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Interactive multiobjective optimization approach to the input-output design of opening new branches

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第2期220卷 530-538页

作者： Park, K. Sam Shin, Dong Eun Korea Univ Sch Business Seoul 136701 South Korea

We demonstrate a real-world application of the interactive multiple objective optimization (MOO) approach to the simultaneous setting of input and output amounts for the opening of new branches. As illustrated by the case example, all the branches of a fast-food company employ multiple inputs to generate multiple outputs. The company launches several new branches each year and, therefore, needs to plan the quantities of inputs and outputs to be used and produced before their operations. Such input-output settings are a vital practical problem that arises whenever a new branch is opened in a host of different industries. In this paper, we show in detail the entire process of the application from modeling the case problem to generating its solution. In the modeling stage, a data envelopment analysis model and a statistical method are subsequently utilized to form a nonlinear MOO problem for the input-output settings. To solve this problem, we then develop and apply an interactive MOO method, which combines the two earlier interactive methods (Geoffrion et al., 1972;Zionts and Wallenius, 1976), while compensating for their drawbacks and capturing their positive aspects. (C) 2012 Elsevier B.V. All rights reserved.

关键词： multiobjective programming Interactive approach Nonlinear programming Data envelopment analysis Input-output design New branches

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multiobjective second-order mixed symmetric duality with a square root term

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APPLIED MATHEMATICS AND COMPUTATION 2012年第14期218卷 7602-7613页

作者： Gupta, S. K. Kailey, N. Indian Inst Technol Patna Dept Math Patna 800013 Bihar India Thapar Univ Sch Math & Comp Applicat Patiala 147004 Punjab India

In this paper, we have formulated a second-order mixed symmetric dual programs for a class of nondifferentiable multiobjective programming problem. Weak, strong and converse duality theorems are then proved for the aforementioned pair using the notion of second-order F-convexity/pseudoconvexity assumptions. Further, special cases are discussed to show that this paper extends some known results of the literature. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Mixed second-order symmetric duality multiobjective programming Second-order F-convexity Efficient solution

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An Interactive Satisficing Method for multiobjective Random Fuzzy programming Problems through the Possibility-Based Probability Model

An Interactive Satisficing Method for Multiobjective Random ...

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IEEE International Conference on Fuzzy Systems (FUZZ 2011)

作者： Katagiri, Hideki Sakawa, Masatoshi Matsui, Takeshi Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

ISBN: (纸本)9781424473175

This paper considers multiobjective linear programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. A new decision making model is proposed in order to maximize both of possibility and probability with respect to the objective function values. An interactive algorithm is constructed to obtain a satisficing solution for a decision maker from among a set of Pareto optimal solutions.

关键词： random fuzzy variable multiobjective programming interactive algorithm possibility measure probability maximization

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Sensitivity Analysis in Differential programming through the Clarke Derivative

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MEDITERRANEAN JOURNAL OF MATHEMATICS 2012年第3期9卷 537-550页

作者： Jimenez Guerra, Pedro Melguizo Padial, Miguel Angel UNED Dept Matemat Fundamentales Fac Ciencias Madrid 28040 Spain Univ Alicante Dept Matemat Aplicada Alicante 03690 Spain

In this paper we deal with the sensitivity analysis in multiobjective differential programs with equality constraints. More specifically, we focused on analyzing the quantitative behavior of a certain set (non necessarily singleton) of optima according to changes of the right-hand side parameters. We prove that the sensitivity of the program is measured by a Lagrange multiplier plus a projection of its derivative. The sensitivity analysis is accomplished by utilizing the Clarke derivative, which transmits its characteristic stability to the obtained result.

关键词： Differential programming multiobjective programming set-valued map tangential regularity Clarke derivative

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Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization

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ANNALS OF OPERATIONS RESEARCH 2012年第1期197卷 47-70页

作者： Ruiz, Francisco Luque, Mariano Miettinen, Kaisa Univ Jyvaskyla Dept Math Informat Technol Jyvaskyla 40014 Finland Univ Malaga E-29071 Malaga Spain

In this paper, we present a new general formulation for multiobjective optimization that can accommodate several interactive methods of different types (regarding various types of preference information required from the decision maker). This formulation provides a comfortable implementation framework for a general interactive system and allows the decision maker to conveniently apply several interactive methods in one solution process. In other words, the decision maker can at each iteration of the solution process choose how to give preference information to direct the interactive solution process, and the formulation enables changing the type of preferences, that is, the method used, whenever desired. The first general formulation, GLIDE, included eight interactive methods utilizing four types of preferences. Here we present an improved version where we pay special attention to the computational efficiency (especially significant for large and complex problems), by eliminating some constraints and parameters of the original formulation. To be more specific, we propose two new formulations, depending on whether the multiobjective optimization problem to be considered is differentiable or not. Some computational tests are reported showing improvements in all cases. The generality of the new improved formulations is supported by the fact that they can accommodate six interactive methods more, that is, a total of fourteen interactive methods, just by adjusting parameter values.

