Modeling uncertainty in multi-criteria decision analysis

his paper provides a review of multiple criteria decision analysis (MCDA) for cases where attribute evaluations are uncertain. The main aim is to identify different tools which can be used to represent uncertain evaluations, and to broadly survey the available decision models that can be used to support uncertain decision making. The review includes models using probabilities or probability-like quantities; explicit risk measures such as quantiles and variances; fuzzy numbers, and scenarios. The practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed.     

A novel two-phase group decision making approach for construction project selection in a fuzzy environment

This paper considers a construction project problem under multiple criteria in a fuzzy environment and proposes a new two-phase group decision making (GDM) approach. This approach integrates a modified analytic network process (ANP) and an improved compromise ranking method, known as VIKOR. To take uncertainty and risk into account, a new decision making approach is presented with multiple fuzzy information by a group of experts, and a risk attitude for each expert is incorporated that can be expressed linguistically. First, a modified fuzzy ANP method is introduced to address the problem of dependence as well as feedback among conflicting criteria and to determine their relative importance. Then, a fuzzy VIKOR method is extended to rank potential projects on the basis of their overall performance. An illustrative example from the literature is provided for the construction project problem to demonstrate the effectiveness and feasibility of the proposed approach. The computational results show that the proposed two-phase GDM approach is suitable to cope with imprecision and subjectivity for the complicated decision making problem. Finally, the associated results of the proposed approach with risk attitudes and without risk attitudes are compared with the results reported by Cheng and Li [1], and the merits are highlighted.     

A compromise weight for multi-criteria group decision making with individual preference

In a multi-criteria group decision making process, it is often hard to obtain a solution due to the possible conflict preferences from different participants and the undeterministic weights assigned to each criterion. This problem can be defined as to identify a set of weights for the given criteria to achieve a compromise of the conflict on different preferences. When such a compromise weight does not exist, we need to adjust (to reverse or to withdraw) some or all of the preferences from different participants. This paper describes a minimax principle based procedure of preference adjustments with a finite number of steps to find the compromise weight. At each iteration, we either find the weight or identify some ‘wrong’ preferences. We also define a consistency index for each participant to measure the distance between the individuals' preference and the final group decision. Corresponding theoretical work is referred to in support of the procedure, and numerical examples are provided for illustration. This study is further extended to the case of multiple assessments.     

Tradeoff-based decomposition and decision-making in multiobjective programming

To facilitate the evaluation of tradeoffs and the articulation of preferences in multiple criteria decision-making, a multiobjective decomposition scheme is proposed that restructures the original problem as a collection of smaller-sized subproblems with only subsets of the original criteria. A priori preferences on objective tradeoffs are integrated into this process by modifying the ordinary Pareto order by more general domination cones, and decision makers are supported by an interactive decision-making procedure to coordinate any remaining tradeoffs using concepts of approximate efficiency. A theoretical foundation for this method is provided, and an illustrative application to multiobjective portfolio optimization is described in detail.     

Genetic algorithm-based multi-criteria project portfolio selection

Project portfolio selection is one of the most important decision-making problems for most organizations in project management and engineering management. Usually project portfolio decisions are very complicated when project interactions in terms of multiple selection criteria and preference information of decision makers (DMs) in terms of the criteria importance are taken into consideration simultaneously. In order to solve this complex decision-making problem, a multi-criteria project portfolio selection problem considering project interactions in terms of multiple selection criteria and DMs?? preferences is first formulated. Then a genetic algorithm (GA)-based nonlinear integer programming (NIP) approach is used to solve the multi-criteria project portfolio selection problem. Finally, two illustrative examples are presented for demonstration and verification purposes. Experimental results obtained indicate that the GA-based NIP approach can be used as a feasible and effective solution to multi-criteria project portfolio selection problems.     

