multiple criteria decision support software

Chapter 24

MULTIPLE CRITERIA DECISIONSUPPORT SOFTWARE

H. Roland Weistroffer, Charles H. Smith, Subhash C. NarulaSchool of BusinessVirginia Commonwealth UniversityBox 844000, Richmond, Virginia 23284-4000USA

{hrweistr,chsmith,snarula}@vcu.edu

Abstract

Keywords:

We present an overview of the current state of multiple criteria decision-making(MCDM) decision support software. Many approaches have been proposed inthe literature to solve multiple criteria decision-making problems, and there is anabundance of software that implements these approaches. Much of the softwareis still quasi-experimental, developed by academic researchers to test specificalgorithms or to solve a specific problem on an ad hoc basis.

DSS, MCDSS, software packages.

990 MULTIPLE CRITERIA DECISION ANALYSIS

1. Introduction

2. Software Overview

It is well known that multiple criteria decision models do not possess a mathe-matically well-defined optimal solution; therefore the decision maker (DM) hasto find a satisfactory (desirable, acceptable) compromise solution from amongmany non-dominated (efficient) solutions. Unless the utility function of theDM is known a priori and explicitly, interactive solution techniques are imper-ative to identify the most preferred solution or a manageable set of desirablecompromise solutions.

Today a wide variety of software has been developed specifically to supportmultiple criteria decision-making. Many general software tools, such as linearprogramming packages and electronic spreadsheets that do not implement spe-cific MCDM techniques, can also be used to analyze multiple criteria problems.MCDM software covers various stages of the decision making process, fromproblem exploration and structuring to discovering the DM’s preferences andthe most preferred compromise solution. Our primary objective in this paper isto report on the state of commercially or otherwise readily available multiplecriteria decision support software.

In the next section we present an overview of multiple criteria decision sup-port software. The software is organized into seven areas based on the type ofproblem to which the software is applied. These areas are qualitative problemstructuring, general multiple attribute decision making, general multiple ob-jective decision making, multiple criteria sorting problems, portfolio analysis,group decision support, and some application specific software. Within eachsection the software is listed in alphabetical order. Table 1 provides a list ofthe software described in each area. The software review is followed by a fewconcluding remarks.

Decision support software can assist DMs at various stages of structuring andsolving decision problems. These stages can include problem exploration andformulation, decomposition, and preference and trade-off judgments. Many ofthe general commercially available decision aids have been included in thebiennial decision support systems reviews in OR/MS Today [14, 15, 16, 17,85, 86]. However, several other approaches that have been suggested in theliterature have only been implemented on an ad hoc basis, to solve a specificproblem situation, or as experimental software to demonstrate the salient pointsof the proposed methodology. While most software developed by academicsis available free of charge, or for a nominal fee, commercial packages sell forhundreds or even thousands of dollars (though some give educational discounts).Most have their own websites and sophisticated marketing literature.

Multiple Criteria Decision Support Software 991

In assessing MCDM software, it is important to consider not only the technol-ogy (i.e., computer hardware and software, and MCDM methodology) aspects,but also the role of the DM in the interactive process, and the user-friendliness ofthe human-computer interface. The MCDM programs developed in the 1970swere mainly oriented towards the study of multiple objective mathematicalprogramming problems [33]. These early systems were primarily developedfor academic purposes. They were implemented on mainframe computers, withno documentation available. They also did not have any visual representationcapabilities, mainly due to the limited capabilities of computer technology atthat time. There are encouraging signs that some psychological and behavioralresearch is being integrated into MCDM theory and practice [87]. Korhonenet al. [62] note that during the 1980’s, emphasis shifted away from the mathe-matical aspects of multiple objective programming towards providing decisionsupport to the DM. Most modern MCDM software tools are designed for theWindows platform and provide graphical interfaces to assist in visualizing theeffects of changes to problem parameters. An increasing number of packagesare also available for interactive use via the Internet. In our coverage we havetried to focus on more recently developed software, though we have also in-cluded older software that appears to be continually maintained. We also notethat information for several commercial and other computer programs is notavailable in a uniform format. This is reflected in the write-ups for the variousdecision support systems.

2.1 Qualitative Problem Structuring

Software in this category addresses the early stages of the decision makingprocess: exploring and formulating the decision problem.

2.1.1 Decision Explorer. http://www.banxia.com/. Decision Ex-plorer is oriented to organize and map qualitative information for complex,ill-structured problems [128]. The fundamental method employed is the causalmapping technique. The aim is to identify useful courses of action by the re-lationships established between variables as a cognitive map is built. DecisionExplorer can facilitate group discussion and understanding by means of its vi-sual development of problem issues. The software includes analytical tools thatassist in evaluating the similarities and differences of sets and in developingand analyzing clusters of information about the problem. The website providesa tutorial, case study, demonstration downloads, and a bibliography of materialrelated to the software or the cognitive mapping method.


2.2 General Multiple Attribute Decision Making(MADM)

MCDM problems can be roughly divided into two main groups, viz. multipleattribute decision-making (MADM) and multiple objective decision-making(MODM) problems. In the MADM problems, the decision-maker must choosefrom among a finite number of available alternatives characterized by a set ofmultiple attributes. Software in this category is designed to deal with any typeof decision problem where one has to choose among a finite set of decisionalternatives characterized by a set of attributes.

2.2.1 Criterium Decision Plus. http://www.infoharvest.com.Criterium Decision Plus 3.0 (CDP), (reviewed by Haerer in [45]), providesusers a choice between a simple multiattribute rating technique and AHP. Theprimary strengths of CDP include, among others, the immediate graphical feed-back from what-if analysis and the support of value of information analyses.Haerer also reports that CDP has been used live on the Internet and has sup-ported decision-making via video conferencing. Users have the option of choos-ing non-linear value functions. Performance scores can be entered into a tableor in a rating window that provides choices among numerical, graphic and ver-bal representations. Uncertainties can be accommodated through a choice ofdistributions or by a customized distribution. An earlier version of this softwarewas evaluated in [130].

