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Über dieses Buch

The organizers of the 12th International Conference on Multiple Cri­ teria Decision Making (MCDM) held June 19-23, 1995 in Hagen received the second time the opportunity to prepare an international conference on MCDM in Germany; the first opportunity has been the 3rd International Conference on MCDM in Konigswinter, 1979. Quite a time ellapsed since then and therefore it might be interesting to compare some indicators of the development of the International Society on MCDM, which has been founded in Konigswinter. Stanley Zionts has been elected first president and all 44 participants of that Conference became founding members. Today our Society has over 1200 members and its own Journal (MCDM World Scan). In Hagen, 1996, we had 152 participants from 34 countries. It is interesting to mention that also other Groups established their organi­ zation, like the European Working Group on Multiple Criteria Decision Aid, the German Working Group on Decision Theory and Applications, the Multi­ Objective Programming and Goal Programming Group, ESIGMA, and some others. It is also interesting to note that the intersection of members of all these Groups and Societies is not empty and there is quite a cooperation among them.





An Algorithm for Vectorial Control Approximation Problems

We consider a convex vectorial control approximation problem and derive necessary and sufficient optimality conditions for solutions of a corresponding scalarized problem using the subdifferential calculus. These optimality conditions can be solved by a proximal point algorithm introduced in [3]. This fact together with some stability results form the base of a dialogue algorithm to generate approximate solutions of the vectorial problem.

H. Benker, A. Hamel, Chr. Tammer

Multiple Criteria Models with the Linear Pseudoboolean Functions and Disjunctive Restrictions

The combination of Artificial Intelligence and Operation Research methods has been significant in recent years. The MCDM models with Boolean variables are most suitable to use them in the Intelligence Decision Making Systems, but these models are insufficiently studied [1].

Vladimir Donskoy, Igor Perekhod

Optimality Conditions in Set-Valued Vector Optimization

In this paper we discuss set-valued vector optimization problems and present optimality conditions with the aid of so-called contingent epiderivatives.

Johannes Jahn

A Multiple Objective Approach to Nash Equilibria in Bimatrix Games

Nash equilibria of bimatrix games may be found by solving a nonconvex quadratic multiple objective programming problem over a linear constraint set. The advantages over traditional approaches are explored. Every efficient solution is a Nash equilibrium point, so one may easily obtain multiple equilibria, which is a capability not found in other approaches. Since it is known that Nash equilibria exist, one also obtains a proof that efficient solutions exist for these nonconvex quadratic multiple objective programming problems. Finally, there is an interesting new interpretation of Nash equilibria obtained, namely, that a multiple objective referee of the game exists, who ensures the optimal play by the two participants.

Michael M. Kostreva

The Bargaining Model for Characteristic-function Game

This paper deals with generalized n-person cooperative market games without side payments derived from unbalanced pure exchange economies. The economic motivation for such investigation is a problem of fair sharing rules in situation of deficit on the market of commodities. Our model allows to take into account as a conflict of interests and an acceptable compromise of them.

Tatiana Kulakovskaya

Calculus of Choquet Boundaries Using Pareto Sets

One of the aim of this paper is to present new properties for the efficient (Pareto) point sets in separated locally convex spaces. Thus, for any non-empty and compact subset, the coincidence result between the set of corresponding Pareto points with respect to a convex cone and the Choquet boundary with respect to a convenient cone of real continuous functions established by us in a previous research work gives interesting topological properties of Pareto sets. An important result shows immediate applications of spline optimal interpolation in multiple criteria decision making problems and two numerical examples based on spline functions in H-locally convex spaces illustrate the possibility of calculus for Choquet boundaries through the agency of Pareto sets and conversely.

Vasile Postolica

Generalized Mond-Weir Duality for Multiobjective Nonsmooth Programming

A general Mond-Weir dual for nonlinear nonsmooth multiobjective programming problem is introduced and some duality results are given.

Vasile Preda, I. M. Stancu-Minasian

The Nucleolus in Multiobjective n-person Cooperative Games

In this paper, multiobjective n -person cooperative games are defined, and the nucleolus is considered in such games. First, a multiobjective game is reduced to single-objective games by using the scalarizing methods of multiobjective programming, i.e., the weighting coefficients method and the weighted minimax method. Second, the nucleolus is defined directly in a multiobjective n-person cooperative game. Computational methods for deriving the nucleolus are shown when excess functions are defined as distance from the ideal point or a Pareto optimal point.

Masatoshi Sakawa, Ichiro Nishizaki

Sufficient Conditions in the Vector-Valued Maximin Problems

Constructive sufficient conditions for existence of Slater maximin in strictly convex (by uncertainty) multicriteria problems without restrictions are introduced.

Mindia E. Salukvadze, Vladislav I. Zhukovskiy

Error Estimates for the Crude Approximation of the Trade-off Curve

The crude global search that is used in Parameter Space Investigation provides an approximation of the trade-off curve. An estimate of the approximation error is obtained and numerical experiments confirm the estimate.

I. M. Sobol’, Yu. L. Levitan

Stability and Sensitivity Analysis in Noncooperative Games

In this paper we discuss stability and sensitivity analysis of Nash equilibria which are fundamental solutions in noncooperative games. The results concerning stability are also closely related to the refinement of Nash equilibria studied actively in these days. In finite two-person noncooperative games (bimatrix games), particularly, we can obtain some interesting results about stability and sensitivity of Nash equilibria by applying the implicit function theorem to the corresponding linear complementarity problems.

