Multiple Criteria Decision Making

Each human is endowed with a priceless super-computer—the brain. Unfortunately, due to their limiting human software (habitual concept and thinking), the super computer could not fully utilize its potential. To be a great MCDM scholar we need to expand and enrich our domains of thinking, which usually can lead us to strikingly better decisions than that ever known before. Using habitual domain (HD) theory, we provide easy but effective human software programs to expand and enrich our thinking.

Implementation of a billion dollar greenfield steel mill project in Taiwan in the early 70’s confronted a host of difficult decision making problems. Success in overcoming these problems is interpreted in retrospect in the light of the concept of habitual domains, which was not yet available during the project implementation in the early 70’s.

This historic tenth meeting is a convenient point at which to explore where our field has been and some ideas as to where it is going, as well as what challenges lie ahead. I do this by first reviewing some aspects of the timing of the meeting, and the state of the field of multiple criteria decision making (MCDM). I then present and discuss ten popular myths of MCDM, and present some ideas for an MCDM method. I also explore the role of microcomputers in MCDM, and discuss some ideas for future research.

We provide a brief review of some principles used in developing interior-point linear programming algorithms. In particular, we develop the affine-scaling primal algorithm and discuss some implementation issues. A few approaches for using this —and other algorithms in its class— for linear programming problems with multiple objectives are discussed as well.

This paper uses one variant of Karmarkar’s interior point linear programming algorithm and modifies it for addressing multiple objective linear programming (MOLP) problems. Specifically, the paper considers the modification of the affine-scaling primal algorithm and develops a procedure for generating search directions that are interior to the polytope formed by the constraints of the linear programming problem. These search directions are combined into a single direction that approximates the gradient of an implicitly-known utility function at the current — interior — solution point. The solution process is comprised of a sequence of steps where search direction are generated and later combined to arrive at the next interior iterate.

The concept of tradeoffs among objectives plays a major role in the methodology of decision making, mathematical programming and specifically multi-criteria decision making. We present here a generalized definition of tradeoffs in terms of the tangent cone of feasible directions in the set of objectives. We call them (Pareto) tradeoff directions, extending the ones defined only at differentiable (i.e., non-degenerate) points. We present properties of these directions and methods of calculating them. We specially investigate methods which are helpful in a multi-objective mathematical programming context. A numerical example will be given which illustrates these directions and methods to calculate them.

The purpose of this paper is to present a new mechanism of multiobjective programming which integrates compromise programming and noninferior set estimation (NISE) methods. The paper begins by first discussing the limitations of the conventional NISE algorithm by Cohon (1978), and then discusses several extended models derived from conventional NISE algorithms including CONNISE and CONWEIGHT algorithms. Next, the new algorithm is expressed in its mathematical form and a numerical example is given to demonstrate its effectiveness (i.e. in controlling the allowable error) and efficiency (i.e. its rapid convergence). Suggestions for further research are also given.

In this paper, a linear programming problem with an interval objective function is treated. First, the previous approaches to this problem are reviewed and the drawbacks are pointed out. To improve the drawbacks, a new approach to this problem is proposed by introducing the minimax regret criterion as used in decision theory. The properties of minimax regret solution are investigated. In order to obtain the minimax regret solution, a method of solution by a relaxation procedure is proposed. It is shown that the solution is obtained by repetitional use of the simplex method. A numerical example is given to illustrate the proposed solution method.

This paper surveys group decision support systems which use multiple criteria decision making tools in generating alternative solutions and/or resolving conflict among the parties involved in reaching a compromise. Two dimensions are considered in the analysis of the existing systems; the particular multiple criteria decision technique used to generate decision alternatives or to choose from a given set, and the method used to facilitate individual compromise and group consensus. The focus of the survey is on cooperative multiple criteria decision problems. Finally, a recapitulation of the survey is provided to detect the underlying trends in the design of existing integrated systems.