2.2.2 DAM. DAM (Decision Analysis Module) [101] was originallydesigned as a module in more complex software used to analyze electric systemexpansion scenarios. DAM utilizes imprecise information about the trade-offsin the form of ranges. The principal decision analysis options supported bythe software include the testing of potential optimality, the identification ofoutperformed and not outperformed alternatives, and visual sensitivity analysis.To solve the linear programs arising from different analysis options, a fairlystraightforward version of the simplex method is used.

2.2.3 Decision Lab. http://www.visualdecision.com.Known asPROMCALC in a previous version, Decision Lab 2000 is an interactive de-cision support system [39] based on the outranking methods PROMETHEE[12, 13] and GAIA [11]. Sensitivity analyses are generated by using techniquesof walking weights, intervals of stability, and the graphical axis of decisiondisplayed by the GAIA method. The software is now suitable for group deci-sion support, providing profiles of actions and multi-scenario comparisons. Themethodology used here requires fewer comparisons from the decision makerthan the AHP method; it permits the user to define his own measurement scale.

The reference [11] describes the method, the decision support system, and alsogives an illustrative example.

2.2.4 ELECCALC. Utilizing a user-friendly graphical interface, a deci-sion maker can globally express preferences about a few reference alternatives,and then the method can specify initial values for parameters of ELECTRE II[107]. A disaggregation-aggregation procedure like that in PREFCALC [50] isused [57].

2.2.5 ELECTRE IS. http://www.lamsade.dauphine.fr/english/software.html#elis. ELECTRE IS is a generalization of the ELEC-TRE I method [105, 107], which enables the use of pseudo-criteria (criteria withthresholds). Given a finite set of alternatives evaluated on a consistent family ofcriteria, ELECTRE IS supports the user in the process of selecting one alterna-tive or a subset of alternatives. The method consists of two parts: constructionof one crisp outranking for modeling the decision-maker’s preferences, andexploitation of the graph corresponding to this relation. The subset searchedis the kernel of the graph. Software implementing ELECTRE IS is availablefrom LAMSADE at the Université Paris-Dauphine. ELECTRE methods arealso discussed in Chapter 4 of this volume.

2.2.6 ELECTRE III-IV. http://www.lamsade.dauphine.fr/english/software.html#el34. ELECTRE III starts with a finite set of actionsevaluated on a consistent family of pseudo-criteria and aggregates these partialpreferences into a fuzzy outranking relation [106, 107]. ELECTRE IV buildsseveral non-fuzzy outranking relations when criteria cannot be weighted. Twocomplete preorders are then obtained through a “distillation” procedure, eitherfrom the fuzzy outranking relation of ELECTRE III, or from the non-fuzzyoutranking relations provided by ELECTRE IV. The intersection of these pre-orders indicates the most reliable part of the global preference. The ELECTREIII-IV software is available from LAMSADE at the Université Paris-Dauphine.ELECTRE methods are also discussed in Chapter 4 of this volume.

2.2.7 Equity. http://enterprise-lse.co.uk. Equity is a multi-criteria decision analysis (MCDA) tool that can be used to obtain better value-for-money in allocating scarce resources. It is highly adaptive and can be used toaddress a variety of problems. In stage 1, an outline of the model is constructed.In stage 2, each option is scored against a set of defined criteria. In stage 3,the decision maker must make a value judgment on the relative importance ofdifferent aspects of the model. In stage 4, the model is analyzed and recommen-dations are presented in stage 5. A 30-day evaluation version of the program isavailable to download.


2.2.8 Expert Choice. http://www.expertchoice.com.Expert Choi-ce (reviewed in [37]) has been closely identified with AHP, and the softwareemploys AHP as its core methodology. The latest versions emphasize groupdecision support and an easy-to-use interface. The software will accept judg-ments from multiple stakeholders using wireless keypads or the Internet. It hasthe capability to weight team members and evaluate outcomes based on teammember demographics. The company website also states that Expert Choiceoffers a “freestyle, interactive technique for building a model that simulatesthe flow of ideas, and helps decision-makers organize the objectives of theirdecision into theme clusters.” Graphs for sensitivity analysis are provided. Thecompany claims that Expert Choice has over 50,000 users, including many largecorporations and government agencies. Expert Choice is one of the packagesevaluated in [130].

2.2.9 HIVIEW. http://www.enterprise-lse.co.uk. HIVIEW is amulticriteria decision analysis (MCDA) tool that can be used to support deci-sions among mutually exclusive options. It is highly adaptive and can be usedto address a variety of problem areas. There are five main stages for modelingin HIVIEW. A model is constructed as a tree structure in stage 1. In stage 2,each action option is scored against the criteria set out in the tree structure. Instage 3, the decision maker must make a value judgment on the relative impor-tance of different aspects of the model. The model is analyzed in stage 4, andrecommendations are presented in stage 5. An evaluation version of HIVIEWis available to download.

2.2.10 Logical Decisions. http://www.logicaldecisions. com.Logical Decisions for structuring and analyzing multiple attribute decision anal-ysis problems has been commercially available for several years. It is currentlyoffered in both single and group user versions. The user interface is considereda significant attraction, with a graphical, point and click way to adjust weights.Historically associated with multiattribute utility theory, according to the web-site Logical Decisions offers five methods for assessing weights, “ranging fromthe easy-to-use ‘Smarter’ method, to the sophisticated ‘tradeoff’ method, to thepopular ‘analytic hierarchy process’.” The results can be displayed in variousways, and one can compare pairs of alternatives to see their major differences.Interactive graphical sensitivity analysis displays are available. Logical Deci-sions is one of the packages evaluated in [130].