Tetsuzo Tanino, Hun Kuk, Masahiro Tanaka

Limiting Solution Set Structure for Converging Multiple Objective Dynamic Problems Sequence

For a given dynamic multiple objective problem a special family of dynamic multiple objective problems is constructed. For this family there is constructed the infinite intersection of the sets of all right ends of the quasimotions, generated from some initial position if all the Slatermaximal strategies for each problem are examined. It is shown that this intersection (or the limiting set) coincides with the set of all right ends of the quasimotions generated from the fixed initial position if all the Slater-maximal strategies of the special problem are examined.

Alexander L. Topchishvili




Choosing and Ranking on the Basis of Fuzzy Preference Relations with the “Min in Favor”

In some MCDM techniques — most notably in Outranking Methods — the result of the comparison of a finite set of alternatives according to several criteria is summarized using a fuzzy preference relation. This fuzzy relation does not, in general, possess “nice properties” such as transitivity or completeness and elaborating a recommendation on the basis of such information is not an obvious task. The purpose of this paper is to study techniques exploiting fuzzy preference relations in order to choose or rank. We present a number of results concerning techniques based on the “min in Favor” score, i.e. the minimum level with which an alternative is “at least as good as” all other alternatives.

Denis Bouyssou, Marc Pirlot

Models of Cooperative Decision Making

Many decision problems involve multiple decision makers with multiple goals. Goals can be divided into two types, goals that are mutual for all the decision makers and goals that are different and require cooperation of multiple decision makers to achieve a consensus. A cooperative decision making requires free communication among decision makers. The paper presents a problem solving approach to achieve a consensus in cooperative decision making.

Petr Fiala

The Predictive Power of the Self Explicated Approach and the Analytic Hierarchy Process: A Comparison

The Analytic Hierarchy Process uses pairwise comparisons to determine the weights of criteria and the desirability of the levels. In the Self Explicated Approach the decision maker rates them explicitly. In this study we have compared the predictive power of these two approaches. The predictive power of both methods is tested with respect to the choice, the ranking and the preference scores of two sets of alternatives. The results of the laboratory study with 180 participants indicate that the Self Explicated approach, even with less input data, can show better results than the Analytic Hierarchy Process.

Eelko K. R. E. Huizingh, Hans C. J. Vrolijk

Group Decision Making and Hierarchical Modelling

The paper presents an original procedure for selection the global compromise scenario of the group decision making problem. The procedure can be divided into two steps. The first step is a typical hierarchical modelling based on the AHP. The result of this step is a matrix of the individual priorities of the scenarios for all the decision makers. For the second step the decision makers must specify their concordance and discordance thresholds that make it possible to derive an index of concordance of the i-th decision maker with the j-th scenario, and the global threshold that expresses a necessary majority to accept the given scenario as a candidate for the global compromise scenario. It is a procedure that derives a set of candidates for the global compromise scenario. By interactive changing of the thresholds it is possible to influence the number of the elements of the set of candidates and in this way to find the global compromise scenario.

Josef Jablonsky

Propagation of Errors in Multicriteria Location Analysis: A Case Study

The multicriteria location problem involves a set of potential (or feasible) locational alternatives and a set of criteria (attributes) on the basis of which the alternatives are evaluated. The problem requires that a choice be made among alternatives described by their attributes and with respect to the decision maker(s) preferences. Here, it is assumed that the preferences are expressed in terms of weights assigned to the evaluation criteria and the location problem can be represented in the form of a simple additive weighting model.

Jacek Malczewski

Reference Distribution — An Interactive Approach to Multiple Homogeneous and Anonymous Criteria

There are several decision problems with multiple homogeneous and anonymous criteria where the preference model needs to satisfy the principle of anonymity (symmetry with respect to permutations of criteria). The standard reference point method cannot be directly applied to such problems. In this paper we develop, as an analogue of the reference point method, the reference distribution method taking into account both the efficiency principle and the principle of anonymity. All the solutions generated during the interactive process belong to the symmetrically efficient set which is a subset of the standard efficient set. It means, the achievement vector of the generated solution is neither dominated by another achievement vector nor by any permutation of some achievement vector.

Włodzimierz Ogryczak

Rank-Ordering of Alternatives in Multiattribute Decision with Incomplete Information

Incomplete information is a set of linear inequalities, which is the decision maker’s information on both utilities and attribute weights. The decision maker under time pressure and lack of knowledge is only willing or able to provide incomplete information. We present a method for establishing pairwise dominance of alternatives under consideration, and propose an algorithm of constructing a dominance graph using the data of pairwise dominance relations. Proposed algorithm uses a graph theoretical technique, which is based on the transitivity of preferences. Dominance graph can be used to aid in selecting an optimal alternative or satisfying alternatives.

Kyung Sam Park, Soung Hie Kim

Structuring Techniques in Multiset Spaces

This paper presents methods to investigate a structure of objects described with qualitative attributes (multicriterial alternatives, textual documents and so on). Proposed algorithms of clustering and ordering are based on the theoretical model of multisets. Techniques take into account qualitative nature of object properties and decision maker preferences.

Alexey B. Petrovsky

The Sensitivity Analysis of “Inexact” Multicriteria Decisions

We elaborate a view of sensitivity analysis as a decision analysis activity. Our two main results concern: 1) a formal concept of “inexact” riskless preference; and 2) illustrative mathematical optimization problems for identifying “large” subsets of value function parameter values that preserve the preferability of a prescribed decision alternative.