An interactive procedure for multiple-objective analysis of linear and non-linear programs is presented. At the decision phase of the procedure, a sample of points, composed of the current point and a number of alternative proposals, is presented to the decision maker (DM). The sample is constructed to ensure a relatively easy evaluation of the sample by the DM. To this end an outranking relation is used as a local preference model in a neighbourhood of the current point. The outranking relation is used to define a sub-region of the non-dominated set the sample presented to the DM comes from. The DM has two possibilities, or degrees of freedom, to move from one sub-region to another which better fits his/her preferences. The first possibility consists in specifying a new reference point which is then projected onto the non-dominated set in order to find a better non-dominated point. The second possibility consists in shifting the current point to a selected point from the sub-region. In both cases, a new sub-region is defined around the updated current point. This technique can be compared to projecting a focused beam of light from a spotlight at the reference point onto the non-dominated set; the highlighted sub-region changes when either the reference point or the point of interest in the non-dominated set are changed.

In this paper we develop an interactive approach for solving the continuous solution space multiobjective decision making problem. We assume that the decision maker’s preferences can be approximately represented by an L_q distance function from an ideal point. In each iteration the decision maker compares a pair of alternatives. Based on the decision maker’s responses a distance function is estimated. We try to converge to a good solution by improving the estimate of the distance function in each iteration. We also discuss some variations of the approach.

The purpose of this paper is to investigate efficient solution schemes for a class of nonseparable optimization problems using multiobjective optimization as a separation strategy. The general conditions are provided for characterizing an optimal solution of a nonseparable problem from among the set of noninferior solutions of the corresponding multiobjective optimization problem. Multilevel solution schemes are discussed. Applications are presented in the areas of general multiple linear-quadratic control, network reliability optimization, and optimal maintenance policies for large-scale deteriorating water distribution systems.

We propose an interactive algorithm to solve multiple objective nonlinear programming problems. The algorithm is based on the reference direction approach. The decision maker has to specify aspiration level for each objective. A number of solutions are generated along the projection of the reference direction onto the efficient surface. Each solution is an (weak) efficient solution. The algorithm is illustrated with an example.

The theoretical model based on multisets is used to study the structure of multicriterial alternatives. The basic concepts of multiset theory is considered.The necessary and sufficient conditions of existing various metrics in a multiset space are suggested. Some of the metric properties are investigated. Ways to use new notions for cluster analysis of multicriterial alternatives are discussed.

We consider parametric linear vector semi-infinite optimization where the index set of the constraints is compact and the constraint functions are continuous. Some stability properties of the solutions are investigated. We prove lower and upper semi continuity of the restricted objective map over the closed balls. This gives a possibility to consider continuity properties in the case when in the image spase we consider the Kuratowski Painleve convergence. A property which characterizes well-posed problems is defined. Under some not too restrictive conditions over the index set we also obtain that this property is fulfilled in a dense subset of the solvability set.

The purpose of this paper is to present a new concept in and algorithm for multiobjective linear fractional programming (MOLFP). The new algorithm integrates the constraint (CON) and noninferior set estimation (NISE) methods, and is termed the CONNISE algorithm. The paper first discusses some issues of the MOLFP algorithms developed by Kornbluth and Steuer (1981) and by Nykowski and Zolkiewski (1985). Second, the mathematical form and iterating process of the CONNISE algorithm are elaborated on. Finally, a numerical example with two linear fractional objective functions is presented to demonstrate the new algorithm’s application. Suggestions for further research are also given.

The shortest path problem is to find the shortest distance between two specified nodes in a network. An arc is called a single most vital arc in the network, if its removal from the network results in the greatest increase in the shortest distance. The most vital arcs problems provide a means by which the importance of arc’s availability can be measured. In the traditional most vital arcs problems, the arc lengths are assumed to be crisp numbers. In this paper, we consider the case that the arc lengths are fuzzy numbers. We first show that the membership function of the shortest distance can be found by using a fuzzy linear programming approach. Based on this result, we give a theorem which may be used to reduce the effort required for finding the membership function of the shortest distance, when an arc is removed. Moreover, we may also reduce the number of candidates for the single most vital arc by using the theorem.