Multicriteria energy policy investments and energy market clearance via integer programming

The deregulation of energy markets has created a framework for policy making, still under evolution, which is much more complex than the previous one. As a consequence, new requirements need to be met, concerning both technical design and financial management. This framework renders the use of multicriteria techniques attractive. Here, the investments in suppliers, depending on the policy implemented, are formulated as an integer programming problem, which consists of different sub-problems according to the assumptions made and the market’s regulations. The equivalent relaxed problem is a mixed integer programming problem that can represent the clearance of the energy market by considering several criteria besides price and quantity. Nonlinearities are reformulated by inserting additional binary variables so that the solution algorithms are more effective and efficient in most realistic cases. The feasible solutions and the optimal solution that maximizes every time the market regulator’s gain are obtained, after imposing some thresholds on the criteria used to evaluate the different energy technologies, thus creating a decision support system for the regulator.     

Multicriteria ranking of alternative locations for small scale hydro plants

Since energy consumption and its costs have recently rapidly increased, ‘small scale’ hydroplants (HP) are being widely used as energy sources. Our objective is to deal with the problem of small HP construction in a wide area covering many regions. The problem is to select some locations for each region by using the same methodology in order to make the unit costs as low as possible. When considering this problem, besides economical criteria, some other criteria must also be taken into account, such as technical, social, environmental etc. Multicriteria analysis is a quite realistic approach to such a complex problem which includes, among the others, some conflicting criteria. We have found that the Promethee method is well adapted to this problem, since its flexibility enables the decision maker to express precisely his preferences and stable results can be easily obtained by a sensitivity analysis. In this paper the problem is formulated, the criteria are estimated and quantified, and location planning is obtained by using the Promethee methodology. The obtained solutions are discussed and the computational results are given.     

A lexicographical compromise method for multiple criteria group decision problems with imprecise information

This paper addresses multiple criteria group decision making problems where each group member offers imprecise information on his/her preferences about the criteria. In particular we study the inclusion of this partial information in the decision problem when the individuals’ preferences do not provide a vector of common criteria weights and a compromise preference vector of weights has to be determined as part of the decision process in order to evaluate a finite set of alternatives. We present a method where the compromise is defined by the lexicographical minimization of the maximum disagreement between the value assigned to the alternatives by the group members and the evaluation induced by the compromise weights.     

OR and energy: Problems of modelling

Attention is focused on three problem areas in energy modelling: (1) identifying the essential elements of the system, (2) coping with multiple criteria, (3) incorporating learning in the system. These aspects are illustrated through examples in current energy systems research, involving the oil market, power systems planning, and the role of nuclear energy.In modelling the word oil market, too heavy emphasis is placed on economic forces, but practically non on the political forces. However, certain economics-oriented studies indicate that financial gains of OPEC may actually be intensitive to the oil pricing policy followed. If that is indeed the case, the significant (political) elements and their motives have to be captured in the model in order to arrive at consistent results.Modelling the different objectives in power systems planning is an area where advances are urgently needed. A method is proposed, where decision alternatives are generated a posteriori, in contrast to recent approaches involving a priori articulation of preferences, or interactive methods. A multicriterion dynamic linear programming model and a fast algorithm are used in generating efficient solutions, which are then grouped, based on the clustering in objective values.The problem associated with changing system objectives is discussed and the nuclear programme is given as an example of how the system objectives move from costs to perceived risks. In line with the real system that ‘learns’ from its experience, we need models that change their objective functions as a result of their own outputs at prior times.     

A new decision support model in multi-criteria decision making with intuitionistic fuzzy sets based on risk preferences and criteria reduction

In this paper, we propose a new model for decision support to address the ‘large decision table’ (eg, many criteria) challenge in intuitionistic fuzzy sets (IFSs) multi-criteria decision-making (MCDM) problems. This new model involves risk preferences of decision makers (DMs) based on the prospect theory and criteria reduction. First, we build three relationship models based on different types of DMs’ risk preferences. By building different discernibility matrices according to relationship models, we find useful criteria for IFS MCDM problems. Second, we propose a technique to obtain weights through discernibility matrix. Third, we also propose a new method to rank and select the most desirable choice(s) according to weighted combinatorial advantage values of alternatives. Finally, we use a realistic voting example to demonstrate the practicality and effectiveness of the proposed method and construct a new decision support model for IFS MCDM problems.     