Mitchell S. Robinson, Richard M. Soland

Goal Programming and Multiple Criteria Decision Making: Some Reflections

Two issues are discussed in this paper. The first is whether an algorithmic approach can be a logical and practical way of selecting the best multi-criteria technique. The second issue relates to the correct election of a goal programming (GP) variant for a given decisional problem. With this purpose the preferential logic underlying the most widely used GP variants (lexicographic, weighted and MINMAX) are connected with the actual preferences of decision maker. From the analysis undertaken some insights and recommendations in choosing the best GP variant or mix of variants arise. Although the output of this paper cannot be considered completely new, it can, however, help analysts in building logically sound GP models which rightly reflect the reality being modelled.

Carlos Romero

Stopping Rules in Collective Expert Procedures

Collective expert interrogation procedures are widely used for group decision-making. There are some forms of the procedures, but in any case an expert procedure is a continuing in time process of group work, and a choice of a moment of its termination is one of important questions of examination. In literature two rules are mainly considered. The first one, the consent rule, speaks that termination is conducted at the reaching of consensus or essential proximity of expert judgments. First, this rule was formulated in the Delphi method. The rule was very popular and for a long time have remained the single stopping rule. Later in a few works there was a criticism of procedures supposing the trend of individual experts’ judgments to yield to influence of authorities or “majority opinion”. These works pay attention to a danger of conformistic trends and “groupthink” when experts refuse in fact their judgments for the sake of unanimity of a group. As a reaction to this criticism the stabilization rule appeared. In accordance with the rule termination is conducted at an achieving a high or complete stabilization (unvariability in time) of experts’ judgments. First this rule appeared in [1], then in [2]. The problem connected with the stopping rule has not studied experimentally. The first effort in this direction devoted to rules of consent and stabilization is given in the work.

Michael Schneidermann

Multiple Criteria Discrete Dynamic Programming

Dynamic programming is classically concerned with maximization of the value assigned by a real-valued function defined over sequences of decisions. Multi-criteria (multi-objective) dynamic programming extends the approach to a vector-valued criterion function. The main purpose of the paper is to give new definitions of separability and monotonicity which allow to extend the theory of discrete multiobjective dynamic programming. The vector principle of optimality and theorems applied in decomposition methods are formulated. Numerical algorithms for such problems are briefly described. The paper ends with examples which illustrate the numerical aspects of the procedures.

Tadeusz Trzaskalik

MCDM and Models of Voting Decision Making

A rational voter’s behaviour can be analysed within the framework of a standard consumer behaviour pattern: voting for candidate(s), the voter is “buying” a policy represented by candidates and maximizing his “utility” subject to a “budget constraint” given by a used voting procedure. In this paper we formulate a model of an individual voter behaviour in the election of a committee, based on so called voting constraint and a utility function, defined over a set of feasible voting strategies. A class of utility functions is suggested on the basis of a multi-criteria optimization problem, in which the voter minimizes a distance between his ranking of the major political issues and the aggregate ranking of these issues by the candidates, generated by the voter’s voting portfolio selected from the set of feasible voting strategies. Using goal programming techniques optimal voting portfolio can be calculated. A game theoretical analysis of the problems associated with voting decision making is suggested.

František Turnovec

Distributed Multiobjective Optimization Problems and Methods for their Solution

Methods for solving distributed multiobjective problems for interrelated linear mathematical models with own linear criterion function are considered in the paper. A general procedure of constructing distributed methods of searching solutions for interrelated multicriterion mathematical programming based on solving a minimax problem formed with respect to a set of criterion function is discussed. The procedure is named distributed as it admits parallel and asynchronous execution of actions for seaching local solutions with next coordination to obtain a solution of the general problem.

V. L. Volkovich

Decision Making: Some Experiences, Myths and Observations

Decision making in management is one of the most important, if not the most important, function of management. How decisions are made, and how managers make the best decisions possible are central issues in management. Managers make decisions, all day long, day in, day out, and many never think about the decisions, except to make them and get them out of the way.

Stanley Zionts


An Interior Multiobjective Linear Programming Algorithm Using Aspirations

We describe in this paper a new multiple objective linear programming (MOLP) algorithm that is based on the single-objective path-following primal-dual linear programming algorithm, and combines it with aspiration levels and the use of achievement scalarizing functions.

Ami Arbel, Pekka Korhonen

A Fuzzy Solution Approach to a Fuzzy Linear Goal Programming Problem

In conventional multiobjective decision making problems, the estimation of the parameters of the model is often a problematic task. Normally they are either given by the decision maker (DM) who has imprecise information and/or expresses his considerations subjectively, or by statistical inference from the past data and their stability is doubtful. Therefore, it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets and a lot of fuzzy approaches to multiobjective programming have been developed.Many decisors might follow a satisfaction criterion rather than the criterion of maximizing an objective function; and the satisfaction criterion leads to the concept of goal. Goal programming (GP) is an appropriate approach to the problem and when attributes and/or goals are in an imprecise environment and they cannot be stated with precision, we work in fuzzy goal programming.This paper presents a fuzzy solution to a GP problem when all the parameters may be fuzzy numbers. The method relies on á-cuts of the fuzzy solution to generate the possibility distribution of the objective functions. Ideas are illustrated with a numerical example.