2.2.11 MACBETH. http://www.umh.ac.be/~smq. MACBETH –Measuring Attractiveness by a Categorical Based Evaluation Technique (Chap-ter 10 of this volume, and Bana e Costa and Chagas [5]) uses semantic judgmentsabout the differences in attractiveness of several stimuli to help a decision maker


quantify the relative attractiveness of each stimulus. It employs an initial, iter-ative, questioning procedure that compares two elements at a time, requestingonly a qualitative preference judgment. MACBETH automatically verifies theconsistency of the judgments and generates a representative numerical scale.Similarly, MACBETH generates weighting scales for the decision criteria, andalso provides sensitivity analysis.

2.2.12 MacModel. http://www.civil.ist.utl.pt/~lavt/ software .html. MacModel is decision tree based software for multicriteria prob-lems, developed at the Instituto Superior Técnico in Lisbon, Portugal [120].

2.2.13 M&P. M&P (MAPPAC and PRAGMA) implements the MAP-PAC [80] and PRAGMA [81] outranking methods also described in Chapter 6of this volume. M&P offers multiple options for preference modeling, such asspecifying trade-off and importance weights, and normalization levels. Someclassical statistical analyses on the evaluations of alternatives are also allowed(average values, standard deviations, correlations between criteria). For eachpair of criteria, suitable indifference thresholds and shapes can be defined. It isalso possible to graphically represent the partial and global profiles and levelsof the alternatives.

2.2.14 MIIDAS. The Multicriteria Interactive Intelligence DecisionAiding System (MIIDAS) [115] is based on the UTA II method (see Chap-ter 8 of this volume). In UTA II, the assessment of the DM’s additive utilitymodel is carried out in a two step procedure: in the first step the DM expressespreferences, and in the second step the system estimates weighting factors of thedecision criteria using special linear programming techniques. MIIDAS uses ar-tificial intelligence, visual procedures, and data analysis techniques to improvethe user interface and the interactive character of the system.

2.2.15 MINORA. MINORA (Multicriteria Interactive Ordinal Regres-sion) [113] is an interactive DSS based on the UTA method [51]. The interactiontakes the form of an analysis of inconsistencies between the decision maker’srankings and those derived from utility measures. The method stops when anacceptable compromise is determined. The result is an additive utility functionwhich is used to rank the set of alternatives.

2.2.16 MUSTARD. The software MUSTARD [9] implements variantsof the UTA [51] and the Quasi-UTA models [10]. It offers the basic deterministicUTA model of disaggregation, as well as its first programmed stochastic version.In both cases, the software proceeds stepwise and interactively helping thedecision maker to formulate the problem and state preferences between projects;


in the stochastic case, the decision maker is also helped to build the criteriadistributions.

2.2.17 NAIADE. http://alba.jrc.it/ulysses/voyage-home/naiade/naisoft .htm. NAIADE (Novel Approach to Imprecise Assessmentand Decision Environments) [94] is a discrete multicriteria method [92] whichprovides an impact or evaluation matrix that may include either crisp, stochastic,or fuzzy measurements of the performance of an alternative with respect to anevaluation criterion. A peculiarity of NAIADE is the use of conflict analysisprocedures integrated with the multicriteria results. NAIADE can give rankingsof the alternatives with respect to the evaluation criteria (leading to a technicalcompromise solution), indications of the distance of the positions of the variousinterest groups (possibly leading to convergence of interests or to coalitionformation), and rankings of the alternatives with respect to the actors’ impactsor preferences (leading to a social compromise solution).

2.2.18 OnBalance. http://www.krysalis.co.uk. OnBalance is ba-sed on a simple weighting approach: each decision option is scored against eachdecision criterion, and each decision criterion is given a weight. The packagethen computes an overall weight for each option. Multiple hierarchies, calledtrees in the package, using different weights, can be created to allow for differentperspectives. Thus the approach appears to be similar to AHP, but no indicationis given as to how the overall weights are calculated. The package is designedto be easy to use by anyone, without much technical understanding required.

2.2.19 PREFCALC. PREFCALC [50] is an earlier implementation ofthe UTA method [51]. A more recent implementation of the UTA method is theUTA Plus system described separately in this chapter and also in Chapter 8 ofthis volume.

2.2.20 PRIAM. PRIAM (PRograrnme utilisant l’Intelligence Artifi-cielle en Multicritère) [66] takes an unstructured interactive approach to findingthe most desirable alternative. The decision maker is required to make only asmall number of pairwise comparisons and is not committed to an irrevocablepath by the choices made on previous comparisons.

2.2.21 PRIME Decisions. http://www.hut.fi/Units/SAL/Downloadables/. PRIME Decisions [44] emphasizes its ability to use incompletepreference information. It relies on the PRIME method that uses interval valuedratio statements of preference. These lead to linear constraints for a series oflinear programming problems. Solving the linear programs leads to dominancestructures. There is an “elicitation tour” to guide the decision maker. The soft-


ware is downloadable for academic use. Because of the large number of linearprograms that must be solved, the approach is best suited to problems withrelatively few nondominated alternatives.

2.2.22 REMBRANDT. The REMBRANDT (Ratio Estimation in Mag-nitudes or deci-Bells to Rate Alternatives which are Non-DominaTed) system[70,71 ] requires that decision-makers make pairwise comparisons both betweendecision criteria to determine their relative importance and between alternativesunder each criterion. Results are aggregated leading to a final impact score foreach alternative, permitting a ranking of the alternatives. The REMBRANDTsystem was developed to overcome perceived flaws in AHP. The approacheswill appear identical to the users because the same inputs are required, but someof the technical aspects are different. For example, direct ratings are on a loga-rithmic scale and weights are determined by use of the geometric mean, whichavoids potential rank reversal. A performance comparison between the REM-BRANDT system and AHP is reported in [97]. An adaptation of the system forapplication in negotiation is found in [122].