In this paper, to cope with the fuzzy environment where human subjective estimation is influential in the linear regression models, fuzzy linear regression models are introduced via the concepts of possibility and necessity. In fuzzy linear regression models, deviations between the observed values and the estimated values are assumed to be depending on the fuzziness of the parameters of the system. Given the fuzzy threshold for the three indices, three types of single-objective programming problems for obtaining fuzzy linear regression models, where input data is a vector of nonfuzzy numbers and output data is a fuzzy number, are formulated as natural extension of usual linear regression models. As an obvious advantage of these formulations, it is shown that all of the formulated problems can be reduced to linear programming ones. Moreover, by considering the conflict between the fuzzy threshold for the three indices and the fuzziness of the fuzzy linear regression model, the multiobjective programming problems for obtaining the fuzzy linear regression models are formulated, where both the fuzzy threshold and the fuzziness of the models are optimized corresponding to the three indices. Then on the basis of the linear programming method an interactive decision making method to derive the satisficing solution for the decision maker for the formulated multiobjective programming problems is developed. Finally, the proposed method is applied to the identification problem of the pork demand function to demonstrate its appropriateness and efficiency.

By considering the imprecise or fuzzy nature of human judgments, two types of fuzziness of human judgments should be incorporated in multiobjective optimization problems. One is the experts’ ambiguous understanding of the nature of the parameters in the problem-formulation process, the other is the fuzzy goals of the decision maker (DM) for each of the objective functions. This paper overviews interactive computer packages, developed by the author’s group based on our proposed interactive fuzzy linear programming methods which deals with both fuzzy goals and fuzzy parameters, in order to facilitate the interaction processes for not only multiobjective linear programming problems but also multiobjective linear programming problems with fuzzy parameters. Moreover, for demonstrating the feasibility and efficiency of the proposed methods as well as the corresponding computer programs, interaction processes for several numerical examples for multiobjective linear programming problems both without and with fuzzy parameters are shown under the hypothetical DM.

In this article, we generalize competence set analysis as an effective tool to model decision problems in an uncertain environment, especially in a fuzzy environment. We discuss the expansion of competence sets when only partially known.

The purpose of this paper is to analyze the potentials of parallel and distributed computing for the solution of mathematical optimization problems as an important task in decision support. First, an overview on existing parallel and distributed computing systems is given. It is followed by a presentation of nonsequential solution approaches in mathematical optimization. Finally, OpTiX-II, a decision support system for the parallel solution of nonlinear optimization problems is introduced and numerical results are presented.

This paper examines some basic concepts for fuzzy extension of multiobjective decision analysis with an implication of related intelligent decision support systems.

This paper explains the development of an expert system benificial assisting in flexible production system design. The expert system can simultaneously examine several kinds of objectives such as machine mechanism functions and machine tool purchasing problems after considering machine precision aspects. In order to decide the multi-objective problems in flexible production system design, the expert system possesses multi-objective evaluation reasoning which incorporates the two-stage reasoning process of elimination reasoning and the comparison of multiplicative utility function values by using knowledge data base. In the comparison certainty equivalents are reasoned by means of if-then rules and forward reasoning.

A new approach to linear programming based on a generalization of the simplex method where the two-dimensional simplex tableau is replaced by a three-dimensional tableau, was developed by the authors. This type of tool is shown to be particularly interesting for the development of an interactive multiple objective linear programming method. In contrast with the methods supported by the classical simplex method, which only permits displacements between faces of dimension zero (vertices), the new approach enables the displacements to be performed between faces of higher dimension.

Man-machine interaction is a fundamental component of multiple criteria decision aid (MCDA) tools, having in mind to amplify the decision makers’ capabilities of information processing and decision making and facilitate the processes of the system’s acceptability and learning. In designing Man-machine interfaces a balance must be obtained between the potentialities that are offered to the user and the ease of learning and use. In this paper we discuss the importance of Man-machine interfaces to contribute to make the interactive decision process more understandable and potentialize the development of new methods. The computational tools developed at Coimbra dedicated to provide decision support in multiattribute and multiobjective problems will be referred, emphasizing their Man-machine interfacing.