Arenas Parra, M. Mar Bilbao Terol, Amelia Rodriguez Uria, M. Victoria, Jimenez Mariano

COPE — ing with V·I·S·A — Integrated Support from Problem Structuring through to Alternative Evaluation

Work in the field of multiple criteria analysis has generally focused on evaluation procedures, taking as its starting point a well defined problem with specified alternatives and criteria. However, in reality problems are rarely so well structured; hence, in order to usefully support decision making in practice, multiple criteria analysts need to address the issue of problem structuring. In this paper we describe a study which sought to integrate SODA (Strategic Options Development and Analysis), an approach to problem structuring which uses the COPE software for cognitive mapping, with multiple criteria evaluation based on a multi-attribute value function using V•I•S•A. The study took the form of a two day action research workshop to explore the strategic direction of the Supplies and Commercial Services Department of a large UK NHS Hospital Trust and to develop an action plan consistent with the agreed direction.

Valerie Belton, Fran Ackermann, Ian Shepherd

An Algorithmic Package for the Resolution and Analysis of Convex Multiple Objective Problems

The aim of this paper is to describe an algorithmic package which allows us to cany out a complete treatment of a general multiple objective convex problem. It includes the generalisation of many of the algorithms used in the linear case, as well as some others developed specially for our problem. This treatment can be divided into two main blocks: • Generation of efficient solutions: both the weighting and the constraint method are developed, through an automatic generation of weights in the former, and of bounds in the latter.• Goal Programming: We include two versions of the traditional lexicographic algorithms, adapted to the convex case under study, and we also allow the possibility to generate the set of solutions which are satisfying and efficient at the same time. Finally, we also cany out a post-optimal analysis on the target values, so as to find whether they can be improved or not. This analysis, which takes the form of an interactive method, can even lead to an efficient, as well as satisfying, solution for the original problem. Some computational results are presented, which show the behaviour of the algorithms, in terms of C.P.U. time, on some test problems with different number of variables and constraints. These algorithms have been implemented in FORTRAN language, on a VAX 8530 computer, and with the aid of the NAG subroutine library, mark 15.

Rafael Caballero, Lourdes Rey, Francisco Ruiz, Mercedes González

From TRIMAP to SOMMIX — Building Effective Interactive MOLP Computational Tools

This paper aims at presenting a path of development of interactive computational tools devoted to provide decision aid in multiple objective linear programming (MOLP) problems, made by a research team at the University of Coimbra. After referring to the motivation of this research area, the main characteristics of the research work which has been carried out in the last years are described, with special emphasis on the MOLP interactive environments TRIMAP, TOMMK and SOMMIX.

João Clímaco, C. Henggeler Antunes, Maria J. Alves

Pareto Simulated Annealing

The paper presents a multiple objective metaheuristic procedure -Pareto Simulated Annealing. The goal of the procedure is to find in a relatively short time a “good” approximation of the set of efficient solutions of a multiple objective combinatorial optimization problem. The procedure uses a sample of generating solutions. Each of the solutions explores its neighborhood in a way similar to that of classical simulated annealing. Weights of the objectives are set in each iteration in order to assure a tendency to approach the efficient solutions set while maintaining a uniform distribution of the generating solutions over this set.

Piotr Czyżak, Andrzej Jaszkiewicz

A Reference Direction Interactive Algorithm of the Multiple Objective Nonlinear Integer Programming

Vassil G. Gouljashki, Leonid M. Kirilov, Subhash C. Narula, Vassil S. Vassilev

Rough Set Approach to Multi-Attribute Choice and Ranking Problems

We propose an original way of applying the rough set theory to the analysis of multi-attribute preference systems in the choice (Pa) and ranking (Py) decision problematics. From the viewpoint of rough set theory, this approach implies to consider a pairwise comparison table, i.e. an information table whose objects are pairs of actions instead of single actions, and whose entries are binary relations instead of attribute values. From the viewpoint of multi-attribute decision methodology, this approach allows both representation of decision maker’s (DM’s) preferences in terms of “if …then…” rules and their use for recommendation in Pa and Py problematics, without assessing such preference parameters as importance weights and substitution rates. The rule representation of DM’s preferences is alternative to traditionally decision support models. The rough set approach to (Pα) and (Pβ) is explained in detail and illustrated by a didactic example.

Salvatore Greco, Benedetto Matarazzo, Roman Slowinski

Concepts of a Learning Object-Oriented Problem Solver (LOOPS)

This presentation discusses concepts of a learning object-oriented problem solver (LOOPS) which is on the one hand a new and general framework for a decision support system (DSS) and on the other hand answers some open or partially neglected questions in multiple criteria decision making (MCDM). These are, for instance: How should implicit knowledge about ‘good alternatives’ be processed? What method should be used? How should its parameters be adjusted?The main methodological goals of LOOPS are 1) learning and 2) the integration of methods. These concepts are discussed and ways of their realization are suggested: Integration is achieved by providing several methods, by utilizing neural networks, and by developing a concept of generalized networks. Learning is realized by evolutionary algorithms. Essential to the implementation of these concepts within LOOPS is the object-oriented paradigm which is also discussed.

Thomas Hanne

Outranking-Driven Search Over a Nondominated Set

We consider the interactive exploration of implicitly or explicitly given large sets of alternatives. Upon review of classical interactive procedures, which usually assume a utility function preference model, we are distinguishing three typical operations used in various interactive procedures: contraction of the explored set, exploration of some neighbourhood of a current alternative, and reduction of a sample of the explored set. After pointing out some weak points of the traditional procedures, we describe three interactive procedures performing the three operations, respectively, using an outranking relation preference model. Due to proposed ways of building and exploiting the outranking relation, the weak points of traditional procedures can be overcome.