2.2.23 RGDB. http://www.ccas.ru/mmes/mmeda/RGDB/index.htm. RGDB (Reasonable Goals for Database) is a tool that supports the selectionof preferable items (say, goods and services) from large lists using a simplegraphic interface. The application server is based on the Reasonable GoalsMethod [52] and is implemented in Java. The prototype application server wasdeveloped by the Department of Mathematical Methods for Economic DecisionAnalysis (MMEDA) of the Russian Academy of Sciences.

2.2.24 SANNA. http://nb.vse.cz/~jablon/sanna.htm.SANNA[49] is an add-in application of MS Excel. It is freeware that enables solvingmulticriteria problems using several methods (WSA, TOPSIS, ELECTRE I,PROMETHEEII and MAPPAC). SANNA can solve problems up to 100 alter-natives and 50 criteria.

2.2.25 TOPSIS. The Technique for Order Preference by Similarity toIdeal Solution (TOPSIS) proposed in [47] is based on the idea that the mostpreferred alternative should be the shortest distance from the ideal solution andthe longest distance from the negative ideal solution. Recent modifications haveextended the method to a fuzzy environment [18] and to inter-company perfor-mance comparisons using an entropy measure to provide objective weights ofcriteria importance [27].

2.2.26 UTA Plus. http://www.lamsade.dauphine.fr/english/software.html#uta+. UTA Plus is the latest Windows implementation of


the UTA method, originally proposed in 1982 [51, 64], The method can be usedto solve multicriteria choice and ranking problems on a finite set of alternatives.It constructs an additive utility function from a weak preference order definedby the user on a subset of reference alternatives. The construction, based ona principle of ordinal regression, requires solving a small LP-problem. Thesoftware proposes marginal utility functions in piecewise linear form basedon the given weak order, and then allows the user to interactively modify themarginal utility functions, helped by a graphical user interface. UTA methodsare also discussed in Chapter 8 of this volume.

2.2.27 VIMDA. http://www.numplan.fi/vimda/vimdaeng.htm.VIMDA is a visual multiple-criteria DSS for MADM problems [59, 61]. VIM-DA is also described in Chapter 16 of this volume, and is one of the packagesevaluated in [130].

2.2.28 VIP Analysis. http://www4.fe.uc.pt/lmcdias/english/vipa.htm. VIP (Variable Interdependent Parameter) Analysis was introducedrecently in [31]. While the approach uses a basic additive value function, itpermits the decision maker to provide imprecise information for the parametersof criteria importance. In the authors’ words, they propose “a methodologyof analysis based on the progressive reduction of the number of alternatives,introducing a concept of tolerance that lets the decision makers use some of theapproaches in a more flexible manner.” Several output options exist dependingon the size of the problem and the nature of the input data. For example, amongthe output displayed is the maximum regret for each alternative. The softwareis available free from the authors through the website, and an online manual isalso available at the site.

2.2.29 V.I.S.A. http://www.simul8.com/products/visa.htm.Thissoftware’s name stands for Visual Interactive Sensitivity Analysis, and the ap-proach is described in [7]. Applying a linear multiattribute value function, ithas been offered in a Windows version since 1994, emphasizing a friendlygraphical interface for adjusting the criteria hierarchy and other componentsof the model. For example, one can interactively provide input of weights andscores using bar charts, thermometer scales, or numerical input. The weightsand scores can be adjusted by dragging the computer mouse, and the effectscan be seen immediately on several output windows. A variety of user licensesare available including a version oriented towards group usage. VISA is one ofthe packages evaluated in [130].

2.2.30 Web-HIPRE. http://www.hipre.hut.fi/.Web-HIPRE is In-ternet accessible software based on AHP and value functions [93]. The web



feature permits information about the alternatives or criteria to be shared by ascattered group. The local use variant is called HIPRE 3+. It permits the userto customize the attribute scale and to combine approaches such as AHP andvalue functions in a single model.

2.2.31 WINPRE. http://www.hut.fi/Units/ SAL/Downloadables/. WINPRE [109] is another software tool available from the SystemsAnalysis Laboratory in Finland, the group that also offers PRIME Decisionsand Web-HIPRE described earlier. WINPRE relies on a methodology calledPAIRS (Preference Assessment by Imprecise Ratio Statements) that permitsthe decision maker to state a range of numbers to indicate preferences amongalternatives. These result in linear constraints that lead to a feasible region foreach criterion that is consistent with the decision maker’s judgments. The soft-ware is available free for academic use.

2.3 General Multiple Objective Decision Making(MODM)

In the MODM models, the criteria are expressed in the form of mathematical ob-jective functions that are to be optimized. The argument vectors of the objectivefunctions are decision variables that can usually take on an infinite number ofvalues. The MODM models may involve linear or nonlinear objective functionsand constraints, and may have continuous or integer decision variables.

2.3.1 ADBASE. ADBASE, originally written in FORTRAN, imple-ments multiobjective linear programming (MOLP) methods to enumerate ex-treme points and unbounded efficient edges [119]. ADBASE is maintained atthe Terry College of Business, University of Georgia, Athens, Georgia, USA.

2.3.2 Feasible Goals Method (FGM). http://www.ccas.ru/mmes/mmeda. The concept of the Feasible Goals Method is to explore possible resultsof all feasible decisions [76]. In the FGM software package, the objective in-formation on the decision situation is displayed in graphical form as variousdecision maps. An efficiency frontier displays an objective (criterion) tradeoffamong two criteria. By changing one efficiency frontier for another, the usercan see how the increment (or decrement) of the value of the third criterioninfluences the efficiency frontier. Decision maps are provided by the InteractiveDecision Maps (IDM) technique [72, 74, 77].