This paper presents a multiple reference point approach that enables oriented strategic search for non-dominated solutions of a multiobjective linear program.Conceptually it is based on the quasi-satisfying rational framework for decision developed by Lewandovski and Wierzbicki. An approach using several reference points that can change dynamically is being developed. This approach supports the DM learning about the non-dominated region to help him in the process of becoming aware of his objectives and of their attainability. Broadly speaking there is a well-defined non-dominated sub-region associated with the first tentative DM aspiration levels. The characterization of this sub-region enables the DM to choose one or more searching directions leading to other non-dominated sub-regions that are associated with other aspiration levels. This process may be continued by helping the DM to learn about the non-dominated region. Parallel processing techniques are used to keep in control all the aspiration levels (and their reference points).The parallel processing environment is a microcomputer equipped with a four transputer plug. The parallelism in transputer architecture systems is based on the sequential communicating process model. Each transputer can be seen as the physical implementation of a process. A short resume about the parallel environment and the results of several tests (carried out with a prototype), will be presented.

This paper concerns an interactive heuristic procedure to support the planning process in decentralized organizations with two hierarchical decision levels. The procedure allows for multiple goals at both decision levels and aims at solving the planning problem interactively in a very low number of information exchanges between the decision levels. Because the procedure contains some heuristic elements, a series of computer simulations with artificial decision makers was conducted to investigate its effect on organizational performance. The results are to provide some insights on the quality of the plan resulting from the procedure and the speed of convergence towards it.

We consider an extension of eigenvector analysis to the data represented by many-way matrices. The results obtained from a non-linear eigenvalue problem can be interpreted as principal components (PC) of the items in each direction of a multimode matrix. Such generalized PC can be used for clarifying the internal structural relationships between variables, visualization of multispace data, ranking objects, and other aims of multicriteria decision analysis.

In the last decade some large scale combinatorial optimization problems have been tackled by way of a stochastic technique called ‘simulated annealing’ first proposed by Kirkpatrick et al. (1983). This technique has proved to be a valid tool to find acceptable solutions for problems whose size makes impossible any exact solution method.

Nature does not consciously optimize. Rather, classical minimum principles serve to select from among all possible events that one event or sequence of events which is actually observed in nature. Here, we show, by way of example, that some principles may be recast as multicriteria minimal principles, and we offer a concept of biological growth based on a postulated minimal principle whose outcome we have termed natural structural shapes.

A new method which presents the overall structure of efficient criterion vectors (N hereafter) for large scale MOLP is introduced. The proposed algorithm ASEOV (Approximation of the Set of Efficient Objective Vectors) insures full coverage of N, with corresponding coverage precision indicated. The DM can guide the determination procedure by assessing the coverage allowance on each criterion. Combined with proper interactive methods, this insight over N obtained through ASEOV can help a DM in assessing his preference and reduce his burden in deriving the final best compromise solution. An illustrative example is presented.

A multiple criteria DSS MC-VISA (Multiple Criteria Visual Interactive System utilizing Approximation) is introduced. MC-VISA is composed of four subsystems: 1) Model manager helps a DM to build, save, retrieve, and edit MOLP models; 2) ASEOV presents the stepwise focused structure of efficient criterion vectors and generates candidate goals for new search directions; 3) VIM displays the efficient trajectories along the search direction and acquires the DM’s preference; and 4) Mediator interfaces the three components and guides a DM through the decision making process. Menus and interactive uses of computer graphics allow a DM much flexibility over problem solving with MC-VISA. MC-VISA is designed in Turbo-Pascal on a personal computer. An illustrative problem solving with MC-VISA is provided.