Andrzej Jaszkiewicz, Roman Słowiński

An Interactive Method for Solving Multiple Objective Quadratic-Linear Programming Models

In this paper, we describe an interactive procedure for solving multiple criteria problems with one quadratic objective, several linear objectives, and a set of linear constraints. The procedure is based on the use of reference directions and weighted-sums. The reference directions for the linear functions, and the weighted-sums for combining the quadratic function with the linear ones are used as parameters to implement the free search of nondominated solutions. This idea leads to the parametric linear complementarity problem formulation. An approach to deal with this type of problems is given as well. The approach is illustrated with a numerical example.

Pekka Korhonen, Guang Yuan Yu

An Approximation to the Value Efficient Set

In this paper we assume a decision making situation under certainty with incomplete information on the decision maker’s preferences, by means of a vector value function defined on the consequence space. From that function we consider an additive value representation with partial information on the scaling constants defined by polyhedral cone and the concept of value efficient set. We introduce an approximation set whose generation may be easier than the one of the value efficient set. Nesting properties based on the interactive reduction of the uncertainty about the scaling constants, which provide more precise vector value functions, lead to better approximations. Finally, we propose an interactive algorithm based on the approximation set and two examples illustrating the method.

Alfonso Mateos, Sixto Rios-Insua

Choosing a Finite Set of Nondominated Points with Respect to a Finite Set of Reference Points

The paper deals with the MOLP problem “max” f(x) = zx ∈ S ⊂ Rn, where f(x) ∈ Rm, all f i (x) are linear functions, the set S is defined by linear constraints, and is bounded and closed.

Boyan Metev, Ilia Braianov

A Method for Searching Rationality in Pairwise Choices

In this paper an operational method is presented for searching rationality into paired comparisons of the alternatives. We base our method on the decomposition of a binary relation in terms of families of quasi orders. With the “mixture of maximal quasi orders”, as the main concept, we attempt to use decision maker’s inconsistencies as a kind of information for modelling his preferences.

Jacinto González-Pachón, Sixto Ríos-Insua

Zero-One Goal Programming Under Interdependence of Actions

An approach to modeling discrete multiple criteria problems under interdependence of actions is presented. The concept of interdependency of actions in multicriteria decision making is explored and its main characteristics discussed. The problem is formulated as a zero-one program; a goal programming technique can then be employed to obtain a suitable subset of efficient solutions.

Siamak Rajabi, D. Marc Kilgour, Keith W. Hipel

An Interactive Fuzzy Decomposition Method for Large-Scale Multiobjective Nonlinear Programming Problems

In this paper, we propose an interactive fuzzy decomposition method for large-scale multiobjective nonlinear programming problems with the block angular structure to obtain the satisficing solution for the decision maker (DM). In the proposed method, after eliciting the membership function for each of the objective functions, the satisficing solution for the DM can be obtained on the basis of the dual decomposition method from Pareto optimal solution set by updating the reference membership values interactively. An interaction processes for a numerical example under the hypothetical DM are illustrated to indicate the feasibility of the proposed method.

Masatoshi Sakawa, Hitoshi Yano

Basic Concepts in Derivation of Fuzzy Multiattribute Utility Functions

This paper concerned with basic concepts in fuzzy decision analysis. Conditions and techniques required in construction of the fuzzy utility function and its multiobjective extensions are discussed. Fuzzy lottery technique with fuzzy certainty equivalent based on possibility measure is presented in contrast with the classical probabilistic lottery technique. Fuzzy preference independence assumptions are examined for derivation of the fuzzy multiattribute utility functions.

Fumiko Seo

Feed-Forward Neural Networks for Approximating Pairwise Preference Structures

In this paper, we introduce a feed-for ward neural network formulation that has the ability to learn and generalize Analytic Hierarchy Process (AHP)-style pairwise preference patterns in the training set, and can accurately approximate imprecise preference ratings based on pairwise preference judgments. A computational experiment verifies the robustness of the feed-forward neural network formulation.

Antonie Stam, Minghe Sun, Marc Haines

A Comparison Between Goal Programming and Regression Analysis for Portfolio Selection

The aim of this paper is to investigate the application of Goal Programming (GP) to portfolio evaluation and selection. The shares analysed are those in the British FTSE 100 index. A two stage model is proposed. The first stage predicts the sensitivity of the shares to specific factors using GP and regression analysis. The second stage of the model selects a portfolio using a GP model based on the decision maker’s scenarios and preferences. A comparison between the sensitivities predicted by the first-stage of the GP model and that of the regression analysis is made. Keywords: Goal Programming, Portfolio Selection, Regression Analysis

M. Tamiz, R. Hasham, D. F. Jones

A General Purpose Interactive Goal Programming Algorithm

This paper reviews currently available goal programming (GP) and multi-objective programming (MOP) interactive algorithms and discusses design issues of interactive algorithms specifically for GP. Two factors which distinguish GP applications from most MOP application are the capability to incorporate a large number of objectives in the modelling and solution practice, and the possible use of a lexicographic priority structure. Therefore any interactive GP or adapted MOP algorithm should be capable of performing well under these conditions. In practice, many existing algorithms fail to operate efficiently under these conditions due to a large amount of information required from, or presented to, the decision maker or the time taken per interactive iteration. The use of the lexicographic structure also adds an extra degree of complexity and may cause problems with utility function based algorithms. Therefore, the remainder of this paper presents a general purpose GP interactive algorithm capable of handling both large scale, and lexicographic, goal programmes. The algorithm is designed to present a suitable amount of information to the decision maker and be efficient both in number of interactive iterations and in time taken per interactive iteration.