2.3.3 Feasible Set in Criterion Space (FSCS). http: //www. ccas.ru/mmes/mmeda. The FSCS software allows visualization of the feasible setin the criterion space for nonlinear problems [73]. The decision maker obtainsa general orientation in the criterion space that may help him or her access the


limits of what is possible in terms of the criteria. In the case of more than twocriteria‚ visualization is based on approximating the feasible set in the criterionspace by simple figures and subsequent on-line displays of the approximationsusing two-criterion slices. Visualization of the FSCS can be incorporated intovarious multicriteria methods. The software was coded in the form of an add-in tool for MS Excel. It consists of four subsystems. The first one helps toformulate a nonlinear model using MS Excel. The second one helps to specifycriteria and approximation parameters. The covering base is constructed in theform of a table in the third subsystem. The last subsystem helps visualize theapproximation and select a preferred goal.

2.3.4 MOMHLib++. http://www–idss.cs.put.poznan.pl/ ~

jaszkiewicz/MOMHLib/.MOMHLib++ (Multiple Objective MetaHeuris-tics Library in C++) is a library of C++ classes that implements a number ofmultiple objective metaheuristics. The library includes Pareto simulated anneal-ing [25]‚ multiple objective simulated annealing [110‚ 121]‚ the Pareto memeticalgorithm [55]‚ multiple objective genetic local search [48‚ 54]‚ multiple objec-tive multiple start local search‚ non-dominated sorting genetic algorithm andcontrolled NSGA II [26‚ 116]‚ and the Strength Pareto Evolutionary Algorithm[131]. Each method is implemented in a separate template class that utilizes anumber of common library classes. The template classes are instantiated withclasses corresponding to solutions of a given problem. In order to adapt oneor more of the multiple objective metaheuristics to a given problem one hasto implement a new class corresponding to the problem’s solution by derivingfrom the library class TMOMHSolution. A detailed design pattern described inthe documentation of MOMHLib++ illustrates the suggested way of adaptingthe library to a given problem. The library is implemented in standard C++.

2.3.5 MultiGen. MultiGen [89] contains both an optimization systemand a heuristic genetic algorithm solver. It can be used for solving linear andnonlinear multiple objective programming models and also large integer prob-lems. It is not a tool for the casual decision maker because several parametersmust be set to guide the genetic algorithm’s search process; however‚ an inter-active environment permits the user to more easily change these parameters. Apublished study shows that the system is capable of finding the optimal solutionbased on decision maker preferences for models with up to 100 constraints and200 variables.

2.3.6 Multistat Optimizer. http://www.multistat.com. MultistatOptimizer is based on a method of visualization for models by projection(VMPF). The VMPF method [99] differs from other multiple objective methodsby working with a multidimensional dataset using visualization techniques.


2.3.7 SOLVEX. http://www.ccas.ru/pma/product.htm. SOLV-EX is an integrated application package intended for solving nonlinear con-strained optimization problems‚ multi-variable global optimization problems‚and nonlinear multicriteria problems [102]. It uses convolution (including goalprogramming) and direct approximation algorithms for the multicriteria prob-lem solving part.

2.3.8 TRIMAP. TRIMAP [19] is an interactive approach that exploresthe Pareto optimal set for three-criterion linear programming models. The aimis to aid the decision maker in eliminating parts of the Pareto optimal solutionset that are judged to be of less value. The limitation to three objectives permitsgraphical displays that facilitate the decision maker’s information processing.The procedure does not converge to a particular solution‚ but the decision makercan stop the process when sufficient information has been learned about thePareto optimal solutions.

2.3.9 TOMMIX. This is an interactive package [4] designed to be aflexible tool for a decision maker. The software incorporates various methodsof multiple objective optimization including STEM‚ Zionts-Wallenius‚ inter-val criterion weights [118]‚ Pareto Race [63]‚ and TRIMAP [19]. Designedfor three-objective problems‚ TOMMIX has an emphasis on graphics and thedecision maker interface.

2.3.10 VIG. http://www.numplan.fi/vig/vigeng.htm. VIG‚ a vi-sual‚ dynamic‚ and interactive DSS for MODM problems‚ can handle linearprogramming constraint matrices with 96 columns and 100 rows‚ of which 10rows may constitute the objective functions [58‚ 60‚ 61]. This software‚ alsodescribed in Chapter 16 of this volume‚ is based on the Pareto Race technique[63].

2.3.11 WWW-NIMBUS. http://nimbus.mit.jyu.fi/. WWW-NIMBUS [88] has been designed to solve differentiable and non-differentiablemulti- and single objective optimization problems subject to nonlinear and lin-ear constraints with bounds on the variables. It can also accommodate integervariables. WWW-NIMBUS can be accessed via the Internet and is free foracademic use.

WWW-NIMBUS implements the classification-based NIMBUS me-thod.The problems are stated as minimization problems. Therefore‚ it is assumed thatthe user prefers less to more for the objective function values. At each iteration‚the decision maker divides the objective functions into five mutually exclusiveclasses and provides the desirable changes. The proximal bundle method andgenetic algorithms are used as underlying solvers.


2.4 Multiple Criteria Sorting Problems

Software in this category is designed to sort decision alternatives into pre-defined groups or classes.

2.4.1 ELECTRE TRI. http://www.lamsade.dauphine.fr/english/software.html#TRI.ELECTRE TRI [29‚ 90‚ 91] sorts alternatives byusing reference alternatives and outranking relations. Two procedures (pes-simistic and optimistic) are provided to deal with situations in which specificalternatives are incomparable with some reference alternatives. The ELEC-TRE TRI software‚ written for Windows in C++‚ was developed jointly byLAMSADE at the University of Paris-Dauphine‚ France‚ and the Institute ofComputer Science at Poznan University of Technology‚ Poland.

