In the paper a definition of the optimal solution of the transportation problem with fuzzy cost coefficients as well as an algorithm determining this solution are proposed.
In the paper a definition of the optimal solution of the transportation problem with fuzzy cost coefficients as well as an algorithm determining this solution are proposed.
We study a multiobjective problem with a feasible set defined by equality and inequality constraints. Then, by using the concept of K-directional derivative, we prove general optimality conditions as well as results c...
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We study a multiobjective problem with a feasible set defined by equality and inequality constraints. Then, by using the concept of K-directional derivative, we prove general optimality conditions as well as results concerning duality theorems.
This paper is devoted to presenting optimality conditions for the sufficiency of the maximum principle for multiobjective optimal control problems with nonsmooth data. Such conditions are the most general as possible ...
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This paper is devoted to presenting optimality conditions for the sufficiency of the maximum principle for multiobjective optimal control problems with nonsmooth data. Such conditions are the most general as possible in the sense that problems in which the set of necessary conditions from the maximum principle are also sufficient, necessarily obey them. A variation of such conditions is also presented, under which the set of optimal solutions of the multiobjective problem can be determined by resolving a related scalar weighting problem.
It is well known that, if a control is Pareto optimal for a multiobjective optimal control problem, then it satisfies the necessary conditions of an optimal control problem with isoperimetric constraints. We introduce...
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It is well known that, if a control is Pareto optimal for a multiobjective optimal control problem, then it satisfies the necessary conditions of an optimal control problem with isoperimetric constraints. We introduce a set of sufficient conditions reversing that implication. Thus, we study some properties of the isoperimetric problems and their applications to the analysis of economic models.
Relief activities are complicated when multiple disasters take place simultaneously at different locations. Designing effective relief networks for these instances involves managing the priorities among regions and pr...
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Relief activities are complicated when multiple disasters take place simultaneously at different locations. Designing effective relief networks for these instances involves managing the priorities among regions and products, developing the capacity to share limited resources and facilities, and engaging with multiple suppliers over several periods. Unfortunately, even after recent experiences in different countries, the management of simultaneous disasters is still understudied. This article introduces a two-stage dynamic formulation for logistics decisions in instances caused by simultaneous disasters. It guides supplier selection, facility location, stock prepositioning, and resource allocation at the first stage, whereas relief distribution, postdisaster procurement, and inventory management are addressed at the second stage. The model minimizes cost and the maximum shortage. Results of numerical experiments show the way the model considers the characteristics of each situation to dispatch limited shared resources. The experiments show that planning for single disasters has a negative impact on performance when faced with situations caused by simultaneous disasters. That is confirmed by findings from the case study in Mexico, which also highlights the preference for prepositioning stock using a mix of different kind of suppliers, and the importance of developing a reliable network of facilities and suppliers to handle simultaneous disasters effectively.
In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either possibilistic programming or multiobjective programming methods. Unfortunately, a...
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In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either possibilistic programming or multiobjective programming methods. Unfortunately, all these methods have shortcomings. In this note, using the concept of comparison of fuzzy numbers, we introduce a very effective method for solving these problems. Then we propose a new method for solving linear programming problems with fuzzy variables. (C) 2000 Elsevier Science B.V. All rights reserved.
The paper presents a dynamic, discrete optimization model with returns in ordered structures. It generalizes multiobjective methods used in vector optimization in two ways: from real vector spaces to ordered structure...
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The paper presents a dynamic, discrete optimization model with returns in ordered structures. It generalizes multiobjective methods used in vector optimization in two ways: from real vector spaces to ordered structures and from the static model to the dynamic model. The proposed methods are based on isotone homomorphisms. These methods can be applied in dynamic programming with returns in ordered structures. The provided numerical example shows an application of fuzzy numbers and random variables with stochastic dominance in dynamic programming. The paper also proposes applications in the following problems: a problem of allocations in the market model, a location problem, a railway routing problem, and a single-machine scheduling problem. (C) 2010 Elsevier B.V. All rights reserved.
Despite the mathematical properties and algorithmic features of an interactive method, that method's success usually lies in the kind of information it requires from the decision maker. In some cases, this informa...
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Despite the mathematical properties and algorithmic features of an interactive method, that method's success usually lies in the kind of information it requires from the decision maker. In some cases, this information constrains the decision maker. If she does not find it easy and comfortable to answer the questions posed by the algorithm, then she will very likely give inconsistent answers, and the method will fail to find her most preferred solution. Therefore, it is of interest to find relations among the different kinds of information (local weights, local trade-offs, reference points, etc.) to allow the decision maker to choose what kind of questions he wants to answer, and to provide him with enough information to give such answers. In this paper, we define equivalent information-that is, different kinds of information-that produces the same solution when used in their corresponding interactive schemes.
In this paper, we establish necessary and sufficient conditions to characterize weakly efficient solutions in nonsmooth quasiconvex multiobjective programming. The results are proved in terms of the Greenberg-Pierskal...
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In this paper, we establish necessary and sufficient conditions to characterize weakly efficient solutions in nonsmooth quasiconvex multiobjective programming. The results are proved in terms of the Greenberg-Pierskalla, Penot, Plastria, Gutierrez and Suzuki-Kuroiwa subdifferentials. The established results can be used to provide powerful tools for sketching numerical algorithms and deriving duality results.
As a special field of mathematical programming, fuzzy chance constrained programming is now emerging as a promising area of study from the view point of its ability to capture fuzziness and randomness simultaneously. ...
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As a special field of mathematical programming, fuzzy chance constrained programming is now emerging as a promising area of study from the view point of its ability to capture fuzziness and randomness simultaneously. In this paper a fuzzy goal programming method has been presented for solving multiobjective chance constrained programming problems in which the right sided parameters associated with the system constraints are uniformly distributed fuzzy random variables. In the proposed approach the fuzzy chance constrained programming problem is converted first into its equivalent fuzzy programming form by using the concept of alpha-cuts. Then the problem is decomposed on the basis of tolerance ranges of fuzzy parameters associated with the system constraints. Next by setting imprecise aspiration level to each of the individual objectives, the membership function is defined to measure the degree of achievements of goal levels of the objectives. Afterwards a fuzzy goal programming model is developed to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing the group regrets consisting of under deviational variables of the fuzzy goals in the decision making context. To explore the potentiality of the proposed approach, an illustrative example is solved and the solution is compared with other technique.
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