M. Tamiz, D. F. Jones

A Tchebycheff Metric Approach to the Optimal Path Problem with Nonlinear Multiattribute Cost Functions

A global optimization problem of finding an optimal path in the network with multiple attributes on links and a nonlinear convex cost function is studied. It is shown that the modified weighted Tchebycheff metric scalarization can generate every nondominated path in the network. Two exact algorithms for solving the bi-attribute optimal path problem are presented and an illustrative example is enclosed.

Malgorzata M. Wiecek, Paul T. Hadavas



Applications in Engineering

Multicriteria Optimization of ABS Control Algorithms Using a Quasi-Monte Carlo Method

The Quasi-Random Weighted Criteria method is proposed for multicriteria design optimization. This quasi-Monte Carlo method features increased computational efficiency and is particularly suitable for exploring alternative design configurations. A quasi-random sequence generates a set of candidate solutions representative of the range of available solutions for each design alternative. The method can be used recursively to produce more detailed Pareto surface descriptions near selected points.In this paper the method is used to select between vehicle anti-lock brake system (ABS) control algorithm approaches and to optimize the parameters within each. An ABS system is highly nonlinear and therefore the control algorithms draw upon the methods of nonlinear control theory. Stochastic optimization was incorporated to ensure that the ABS system will perform well despite the uncertainties in the vehicle and in the environment. A variety of ABS design studies are presented.

Timothy Ward Athan, Panos Y. Papalambros

Dynamic System Design via Multicriteria Optimization

Dynamic system design is formulated as a multicriteria optimization problem. The dynamic behavior of dynamic systems is described by nonlinear differential equations of motion found from the multibody system approach. Parameters of the multibody system serve as design variables in order to optimize the system with respect to its dynamic behavior which is evaluated by multiple integral type objective functions. Multicriteria optimization strategies are used to reduce the design problem to nonlinear programming problems. The gradients required for optimization are found from a semi-analytical sensitivity analysis. Problems resulting from an application of conventional optimization strategies to a vehicle design problem are discussed.

Dieter Bestie, Peter Eberhard

Quality-Driven Decision Making in Digital System Design

Digital system design is a competitive business, with high complexity and a multi-aspect character. Together with nowadays increasing demand of application-and customer-specific embedded systems, suiting supporting design techniques and tools are needed. We are considering the concept of quality within digital system design in order to assure that the systems designed comply as much as possible with the requirements of their future customers. Aim of the paper is to provide and discuss backgrounds, ideas, and direction for future work in the field of quality-driven design decision making.

L. Jóźwiak, S. A. Ong

Deriving A Maintenance Strategy Through The Application Of A Multiple Criteria Decision Making Methodology

This paper analyses the process of formulating and evaluating an appropriate maintenance strategy using the Analytic Hierarchy Process (AHP) methodology in a group decision making environment The work presented is based on the process of formulating a maintenance strategy which involves several key decision makers in a leading automotive manufacturing company. The AHP methodology was developed to systematise the decision process. Whilst, the work is based on this application, the methodology used was constructed to provide a generic framework for the formulation of maintenance strategy. The effects on group decision making for such an application are discussed. The AHP has enabled subjective decisions to be made by a group through a vigorous and structured process involving sometimes conflicting personal objectives within a multiple criteria decision process.

Ashraf W. Labib, Glyn B. Williams, Richard F. O’Connor

Ring Network Design: an MCDM Approach

Telecommunication networks, are optimised so to reduce the impact of fixed costs and to take advantage of system economy of scale. Satisfactory protection target expressed in terms of availability, survivability and soft failing performances should be guaranteed by the designer. In ring networks with self-healing capability such figures are related to the topological features of the network. To rationalise the comparison of different design alternatives and to drive automatic tools balancing all the conflicting criteria involved in the evaluation, the design problem can be formulated as an MCDM process. In the paper, an interactive MCDM procedure based on dynamic aspiration levels and achievement scalarising functions, is proposed to solve the multiple ring network design problem where both cost and protection are taken as simultaneous objectives.

Ugo Mocci, Luigi Primicerio

A Construction Accuracy Control System of Cable Stayed Bridge Using a Multi-objective Programming Technique

Cable-stayed bridges are gaining much popularity in Japan due to their beautiful shape. During and after construction, this kind of bridge needs to have the cable length adjusted in order to attain errors of cable tension and camber within some allowable range. Since the cable length is affected by the change of temperature, the operation of acuracy control has to be completed whithin a short period, say 2:00 to 8:00 in early morning. So far, this construction accuracy control has been performed by judgment based on the experiences of experts, or goal programming. In either case, however, many trial and errors are usually made in order to attain a satisfactory solution, and it is difficult to complete the operation within the time limit. To this aim, the autors developed a construction accuracy control system using the satisficing trade-off method which has been observed to be effective to many kinds of multi-objective programming problems. The system has a user-friendly human interface of graphic input-output, and hence is simple and easy to implement. The results of applications of the system to real bridges are also reported in this paper.

