This paper deals with multiobjective programming in which the objective functions are nonsymmetric distances (derived from different gauges) to the points of a fixed finite subset of ?n. It emphasizes the case in whic...
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This paper deals with multiobjective programming in which the objective functions are nonsymmetric distances (derived from different gauges) to the points of a fixed finite subset of ?n. It emphasizes the case in which the gauges are polyhedral. In this framework the following result is known: if the gauges are polyhedral, then each Pareto optimum is the solution to a Fermat—Weber problem with strictly positive coefficients. We give a new proof of this result, and we show that it is useful in finding the whole set of efficient points of a location problem with polyhedral gauges. Also, we characterize polyhedral gauges in terms of a property of their subdifferential.
This study addresses a fundamental difficulty in designing cellular manufacturing (CM) systems, the cell formation problem. This problem has its strategic importance in that it affects the fundamental structure and ov...
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This study addresses a fundamental difficulty in designing cellular manufacturing (CM) systems, the cell formation problem. This problem has its strategic importance in that it affects the fundamental structure and overall layout of a CM system. A heuristic model is developed which assigns parts and machines to manufacturing cells while taking into account machine capacities, product routings, relevant costs, and several objectives of production systems. A full factorial experimental design is used to evaluate the effects of environmental factors on the performance of the heuristic model. Large cell formation problems are solved with the heuristic model to further characterize the model with respect to solution characteristics and computer run time.
Organization are frequently required to make decisions about multiobjective problems. The complexity of such decision processes increases drastically when the participation of multiple decision makers becomes necessar...
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Organization are frequently required to make decisions about multiobjective problems. The complexity of such decision processes increases drastically when the participation of multiple decision makers becomes necessary. This is primarily due to the unique preference structures of the participants whose individual judgements of the 'best compromise solution' may not coincide. Nominal and/or interacting groups have been found to improve the decision-making effectiveness and efficiency associated with such multiple objective, multiple decision-maker problems. This study reports the results of a laboratory experiment involving the use of an interactive multiobjective group decision aid. The effect of two independent variables on a set of performance measures is investigated. The first independent variable is the presence or absence of a formal preference aggregation procedure in a group decision aid. The strength of decision-maker's linear programming background is the second independent variable. The dependent variables are solution quality, speed of convergence to a final agreement, and user confidence in the best compromise solution. Analysis and implications of the experimental results are provided and future research work is outlined.
At the Naval Military Personnel Command (NMPC), multiple objectives must be considered in assigning personnel to billets. For the assignment of Naval officers, these objectives in decreasing order of importance are to...
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At the Naval Military Personnel Command (NMPC), multiple objectives must be considered in assigning personnel to billets. For the assignment of Naval officers, these objectives in decreasing order of importance are to satisfy the needs of the Navy, to enhance the careers of officers, to fulfill the desires of officers, and to minimize cost. To assist in this complicated task, a procedure which considers these four objectives in their order of importance is proposed. Each time, a standard assignment problem is solved by optimizing one objective with the additional constraint that values of the other more important objectives remain above specified levels. A modification of a multiobjective programming technique, the Noninferior Set Estimation method, is used to guarantee integer solutions to an assignment problem with these additional constraints. An application of the procedure to an actual Navy officer assignment problem indicates its potential as a decision aid to NMPC officers and other decision makers.
The purpose of this paper is to present some results about the convergence of interactive reference point methods in multiobjective programming. In particular, we describe how dual information may guide the decision m...
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The purpose of this paper is to present some results about the convergence of interactive reference point methods in multiobjective programming. In particular, we describe how dual information may guide the decision maker in his choice of the successive reference points. In the literature different convergence models have been proposed. The analyst may induce convergence by selecting appropriate rules of the communication. Or he may rely on the learning process of the decision maker to induce some kind of ‘psychological’ convergence. In neither case are the activities of the decision maker precisely described. Consequently, the quality of the final decision cannot be established, and the question of convergence remains an unsolved issue. We describe different ways in which the decision maker may select his successive reference points, and we discuss the convergence of the resulting reference point procedures. Also, we comment on the relevance of these different assumptions about the decision maker's behavior. The procedures are illustrated by a small numerical example. [ABSTRACT FROM AUTHOR]
We define the multiobjective Quadratic Assignment Problem. Because of the difficulties of the weighted objectives method we develop local algorithms which are based in the methodologies of efficient, lexicographic and...
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Using a theorem of Tijs, we derive results about approximate solutions for Nash equilibrium theory and for multiobjective problems. We describe conditions under which one can replace an infinite strategy set, an infin...
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Using a theorem of Tijs, we derive results about approximate solutions for Nash equilibrium theory and for multiobjective problems. We describe conditions under which one can replace an infinite strategy set, an infinite alternative set, or an infinite set of criteria by a finite subset without losing all approximate solutions of the problem under consideration.
In this paper we investigate two generalizations of the Pareto minimality concept: infimality and approximate minimality. It is shown that existence conditions for these optimality notions are much weaker and that the...
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In this paper we investigate two generalizations of the Pareto minimality concept: infimality and approximate minimality. It is shown that existence conditions for these optimality notions are much weaker and that they allow a more complete characterization via linear and nonlinear scalarization than Pareto minimality. We further study some relations between those optimality structures and apply the results to the image of a vector-valued mapping.
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