and use of thresholds. Two conjectures resulted from this characterization.     

A data model for algorithmic multiple criteria decision analysis

Various software tools implementing multiple criteria decision analysis (MCDA) methods have appeared over the last decades. Although MCDA methods share common features, most of the implementing software have been developed independently from scratch. Majority of the tools have a proprietary storage format and exchanging data among software is cumbersome. Common data exchange standard would be useful for an analyst wanting to apply different methods on the same problem. The Decision Deck project has proposed to build components implementing MCDA methods in a reusable and interchangeable manner. A key element in this scheme is the XMCDA standard, a proposal that aims to standardize an XML encoding of common structures appearing in MCDA models, such as criteria and performance evaluations. Although XMCDA allows to present most data structures for MCDA models, it almost completely lacks data integrity checks. In this paper we present a new comprehensive data model for MCDA problems, implemented as an XML schema. The data model includes types that are sufficient to represent multi-attribute value/utility models, ELECTRE III/TRI models, and their stochastic extensions, and AHP. We also discuss use of the data model in algorithmic MCDA.     

A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach

Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and multiple outputs. In this technique, the weights for inputs and outputs are estimated in the best advantage for each unit so as to maximize its relative efficiency. But, this flexibility in selecting the weights deters the comparison among DMUs on a common base. For dealing with this difficulty, Kao and Hung (2005) proposed a compromise solution approach for generating common weights under the DEA framework. The proposed multiple criteria decision-making (MCDM) model was derived from the original non-linear DEA model. This paper presents an improvement to Kao and Hung's approach by means of introducing an MCDM model which is derived from a new linear DEA model.     

A DSS for multiple criteria decision analysis with imprecisely specified trade-offs

The paper describes a decision support system (DSS) for multiple criteria decision analysis (MCDA). It is assumed that the information about the trade-offs is given in the form of lower and upper bounds. The software helps the user to identify candidate solutions from a finite set of decision alternatives and can be used in an interactive decision process. The choice of the software features is based on the author's experience with an environmental case study, which is discussed.     

The SIR method: A superiority and inferiority ranking method for multiple criteria decision making

In this paper, a superiority and inferiority ranking (SIR) method is proposed. This new method uses two types of information, the superiority and the inferiority information, to derive two types of flows, the superiority flow and the inferiority flow, by which the set of alternatives are ranked partially or completely. Relationships between the SIR method and some of the classical multiple criteria decision making (MCDM) methods (such as SAW, TOPSIS and PROMETHEE) are explored. It is proved that the SIR method is a significant extension of the well-known PROMETHEE method.     

Fuzzy cross-efficiency evaluation: a possibility approach

Cross-efficiency evaluation is an extension of data envelopment analysis (DEA) aimed at ranking decision making units (DMUs) involved in a production process regarding their efficiency. As has been done with other enhancements and extensions of DEA, in this paper we propose a fuzzy approach to the cross-efficiency evaluation. Specifically, we develop a fuzzy cross-efficiency evaluation based on the possibility approach by Lertworasirikul et al. (Fuzzy Sets Syst 139:379–394, 2003a) to fuzzy DEA. Thus, a methodology for ranking DMUs is presented that may be used when data are imprecise, in particular for fuzzy inputs and outputs being normal and convex. We prove some results that allow us to define “consistent” cross-efficiencies. The ranking of DMUs for a given possibility level results from an ordering of cross-efficiency scores, which are real numbers. As in the crisp case, we also develop benevolent and aggressive fuzzy formulations in order to deal with the alternate optima for the weights.     

A multiple criteria ranking method based on game cross-evaluation approach

The application of Data Envelopment Analysis (DEA) as an alternative multiple criteria decision making (MCDM) tool has been gaining more attentions in the literatures. Doyle (Organ. Behav. Hum. Decis. Process. 62(1):87?C100, 1995) presents a method of multi-attribute choice based on an application of DEA. In the first part of his method, the straightforward DEA is considered as an idealized process of self-evaluation in which each alternative weighs the attributes in order to maximize its own score (or desirability) relative to the other alternatives. Then, in the second step, each alternative applies its own DEA-derived best weights to each of the other alternatives (i.e., cross-evaluation), then the average of the cross-evaluations that get placed on an alternative is taken as an index of its overall score. In some cases of multiple criteria decision making, direct or indirect competitions exist among the alternatives, while the factor of competition is usually ignored in most of MCDM settings. This paper proposes an approach to evaluate and rank alternatives in MCDM via an extension of DEA method, namely DEA game cross-efficiency model in Liang, Wu, Cook and Zhu (Oper. Res. 56(5):1278?C1288, 2008b), in which each alternative is viewed as a player who seeks to maximize its own score (or desirability), under the condition that the cross-evaluation scores of each of other alternatives does not deteriorate. The game cross-evaluation score is obtained when the alternative??s own maximized scores are averaged. The obtained game cross-evaluation scores are unique and constitute a Nash equilibrium point. Therefore, the results and rankings based upon game cross-evaluation score analysis are more reliable and will benefit the decision makers.     

Finding common weights based on the DM's preference information

Data Envelopment Analysis (DEA) is basically a linear programming-based technique used for measuring the relative performance of organizational units, referred to as Decision Making Units (DMUs). The flexibility in selecting the weights in standard DEA models deters the comparison among DMUs on a common base. Moreover, these weights are not suitable to measure the preferences of a decision maker (DM). For dealing with the first difficulty, the concept of common weights was proposed in the DEA literature. But, none of the common weights approaches address the second difficulty. This paper proposes an alternative approach that we term as ‘preference common weights’, which is both practical and intellectually consistent with the DEA philosophy. To do this, we introduce a multiple objective linear programming model in which objective functions are input/output variables subject to the constraints similar to the equations that define production possibility set of standard DEA models. Then by using the Zionts–Wallenius method, we can generate common weights as the DM's underlying value structure about objective functions.