H. Nakayama, K. Kaneshige, S. Takemoto, Y. Watada

MCDM in Water Resources Investment Planning

A state agency faces the problem of allocating its available funds to the high evaluated projects. The projects are evaluated in terms of different criteria, expressing economic, environmental, and social impacts. The criteria are defined for specific project groups: multipurpose reservoirs, water supply systems, irrigation systems, wastewater treatment plants. The data are provided by designers. Investment planning is considered as a dynamic process. The multicriteria decision making procedure is developed, based on the Compromise Ranking Method. As an illustrative example, the water resource projects evaluation and investment planning by Water Resources Fund of Serbia is presented.

Serafim Opricovic, Branislav Djordjevic

Optimal and Robust Shapes of a Pipe Conveying Fluid

An optimal and robust shape is determined for a pipe conveying a fluid. The problem is formulated as a structural optimization problem with the radius of the circular cross section as design variable. The critical velocity of the fluid flow in the pipe serves as the first criterion. The critical velocity is related to the upper limit of the nonconservative fluid force. It is furthermore desired that the critical velocity be insensitive to perturbations in the pipe shape and we thus consider the design’s robustness with respect to such perturbations as the second criterion. The two criteria are ordered in accordance with their importance with the maximum of the follower force as the primary criterion. The optimal design for the force is considered first and this design is then modified to improve the robustness. The results are illustrated for a silicon rubber pipe conveying water at constant velocity.

Masao Tanaka, Shinji Tanaka

Multi-Objective Modeling for Engineering Applications in Decision Support

In engineering computer-aided design, the final choice of the design might be supported by multicriteria optimization; we show here, however, that multicriteria optimization can be also used as a tool of helping in a flexible analysis of various design options or various modeling and simulation variants, even from the beginning stages of model construction. Various formats of defining linear and nonlinear models are discussed together with related problems of inverse and softly constrained multi-objective simulation. Such techniques are illustrated by engineering applications of a software package DIDASN++ in mechanics, automatic control and ship navigation.

Andrzej P. Wierzbicki, Janusz Granat

Applications in Environment

Multi-Criteria Decision Making to Rank The Jordan-Yarmouk Basin Co-riparians Water Allocations According to The Helsinki and ILC Rules

The Jordan River system which is shared by Jordan, the Palestinians in the occupied territories, Syria, Lebanon and Israel is a major issue in the current Middle East peace negotiations. This study identifies the water resources of the system, review of the development plans in the basin, and the relevant legal riparian issues and practices related to the basin. The main conclusion is that the application of the Helsinki and ILC international rules separately to allocate shared water resources in the basin between the different countries is not suitable to a region which is in conflict in every issue, since all relevant rules are not considered together and a conclusion is not reached on the basis of the whole rules; this necessitates the need for applying the Multi-Criteria Decision Aid (MCDA) as a mathematical tool to help to solve the problem based on recognised water rights and sharing the water in a neighbourly way to avoid any future major conflict. The PROMETHEE method [1] as an MCDA method was applied. The results of the relative ranking of the Jordan-Yarmouk co-riparians indicated that Jordan (first) and the Palestinian in occupied territories (second) ranked high in this analysis (compared to Israel, Syria, and Lebanon) after selecting a complete and comprehensive set of rules adapted from the existing international laws with their relative importance, and measurement scale. In addition, sensitivity analysis was carried out to check the ranges of stability of the results. Furthermore, analysis regarding possible allocations of future investments in the basin subjected to different constraint was demonstrated using the new version of PROMETHEE V.

B. Al-Kloub, T. T. Al-Shemmeri

Multi-Criteria Decision Support System for Water Strategic Planning in Jordan

The Nominal Group Technique as a structured group decision support process and PROMETHEE as a multi-criteria decision aid software are utilised to develop a future water sector strategy, and a system methodology to rank and select water development projects in the presence of conflicting objectives and constraints. The task described is novel in that it integrates the various decision analytical management techniques in order to increase the flexibility and efficiency of the current decision making process.

Bashar Al-Kloub, Tarik Al-Shemmeri, Alan Pearman

An Application of MCDM in Local Water Resources Management

This paper presents a practical application of MCDM in local water resources management problems. A stochastic dynamic programming model with a fuzzy criterion is proposed to monthly reservoir operations. A series of goal programming models are built for water supply and allocation by different planning and operating levels. DP-GP models fulfill the optimal operation tasks for Qinhuangdao water resources management.

Jifa Gu, Xijin Tang

Application of ELECTRE III for the Integrated Management of Municipal Solid Wastes in the Greater Athens Area

The present work demonstrates the applicability of multicriterial aid for decisions (MCDA) in the area of municipal solid waste management in Greece by means of a case study for household wastes in the Greater Athens Area. For the case study area, a concise family of 24 evaluation criteria is proposed. Through these, five selectively composed alternatives for the integrated management of household waste are compared and ranked in a partial pre-order by means of the ELECTRE III MCDA method. First results favour integrated systems emphasizing on separate collection at the source, whereas the need for careful analysis of their sensitivity to inter- and intra-criteria information is demonstrated by a conducted robustness analysis.

Avraam Karagiannidis, Nicolas Moussiopoulos

Applications in Management

A Multidimensional Framework for Strategic Decisions

Literature offers a wide variety of approaches for solving strategic decisions in the firm. Within firms one can often observe a clear gap between the strategic and financial evaluations of major decisions. In this paper we describe how different types of evaluations are being made, describe the gap between the approaches and give some reason for its existence. Since we are convinced that a more integrated approach to solving decisions is desirable, we present a synthetic framework.Given the nature of the decision problems involved, the framework allows for both quantitative and qualitative information. In addition, the framework is quite naturally one which encompasses a multiplicity of goals, constraints and viewpoints. In this way the multicriteria decision methodology offers a tool for learning and communication, bringing together disciplines and approaches which would otherwise be hardly capable of communicating. The framework is illustrated by a real-life example of a new product decision in a Finnish drug company.