2.4.2 IRIS. http://www4. fe. uc.pt/lmcdias/iris.htm. IRIS (In-teractive Robustness analysis and parameters’ Inference for multicriteria Sort-ing problems) is a DSS for sorting a set of actions (alternatives‚ projects‚ candi-dates) into predefined ordered categories‚ according to their evaluations (perfor-mances) on multiple criteria [30]. Application examples would be sorting fund-ing requests according to merit categories‚ such as “Very good”‚ “Good”‚ “Fair”‚“Not eligible”‚ or sorting loan applicants into categories such as “Accept”‚ “Re-quire more collateral”‚ “Reject”. IRIS uses a pessimistic concordance-only vari-ant of the ELECTRE TRI method [29]. Rather than demanding precise valuesfor the ELECTRE TRI parameters‚ IRIS allows one to enter constraints onthese values. It adds a module to identify the source of inconsistency amongthe constraints when it is not possible to respect all of them at the same time‚according to a method described in [20]. On the other hand‚ if the constraintsare compatible with multiple assignments for the actions‚ IRIS allows drawingrobust conclusions by indicating the range of assignments (for each action) thatdo not contradict any constraint.

2.4.3 PREFDIS. PREFDIS [133] is based on a preference disaggre-gation approach. Different sorting techniques are available‚ and the systemprovides a graphical user interface. It has been used in several applications‚especially in financial management. These applications have included portfolioselection and management‚ country risk assessment‚ and the evaluation of bankbranches.

2.4.4 PROAFTN. PROAFTN is a fuzzy multicriteria classification me-thod belonging to the class of supervised learning algorithms; it enables thedetermination of fuzzy indifference relations by generalizing the indices (con-cordance and discordance) used in the ELECTRE III method. The fuzzy belong-ing degree of the alternatives is assigned to the categories. A clinical application


of the proposed method in the cytopathological diagnosis of acute leukemia ispresented in [6].

2.4.5 TOMASO. http://cassandra.ro.math.ulg.ac.be/. TO-MASO (Tool for Ordinal Multiattribute Sorting and Ordering) is freeware writ-ten in Visual Basic for sorting in the presence of qualitative interacting pointsof view [79]. The underlying methodology is described in [104]. TOMASO isdescribed in more detail in Chapter 12 of this volume.

2.5 Portfolio Analysis

Software in this category deals with problems where a set‚ or portfolio‚ ofalternatives is required‚ rather than the best single alternative.

2.5.1 HiPriority. http://www.krysalis.co.uk. HiPriority is de-signed to find best portfolio solutions‚ i.e. each solution is a set of alternativessubject to resource constraints. Weights are assigned to criteria and alternatives‚and the software allows specifying dependencies between alternatives‚ as wellas specifying mutually exclusive alternatives. To visualize benefit/cost ratios‚the package creates simple value trees of cost elements together with their cor-responding benefits‚ where cost is defined as any scarce resource. Miniaturegraphical views of the models are used as navigational tools.

2.6 Group Decision SupportSoftware in this category is specifically designed to deal with the situation ofmultiple decision makers. However‚ several of the other packages described inthis chapter also claim to be able to handle multiple decision maker situations.

2.6.1 AGAP. AGAP (Aid to Groups for Analysis and evaluation ofProjects) is a distributed group decision support system allowing multiple deci-sion makers to cooperate in the evaluation and selection of investment projects[22]. AGAP supports both synchronous and asynchronous usage‚ providingdecision support at individual‚ inter-personal‚ and collective levels. For indi-vidual multi-criteriaevaluation‚ AGAP offers additive and multiplicative utilityfunctions‚ as well as the PROMOTHEE I and II methods [12]. For the sortingof projects‚ AGAP incorporates ELECTRE TRI‚ described separately in thischapter.

2.6.2 ARGOS. ARGOS is a software tool described in [21]‚ which fo-cuses on facilitating a small group in ranking projects or candidates using theoutranking methods. It is illustrated in the reference by applying the method-ology to a jury with the task of evaluating a group of candidates for a scientific


award. ARGOS is ran in two phases: a multicriteria phase and a multijudgephase. The first phase uses the outranking methods to determine the rankingof candidates for individual judges. In the second phase ARGOS uses severalfunctions of social choice to arrive at the winning candidate.

2.6.3 CTLite. http: //www. CTLite. com. ClearThinking Lite (CTLi-te) is an internet based‚ collaborative‚ multi-criteria decision modeling envi-ronment for evaluating and ranking alternatives along parameter sets. It usesa hierarchical or network approach‚ where criteria or attributes are establishedwithin “communities” of decision makers and weighted by the decision makers.The decision makers also score the decision alternatives with respect to eachattribute. Multiple “communities” of decision makers are accommodated byadding another level to the hierarchy. CTLite is an end-to-end XML applicationbuilt on an Oracle 8i database using Oracle XML Developer Kit and relatedcomponents.

2.6.4 GMCR. The decision support system GMCR (Graph Model forConflict Resolution) [46] can model strategic decisions‚ forecast compromisesolutions‚ and assist in assessing the political‚ economic‚ environmental‚ andsocial viability of alternative scenarios to resolving conflicts. The software isbased on the graph model for conflict resolution [36].

2.6.5 Joint Gains. http://www.jointgains.hut.fi/mid.html. JointGains is negotiation support software based on the method of improving direc-tions [34]. In this method‚ joint gains are searched starting from an initial point‚such as a previously reached agreement. Each iteration in the mediation pro-cess tries to find a jointly preferred alternative to the current one. An improvingdirection and a most preferred alternative in that direction is obtained from theparticipants by pair wise comparison questions. Joint Gains uses an algorithmbased on optimization theory and the golden section method in identifying themost preferred direction. Alternatives are represented to the participants in theform of decision variable values and criteria function values. This software isweb-based.