Multiple criteria linear programming model for portfolio selection

The portfolio selection problem is usually considered as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model the risk is measured with variance, thus generating a quadratic programming model. The Markowitz model is frequently criticized as not consistent with axiomatic models of preferences for choice under risk. Models consistent with the preference axioms are based on the relation of stochastic dominance or on expected utility theory. The former is quite easy to implement for pairwise comparisons of given portfolios whereas it does not offer any computational tool to analyze the portfolio selection problem. The latter, when used for the portfolio selection problem, is restrictive in modeling preferences of investors. In this paper, a multiple criteria linear programming model of the portfolio selection problem is developed. The model is based on the preference axioms for choice under risk. Nevertheless, it allows one to employ the standard multiple criteria procedures to analyze the portfolio selection problem. It is shown that the classical mean-risk approaches resulting in linear programming models correspond to specific solution techniques applied to our multiple criteria model. This revised version was published online in June 2006 with corrections to the Cover Date.     

Selection of technology acquisition mode using the analytic network process

Selecting the appropriate acquisition mode for a required technology, is one of the critical strategic decisions in formulating a technology strategy. Although a number of factors were found to be influential in the choice of technology acquisition mode, it still remains a void in the literature how to make a strategic decision, based on a huge set of those factors with the help of a systematic approach. This study deals with the selection of technology acquisition mode as a multiple criteria decision making (MCDM) problem. The proposed solution to the problem in this study, is the analytic network process (ANP) approach. Since the ANP is a MCDM method that can accommodate interdependency among decision attributes, it is capable of providing priorities of alternatives with consideration of interrelationships among strategic factors. The 21 influential factors identified from the empirical studies are included as sub-criteria in the ANP model, and they are grouped into five criteria: capability, strategy, technology, market, and environment. The final decision can be made based on the resulting priorities of the alternative acquisition modes. The proposed approach is expected to effectively aid decision making on which mode is adopted for acquisition of required technologies. A case of a software company is presented for the illustration of the proposed approach.     

Project prioritization under policy restrictions. A combination of MCDA with 0–1 programming

Multiple Criteria Decision Aid methods are increasingly used in financial decision making in order to capture the multifaceted character of modern enterprises activated in a complex and versatile market environment. This paper presents a multiple criteria approach for the selection of firms applying for financial support from public funds. Besides the budget constraint, the specific decision situation imposes the consideration of additional policy constraints that prevent from directly exploiting rankings provided by a multiple criteria method. In such a case the problem solution is to find a set of alternatives satisfying the constraints and at the same time maximizing a measure of global performance. The proposed procedure relies on the PROMETHEE V method which belongs to the well-known PROMETHEE family of multiple criteria outranking methods and is combined with an integer programming formulation capable to effectively deal with the problem’s combinatorial character. This method is modified in order to avoid any bias in the selection of the optimal set that may arrive because of the apparent contradiction between the rate of resources consumption and the coefficients of the alternatives in the additive objective function.     

A hybrid model for selection of an outsourcing provider

Outsourcing is a good strategy for firms that need to reduce operating costs and improve competitiveness and it is important that firms scientifically select appropriate outsourcing providers. Some efforts have been made to find systematic ways to deal with outsourcing problems, but these efforts incorrectly assumed that the criteria used in the decision process are independent, which is not true in the real world. In this study, we propose a new hybrid multiple criteria decision-making (MCDM) model, which addresses the dependent relationships between the various criteria. The relations-structure among the criteria is built with the aid of the decision-making trial and evaluation laboratory (DEMATEL) method. Decision-makers tend to hold diverse opinions about their preferences due to incomplete information and knowledge, or inherent conflict between various departments. We further used the fuzzy preference programming and the analytic network process (ANP) to form a model for the selection of partners for outsourcing providers. The proposed model can help practitioners improve their decision making process, especially when criteria are numerous and inter-related. The method is demonstrated using data from a Taiwanese airline.     