Malin Brännback, Jaap Spronk

The Multiobjective Metaheuristic Approach for Optimization of Complex Manufacturing Systems

The group technology approach is based on the idea that parts which require similar operations and machines should as much as possible be grouped together into part families and machine ceils. Such an approach, reduces usually the flow of parts and tools, set-up times, throughput times and work-in process inventory. In the ideal case, each part family should be processed by its own machine cell. However, in practice, some parts need to be processed by different cells. It results in some bottlenecks.

Piotr Czyżak, Andrzej Jaszkiewicz

Portfolio Selection Using the Idea of Reference Solution

This paper proposes a decision aiding procedure for security selection. The presented procedure uses a multicriteria discrete analysis method based on the idea of reference solution. Application of the decision aiding procedure is demonstrated through the numerical example based on real world data from the Warsaw Stock Exchange.

Cezary Dominiak

Model “Inflation — Non payment — Production — Loans” and its implementation in Russia

Inflation in Russia was over 20% per month in 1992, but now it is in range 5–8% per month. The financial decision in such conditions differs from ones under inflation 3–5% per year. Now Russian government sets the problem of inflation decrease to 1–2% per month as the main goal of its work.

Oleg Dranko

Equity and MCDA in the Event of a Nuclear Accident

Decision making on countermeasures in the event of a nuclear accident such as Chernobyl is complex. Many criteria are involved. Aside from obvious ones related to the direct effects of radiation, there are issues relating to psychological stress, public acceptability and the need to consider the longer term economics of the affected regions. Thus there are many ways in which multi-criteria decision analysis (MCDA) can provide insights and support to the decision makers. Decisions on countermeasures will be made, at least initially, in the face of considerable uncertainty and the interplay between equity and uncertainty in the evaluation of different countermeasure strategies is far from straightforward. Apparently reasonable approaches, which appear to treat different population groups equitably, can, on closer examination, have unreasonable effects. The paper describes the MCDA components in relation to equity judgements of a decision support system (RODOS) for such emergencies being built by a consortium of institutes within the European Union, Eastern Europe and the former Soviet Union.

Simon French, Emma Halls, David Ranyard

The Evolving Role of MCDM in Risk Management

The fundamental task that faces risk managers at all levels of decision making is the need, ability, and sometimes the courage, to make the required trade-offs among risks of various nature and among their associated costs and benefits. Quantifying multifarious risks and determining the acceptability level of each risk and its associated costs and benefits are the critical challenges at the heart of the Multiple Criteria Decision Making (MCDM) field.

Yacov Y. Haimes

Integer Goal Programming Model for Nursing Scheduling: A Case Study

No shortage of one nurse allowed in any shift since there is no nursing agent in Taiwan. The reallocation of one nurse in some unit to another unit is not usual. Furthermore, nurses are used to request a certain shift or a day-off on some certain days. The workload for each shift is determined by the hospital and the Department of Health. The remaining job for a head nurse is to assign a specific shift assignment to the nurses in her/his own unit. A model is proposed to help a head nurse for the above nursing scheduling problem. Firstly, the nurses in a unit split into several groups. Secondly, the nurses are assigned their specific shift assignment/day-off in a two-week palnning horizon by an integer goal programming (GP) model.

Fenghueih Huarng

Multiple Criteria Vendor Selection: A Case Study

In this article, vendor selection in the hydraulic pump gear division of a manufacturing company is explained. Division wants to find appropriate vendors and amount to buy from them while minimizing cost and maximizing quality and delivery reliability. Visual Interactive Goal Programming (VIG) is used as a decision support system. Interaction with decision makers during model building and solution process is discussed.

Birsen Karpak, Rammohan Kasuganti, David Adams

Scheduling of Unit Processing Time Jobs on a Single Machine

In this paper we address the scheduling problem of unit processing time jobs on a single machine considering number of tardy jobs and a measure of earliness. We consider total absolute lateness, total earliness and maximum earliness, as earliness measures.We provide a simple rule to solve the total earliness and maximum earliness problems in a unit execution time single machine environment.Unit processing times allow for the formulation of the scheduling problem as an assignment problem. When there are two criteria the formulation includes side constraints. We formulate the problem and solve it to generate all efficient solutions. We provide computational results on a set of problems.

Suna Köksalan Kondakci, Elif Emre, Murat Köksalan

Linear Goal Programming Model for Managing Balance Sheet of a Commercial Bank

This paper develops the deterministic dynamic model to support the management of the bank balance sheet. It takes into account all main managerial goals and legal requirements and its planning horizon is unlimited. For numerical test we adopt the linear goal programming method. Parameters and initial values were chosen so they fit the situation in a Polish commercial bank. We found that this kind of model can be a useful aid in the strategic planning process of a bank.

Jerzy Michnik, Tadeusz Trzaskalik

Local Tax Planning with AHP and Delphi

A tax model for the city of Richmond is developed and tested, in close cooperation with local public leaders and with tax experts. To construct and test the model, Expert Choice, a commercially available decision support system based on the analytic hierarchy process is used. A Delphi approach is used to have tax experts compare the alternative tax plans with respect to specific decision criteria.

H. Roland Weistroffer, Blue E. Wooldridge, Rahul Singh


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