The purpose of a Negotiation Support System (NSS) is to help negotiators reach consensus quickly with terms that are favorable to all. A NSS promotes information exchange and facilitates the use of group decision and negotiation methods. This paper proposes a hybrid design approach that combines multi-attribute utility theory with data induction methods such as case-based reasoning and neural network techniques. The approach is illustrated by the implementation of NEGOTIATOR — a bilateral, multiple-issue NSS.

We assume that a group of experts can provide their evaluations in the form of fuzzy intervals for the project selection under incomplete information and knowledge. Using pessimistic aggregation scheme, we propose a fuzzy multiple criteria mathematical programming model and a fuzzy multiattribute project selection model. We develop an interactive algorithm to solve the latter model.

Operational Research has contributed in a number of ways to production scheduling; the development of algorithms to identify optimal solutions to simple problems; the development of heuristics to quickly find good solutions to complex problems; and the use of visual interactive modelling to provide a flexible and easy to use tool for production schedulers.These contributions have had significant practical impact. However, some difficulties remain and one of these is related to the multiple criteria nature of the problem. Commonly used heuristics tend to be based on a single criterion rule, a very simple example being “Schedule the job with shortest processing time first”. The heuristic may produce a schedule which performs well against one objective, for example, to minimise the number of jobs late, but does not meet the scheduler’s requirements against other criteria, for example, minimising stock, or controlling maximum lateness. However, although the scheduler can easily identify shortcomings of a schedule with the support of appropriate software, he or she may be unable to identify what changes to make to improve the situation.The aim of our research is, through the development of a multiple criteria scheduling heuristic, to provide the scheduler with a control mechanism. This will allow him or her to indicate how they would like the solution to change and by appropriately adjusting the heuristic produce a new schedule which moves towards the specified objectives.As a first step we have been working with a simple multiple criteria heuristic, implemented as a visual interactive decision support system, to investigate the feasibility of such a control mechanism. In this paper we will demonstrate this system and report on the results of some initial experimental work. The next stage of the research will depend on the results of this experimental work; if the multiple criteria heuristic used yields the desired results we can move towards implementing the control mechanism, for which we will explore the use of expert systems and neural networks; if the simple heuristic proves to be ineffective we will have to investigate a more complex approach. We will report on progress at the Conference.

A double model based on fuzzy synthetic decision and approximation reasoning is presented for the evaluation of transit operations performance. A heuristic algorithm for evaluating Taipei transit system performance is developed and domonstrated in a case study. In the end, we will compare the traditional approach with our model.

In this study we consider the bicriteria problem of minimizing total flowtime and maximum tardiness penalties for a given set of jobs on a single machine. We discuss some properties of the efficient solutions and develop an algorithm that generates all efficient schedules in polynomial time.

Several kinds of techniques for multiple criteria decision making have been developed for the last few decades. Above all, the aspiration level approach to multi- objective programming problems and AHP are widely recognized to be effective in many practical fields.The author has been trying to apply the satisficing trade-off method, which is one of the aspiration level approaches, to several kinds of practical problems, Some of them were already performed in real life. In this paper, recent results in feed formation in stock farms and erection management of cable stayed bridges will be reported. In addition, a new application of AHP to multi-objective route search in car navigation systems will also be reported.

Abstract: To help protect the Rhine delta from North Sea floods, the Dutch installed sluices at Haringvliet in the late 1960s and converted the Haiingvliet-Hollandsch Diep-Biesbosch (HHB) estuary into a tidally-damped, fresh-water system. Two decades later, the Dutch Rijkswaterstaat commissioned a study of alternative policies for managing the sluices and removing contaminated bottom sediments, including policies which would at least partially restore estuarine conditions to the HHB. This paper describes the public policy analysis comprising that study, focussing on the role and successful application of formal multicriteria analysis (MCA), in particular the Analytic Hierarchy Process.

This paper is concerned with a traditional asset allocation of the Markowitz type and develops an efficient algorithm to design an index fund which is a compromise solution to the bicriteria optimization problem. A numerical example is provided to illustrate our algorithm.