Spatial multicriteria decision support for robust land-use suitability: The case of landfill site selection in Northeastern Greece

Multicriteria spatial decision support systems (MC-SDSS) have emerged as an integration of geographical information systems (GIS) and multiple criteria decision aid (MCDA) methods for incorporating conflicting objectives and decision makers’ preferences into spatial decision models. In this paper, we present spatial UTASTAR (S-UTASTAR), a raster-based MC-SDSS for land-use suitability analysis. The multicriteria component of the system is based on the UTA-type disaggregation-aggregation approach. S-UTASTAR is applied in a raster-based case study concerning land-use suitability analysis to identify appropriate municipal solid waste landfill (MSW) sites in Northeast Greece. Moreover, robustness analysis tools are implemented to guarantee robust decision support results. More specifically, during the aggregation phase, the Stochastic Multiobjective Acceptability Analysis (SMAA) is used to indicate the frequency at which a site achieves the best ranking positions within a large set of alternative landfill sites.     

IPSSIS: An integrated multicriteria decision support system for equity portfolio construction and selection

A fundamental principle of modern portfolio theory is that comparisons between portfolios are generally made using two criteria, corresponding to the first two moments of return distributions, namely the expected return and portfolio variance. According to this model and according to most of the portfolio models derived from the stochastic dominance approach, the group of portfolios open to comparisons is divided into two parts: on the one hand there are the efficient portfolios (those that are not dominated by any other portfolio in the group), and on the other, those that are dominated. In other words, these models do not solve for one optimal portfolio, but rather solve for an efficient set of portfolios, among which the investor must choose, given his preference system. One criticism over these models, which has often been addressed both by practitioners and academics, is that they fail to embody the objectives of the decision maker (DM), through the various stages of the decision process. Our purpose in this article is to present an integrated and innovative methodological approach for the construction and selection of equity portfolios, which will take into account the inherent multidimensional nature of the problem, while allowing the DM to incorporate his preferences in the decision process. The proposed approach, which grounds its basis on the field of multiple criteria decision making (MCDM) and more specifically on multiobjective mathematical programming (MMP), is implemented in the IPSSIS (Integrated Portfolio Synthesis and Selection Information System) decision support system (DSS). The validity of the proposed approach is tested through an illustrative application in the Athens Stock Exchange (ASE).     

Using SSM to rethink the analysis of energy efficiency initiatives

This paper reflects an attempt to rethink the process of analysis of energy efficiency initiatives using soft systems methodology (SSM) as a problem structuring tool. The aim of the work is to provide public and private initiative promoters or evaluators with a structured support for a more informed decision regarding the implementation of energy efficiency measures. The SSM approach contributed with the identification of all market players and their relations, as well as the insight into the deficiencies of current methodologies. Some future work directions are also proposed.     

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.     

Evaluating a system of furniture retail outlets using an interactive ordinal regression method

The aim of this paper is to show some important properties of multicriteria decision-making modelling in organizations through a real-world study: the evaluation of retail outlets of a sales network in France for the launching of a new furniture line.A multicriteria evaluation model based on a large number of qualitative and quantitative criteria was proposed, taking into account the commercial policy of the company and the preferences of the decision makers. The UTA ordinal regression method, by Jacquet-Lagrèze and Siskos, was applied on a small number of stores, among the well-known to the decision makers, to assess multicriteria additive value functions. The method has been used interactively through a trial-error process in order to modelize the evolution of the decision maker's preference system. Thus, the results of the method influenced the criteria definition, the a priori preferences and, finally, the problem formulation.