2.6.6 MEDIATOR. MEDIATOR is a negotiation support system (NSS)based on evolutionary systems design (ESD) and database-centered implemen-tation [53‚ 111]. It supports negotiations by consensus seeking through exchangeof information and‚ where consensus is incomplete‚ by compromise. The nego-tiation problem is shown graphically in three spaces as a mapping from controlspace to goal space and (through marginal utility functions) to utility space.Within each of these spaces the negotiation process is characterized by adap-tive change‚ i.e.‚ mappings of group target and feasible sets by which these


sets are redefined in seeking a solution characterized by a single-point inter-section between them. Each player employs private and shared database views‚using his/her own micro-computer decision support system enhanced with acommunications manager to interact with the MEDIATOR DSS.

2.6.7 SCDAS. (Selection Committee Decision Analysis and Support)This tool [67] is designed to support groups that have a common goal and needto work cooperatively to select a best alternative. It aids in identifying aspira-tion levels‚ assessing disagreements‚ aggregating the assessments of individualgroup members‚ etc.

2.6.8 WINGDSS. WINGDSS [24] is a group decision support systemfor multiple attribute problems. WINGDSS provides a final score for everyalternative and thus a complete ranking. Voting powers are assigned to eachdecision maker for each criterion. Preference weights are given directly bythe users. Sensitivity analysis permits studying the effect of the variations ofparameters such as individual preferences‚ voting powers‚ and scores.

2.7 Some Application Specific Software

Here we reference some decision support software packages that have beendeveloped for very specific applications. A large number of such packagesexist and have been published in several journals and technical reports. We donot claim that our list is even close to being complete.

2.7.1 ACADEA. ACADEA is a multi-criteria decision support systemfor the performance review of individual faculty in a university [1]. The systemconsiders the aggregate performance of an academic department using the resultof individual faculty member evaluations. Criteria are established in the areasof research output‚ teaching output‚ external service‚ internal service and cost.Incorporating the approach of data envelopment analysis‚ the system can beused as an academic policy aid.

2.7.2 AgentAllocator. This is an agent-based multi-criteria DSS fortask allocation [82].

2.7.3 AutoMan. http://www.ntis.gov. AutoMan [125] is an im-plementation of AHP [108] designed to support decisions about automatedmanufacturing investments. It is one of the packages evaluated in [98].

2.7.4 BANKADVISOR. Focused on industrial clients‚ this decisionsupport tool [78] assists financial analysts in making decisions‚ such as offeringloans and setting their terms. This DSS uses financial data from balance sheets


and income statements. The multicriteria part is based on the PROMETHEE[13] method.

2.7.5 CASTART. CASTART is an interactive multicriteria package forselecting electricity production alternatives [38].

2.7.6 CGX. This is an expert system [117] designed to support creditgranting decisions in non-financial firms. In addition to an inference engine‚ ituses AHP [108] to link credit evaluation and credit limit determination.

2.7.7 DIDASN++. DIDASN++ is an interactive‚ multi-criteria based‚system for modeling engineering applications [42‚ 129]. It is a modular andmore modern version‚ written in C++‚ of the older program DIDASN‚ originallywritten in Pascal [65].

2.7.8 DIMITRA. DIMITRA is a DSS for agricultural products devel-opment decisions [84].

2.7.9 Electrical Power Districting DSS. This DSS allows decisionmakers to partition a power grid into economically viable units as might berequired under deregulation [8]. Criteria include measures of revenue balanceamong districts and the geographical compactness of districts. A genetic al-gorithm was used as the search engine for Pareto optimal solutions. Decisionmakers can use the DSS to explore non-Pareto optimal alternatives based onjudgment applied to the less structured aspects of the problem.

2.7.10 ESY. ESY (Evaluation SYstem) [100] helps decision makersmake more rational decisions and promote consistency in their decision makingthroughout all phases of a nuclear emergency. There are different requirementsat each phase. For example‚ during the early phase‚ the decision makers areunder pressure to take a decision in a short period of time whereas during themiddle phases‚ the decision makers have more time to balance the costs andbenefits of the protective actions. The ESY provides decision support not onlyin the evaluation of the strategies‚ but also in the formulation and appraisal ofthe decision problem. The authors also mention several other decision supportsystems‚ ranging from rule-based systems to those using multi-attribute valueand utility theory‚ which evaluate strategies in nuclear emergencies.

2.7.11 FINCLAS. http://www.dpem.tuc.gr/fel/. The FinancialClassification (FINCLAS) multicriteria decision support system [132‚ 134] in-corporates financial modeling tools‚ along with preference disaggregation meth-


ods that lead to the development of additive utility models for the classificationof the alternatives into predefined classes.

2.7.12 FINEVA. FINEVA is a knowledge based multi-criteria DSS forthe assessment of corporate performance and viability [135].

2.7.13 INVEX. INVEX (Investment Advisory expert system) [124]combines several methods to aid business decision makers in selecting capi-tal investment projects. The part that uses a multicriteria method relies on anextension of the PROMETHEE [13] approach. Several static and dynamic mea-sures can be used‚ e.g.‚ mean net present value of the investment‚ coefficientof variation for the return on investment‚ etc. Knowledge from experts and riskassessment methods are also employed in this system that the authors describeas a “multiparadigm” method.

2.7.14 MARKEX. Market Expert (MARKEX) [83‚ 112] provides de-cision support for various stages in the product development process. The sys-tem’s model base encompasses statistical analysis‚ multicriteria analysis‚ andconsumer choice models.

2.7.15 MEDICS. This is a knowledge-based system [32] to aid in med-ical diagnosis by distinguishing among possible diseases. It includes a finalPROMETHEE [13] multicriteria analysis to improve results.

2.7.16 MOIRA. MOIRA is a DSS for selecting remedial strategiesto restore water systems after accidental introduction of radioactive substances[103]. It includes an evaluation module based on a multi-attribute value model torank alternatives and a module to perform multi-parametric sensitivity analyseswith respect to both weights and values.

