Multi-objective Decision-making Problem Research Articles

Two-level Decision Problems and their New Solution Methods by a Penalty Method

This paper discusses theory and algorithms for two-level decision problems such as Stackelberg, Min-Max, General Resource Allocation, Optimization-Satisfaction, and Multi-Objective Decision Problems, all of which are characterized by plural objectives and a parametric approach. These decision problems are represented by a hierarchical optimization, where a part of constraints in the upper-level problem consists of constrained parametric optimization ones in the lower level. New computational methods are proposed based on the theory of penalty function method

Preference Conditions for Multiattribute Value Functions

This paper examines conditions on preferences that simplify the assessment of multiattribute value functions for use in the analysis of multiobjective decision problems. It is shown that when these conditions hold the value function must have a simple analytic form. A procedure is presented for testing whether the conditions hold and determining the value function when the conditions are found to be valid.

An integrated approach for improving decisionmaking processes

This article deals with decision making at the organization level, but it is perhaps applicable to all other levels. Decision-making processes generally have multiple purposes and are made with uncertainty. The objectives are usually noncommensurate and in conflict with one another. The processes involve two phases: analytical and judgmental. For the analytical phase, mathematical optimization methods such as mathematical programming are efficiently applied. The nesting method of Lagrangian multipliers is one device intended to bridge the gap between both phases of decision-making processes. The System and Decision Science Area of the International Institute for Applied Systems Analysis has been very involved with multiobjective decision problems. This study is one of several works on methodological development for a multicriteria decision-making process.

On "A Programming Model of Consumer Choice Among Multiattributed Brands"

Finding an overall ranking of a group of products from rankings over multiple salient attributes is a problem of considerable interest. Assume an individual is faced with ranking m products or choice items. Assume the individual has n attributes, which s/he is using to describe the products, and has, for each attribute, an ordinal preference function ranking the choice items over that attribute. In other words, s/he has n rankings, each corresponding to an attribute. The problem of overall ranking involves combining these n rankings in some rational manner to form an overall preference ranking. This problem is analogous to a multi-objective decision problem in which the attributes constitute the objectives and the choice items are the alternatives. The problem is also analogous to the selection of a social welfare function from individual welfare functions. In this case, the attributes would correspond to the individuals in the society, and the choice items would correspond to the various possible economic bundles. A considerable body of literature has been written on these problems (see Arrow 1951; Luce and Raiffa 1957). Of particular interest are some of the concepts concerning criteria for rationally combining the attribute rankings to form the overall ranking. The first concept of interest is Pareto optimality. Assume A and B are two choice items, and that B is ranked above A by every attribute. Pareto optimality requires that B be ranked above A in the overall ranking. The second concept is that of positive association between the individual orderings and the overall ordering. All else being equal, this requires that if Item A improves with respect to Item B on one attribute's ranking, then A's ranking with respect to B in the overall ranking will not decrease. In a sense, this requirement ensures that the overall ranking is determined by the individual rankings. The final concept of interest is indifference to irrevelant alternatives. Assume we have a set of choice items and a group of attribute preference orderings, and that this leads to an overall ranking in which A > B. Assume we add an additional choice item, and that the attribute rankings are only modified by the insertion of this new item at its appropriate place in the individual rankings. Then the criteria of indifference to irrelevant alternatives implies that A will still be higher than B in the new overall ranking.

Necessary and sufficient conditions for local and global nondominated solutions in decision problems with multi-objectives

In this paper, the decision problem with multi-objectives is considered, and the nondominated solutions associated with a polyhedral domination cone are discussed. The necessary and sufficient conditions for the solutions are given in the decision space rather than the objective space. The similarity of the solution conditions obtained in this article to the Kuhn-Tucker condition of a convex programming problem is examined. As an application of the solution condition, an algorithm to locate the set of all nondominated solutions is shown for the linear multi-objective decision problem.

Kuhn-Tucker multipliers as trade-offs in multiobjective decision-making analysis

Useful relationships between the optimal Kuhn-Tucker multipliers and trade-offs in the multiobjective decision-making problems are developed based on the sensitivity interpretation of such multipliers. Practical and theoretical applications of these results are discussed. The results provide a convenient way for obtaining necessary (trade-off) information for continuing into the analyst-decision-maker interactive phase of the multiobjective decision-making process. This paper further extends the theoretical basis of the Surrogate Worth Trade-off (SWT) Method; a multiobjective optimization method which first appeared in the scientific literature in 1974.

Financial Planning with Multiple Objectives

* In recent years, there has been much interest in models of multiobjective decision-making. The finance literature reflects this with the formulation of problems in capital budgeting [6, 8, 13], working capital management [10], portfolio selection [7, ch. 9], and commercial bank management [2, 4, 5, 9, 11] as multiobjective decision-making problems. Given multiple conflicting objectives, resolution of any planning problem depends on subjective judgments and relative preferences of decision-makers. Unfortunately, how to include managerial preferences in normative decision models, and the effect of these preferences on optimal solutions, has scarcely been explored. Moreover, there has been little if any research on the relative merits of various programming techniques in dealing with multiobjective problems. The purposes of this paper are to discuss introducing the subjective preferences of decisionmakers into multiobjective programming models and to compare the characteristics of goal programming and multiobjective linear programming in dealing with multiobjective problems. Multiobjective Problems and Programming Techniques

Multiple objective decision-making using fuzzy sets

One of the most useful aspects of fuzzy set theory is its ability to represent multio-bjective decision problems involving vague or fuzzy objectives. This paper presents a model for solving multi-objective decision problems when the objectives are of varying degrees of importance. This is done by assigning to each objective a power indicative of its importance and then raising each fuzzy set to its appropriate power. These powers are obtained by getting the eigenvector of the maximum eigenvalue of a matrix of paired comparisons of the objectives.

Principles of controlling traffic noise: Solving a multi-objective decision problem

The main objectives for a government to control traffic noise are such as economic efficiency, a reasonable welfare distribution and acceptable noise standards. The instruments available for arriving at these objectives are traffic control, emission regulation and environment protection. This paper analyzes how to make trade-offs between such objectives and how to choose a combination of noise control instruments. Special attention is then made to one welfare distribution objective, namely the ‘polluters-pay-principle’. That principle demands using the vehicle tax to finance investments to protect environment. And in order to stimulate the development of less noisy vehicles such a tax has to be progressively increased for noisy cars. The analysis is demonstrated on the situation of Sweden where a differentiation of norms as well as of vehicle taxes is proposed.

Principles of controlling traffic noise Solving a multi-objective decision problem

The main objectives for a government to control traffic noise are such as economic efficiency, a reasonable welfare distribution and acceptable noise standards. The instruments available for arriving at these objectives are traffic control, emission regulation and environment protection. This paper analyzes how to make trade-offs between such objectives and how to choose a combination of noise control instruments. Special attention is then made to one welfare distribution objective, namely the ‘polluters-pay-principle’. That principle demands using the vehicle tax to finance investments to protect environment. And in order to stimulate the development of less noisy vehicles such a tax has to be progressively increased for noisy cars. The analysis is demonstrated on the situation of Sweden where a differentiation of norms as well as of vehicle taxes is proposed.