2.7.17 SANEX. http://www.iees.ch/EcoEng00l/EcoEng00l _R3.html. SANEX is a non-commercial computer program to support plannersin assessing the suitability of sanitation systems (e.g. latrines‚ septic tanks‚and sewerage) [68]. It uses socio-cultural‚ financial and technical criteria inconnection with multicriterion decision analysis techniques [69]. SANEX wasdeveloped at the Advanced Wastewater Management Centre (AWMC) at theUniversity of Queensland‚ Australia.

2.7.18 Skills Evaluator. http://www.astrolavos.tuc.gr/contents/skills_evaluator.htm. Skills Evaluator (SE) is a DSS for the evalua-tion of an individual’s information technology qualifications and skills [3]. SEmodels the qualitative criteria that make up the problem‚ and uses a multicri-


teria approach of evaluation‚ based on aggregation-disaggregation procedures.It produces input data for the ELECTRE-TRI method described separately inthis chapter‚ which can then be used to classify the individual based on his orher qualifications.

2.7.19 Steel Hot Rolling Mill Scheduling DSS. This multi-criteriadecision support system [23] provides semi-automatic schedules using a varietyof bespoke local and tabu search [40] heuristics.

2.7.20 TELOS. TELOS is marketing research software for evaluatingcustomer satisfaction. Its features and capabilities are described in [43]. Thisreference also reviews other customer satisfaction-oriented software and themethodology on which TELOS is based‚ described as a multicriteria prefer-ence disaggregation method using ordinal regression. The main objective isthe aggregation of individual preferences into a collective value function basedon the notion that a customer’s global satisfaction depends on a set of criteriarepresenting the product’s appeal. The individuals completing a questionnaireprovide both a global indicator of satisfaction and judgments concerning indi-vidual attributes. The model develops marginal satisfaction functions to renderthe global satisfaction criterion as consistent as possible with customer’s judg-ments on the individual criteria. An advantage of TELOS is that it provides forqualitative customer preference inputs.

2.7.21 Water Quality Planning DSS. http://www.ccas.ru/mmes/mmeda/papers/vodhoz.htm. The Water Quality Planning DSS [75] is basedon the Feasible Goals Method [76]‚ which provides experts and decision makerswith objective trade-off curves among cost and pollution criteria. The informa-tion improves their understanding of the problem and helps to identify waste-water treatment strategies which provide reasonable balance between cost andpollution.

3. Concluding Remarks

A number of authors have provided overviews of the available MCDM method-ology and software. One of the earliest overviews was a user-oriented listingof MCDM methods by Despontin‚ Moscarola‚ and Spronk [28]. Evans [35]gave an overview of techniques for multiobjective programs‚ and Korhonen‚Moskowitz‚ and Wallenius [62] published a review of multiple criteria decisionsupport. Aksoy‚ Butler‚ and Minor [2] provided a comprehensive overview ofcomparative studies in interactive multiple objective mathematical program-ming‚ and Weistroffer and Narula [126] reported on the state of the art ofMCDM software in 1997. Siskos and Spyridakos [114] also presented a surveyof multicriteria decision support systems in 1999. Various attempts at assessing


and evaluating MCDM techniques and software have also been reported. Mostof these involve the testing of a newly developed technique by comparing anexperimental implementation with one or two other approaches. Olson [95] pro-vided a review of empirical studies conducted between 1973 and 1990‚ and alsorecently reported a comparison of three multicriteria methods‚ SMART‚ PRO-METHEE‚ and a centroid method [96]. Weistroffer‚ Narula‚ and Kim [127]did an exploratory study in which they compare four commercially advertisedMCDM software packages. Goicochea and Li [41] also conducted an experi-mental evaluation of four MCDM packages. Zapatero‚ Smith‚ and Weistroffer[130] undertook an extensive comparative evaluation of five MCDM packagesand compared their effectiveness to that of a simple spreadsheet package. Os-sadnik and Lange [98] used AHP to evaluate three packages implementing AHP.Any evaluation of MCDM software‚ of course‚ tests specific implementationsof MCDM techniques‚ and it is not easy to separate the software features fromthe characteristics of the methodology. One problem with experimental evalua-tions is that more commercially oriented software packages have new releasesalmost every year‚ rendering any comparative results quickly obsolete.

Though a large variety of MCDM methods has been proposed in the lit-erature‚ dealing with all aspects of the decision problem‚ a large majority ofcommercially marketed packages deal primarily with MADM problem mod-els and focus on the comparison of alternatives and the identification of themost acceptable solution. Furthermore‚ these packages tend to use the simpleralgorithmic approaches‚ whereas the MCDM literature is full of sophisticatedand complex solution approaches to MCDM problems. In our list of softwarepackages‚ in Section 2‚ we included commercially available packages as well assoftware packages developed at academic or research institutions. These latterpackages‚ more likely‚ implement newer and more sophisticated methodology.Only a few of the commercial packages handle MODM problems‚ though manymethods for dealing with these problems exist.

Many approaches that have been suggested in the literature have only beenimplemented on an ad hoc basis‚ to solve a specific problem situation‚ or asexperimental software to demonstrate the salient features of the proposed un-derlying methodology. One example of such software is the interactive referencedirection algorithm for multiobjective convex nonlinear integer programmingproblems of Vassilev‚ Narula‚ and Gouljashki [123]. A paper by Karaivanovaand Narula [56] presents an overview of multiobjective integer programmingmethods‚ many of which have been implemented as experimental software only.We did not include these packages in our listing of software in Section 2.

An area where there is also an apparent need for more or better software is theportfolio selection problem‚ i.e.‚ the situation where a set of solutions is required‚rather than the best compromise solution. Only one of the available packages


listed in Section 2 is specifically designed for portfolio selection although otherscan be used to assist in addressing this problem.

We also note that several chapters in this volume describe specific MCDMsoftware.

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