关键词： multiobjective programming Multiple objectives Interactive methods Reference point methods Classification Marginal rates of substitution Global system Pareto optimality

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Duality for nondifferentiable multiobjective higher-order symmetric programs over cones involving generalized (F, α, ρ, d)-convexity

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2012年第1期2012卷 1-16页

作者： Gupta, S. K. Kailey, N. Kumar, Sumit Indian Inst Technol Dept Math Patna 800013 Bihar India Gulzar Inst Engn & Technol Dept Appl Sci Khanna 141401 India Indian Inst Management Udaipur 313001 India

In this paper, a pair of Wolfe type higher-order symmetric nondifferentiable multiobjective programs over arbitrary cones is formulated and appropriate duality relations are then established under higher-order-K-(F, alpha, rho, d)-convexity assumptions. A numerical example which is higher-order K-(F, alpha, rho, d)-convex but not higher-order K-F-convex has also been illustrated. Special cases are also discussed to show that this paper extends some of the known works that have appeared in the literature. MSC: 90C29;90C30;49N15

关键词： higher-order symmetric duality support function multiobjective programming cones efficient solutions

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Interactive multiobjective Random Fuzzy programming Problems through the Possibility-Based Fractile Model

Interactive Multiobjective Random Fuzzy Programming Problems...

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IEEE International Conference on Systems, Man and Cybernetics (SMC)

作者： Katagiri, Hideki Sakawa, Masatoshi Matsui, Takeshi Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

ISBN: (纸本)9781457706530

This paper considers multiobjective linear programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. A new decision making model is proposed by incorporating the concept of fractile optimization into a possibilistic programming model in order to maximize both of possibility and probability with respect to the objective function values. An interactive algorithm is constructed to obtain a satisficing solution for a decision maker from among a set of Pareto optimal solutions.

关键词： random fuzzy variable multiobjective programming interactive algorithm possibility measure fractile criterion optimization

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SATISFICING SOLUTIONS FOR multiobjective STOCHASTIC LINEAR programming PROBLEMS

SATISFICING SOLUTIONS FOR MULTIOBJECTIVE STOCHASTIC LINEAR P...

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作者： SEGUN ADEYEMI ADEYEFA University of South Africa

学位级别：博士

multiobjective Stochastic Linear programming is a relevant topic. As a matter of fact, many real life problems ranging from portfolio selection to water resource management may be cast into this framework. There are severe limitations in objectivity in this field due to the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice does not hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this thesis, we resort to the bounded rationality and chance-constrained principles to define satisficing solutions for multiobjective Stochastic Linear programming problems. These solutions are then characterized for the cases of normal, exponential, chi-squared and gamma distributions. Ways for singling out such solutions are discussed and numerical examples provided for the sake of illustration. Extension to the case of fuzzy random coefficients is also carried out.

关键词： Satisficing solution chance constrained Linear programming multiobjective programming stochastic programming expected value optimality/efficiency variance optimality/efficiency expected value and standard deviation optimality/efficiency minimum ri

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Optimality and duality in nondifferentiable multiobjective mathematical programming involving higher order (F, alpha, rho, d)-type I functions

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2008年第1-2期27卷 345-364页

作者： Gulati, T. R. Agarwal, Divya Indian Inst Technol Dept Math Roorkee 247667 Uttar Pradesh India Inst Technol & Management Dept Applies Sci & Human Sector 23-A Gurgaon India

In this paper, a nondifferentiable multiobjective programming problem is considered where every component of objective and constraint functions contain a term involving the support function of a compact convex set. A new class of higher order (F, alpha, rho, d)-type I function is introduced. Necessary optimality conditions and the duality theorems for Wolfe and unified higher order dual problems are established. Several known results can be deduced as special cases.

关键词： multiobjective programming (F, alpha, rho, d)-type I function Efficiency Higher order duality Support function

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Designing content distribution networks for optimal cost and performance

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INFORMATION TECHNOLOGY & MANAGEMENT 2012年第1期13卷 1-15页

作者： Deane, Jason K. Rakes, Terry R. Agarwal, Anurag Univ S Florida Dept Informat Syst & Decis Sci Coll Business Adm Sarasota FL 34243 USA Virginia Tech Dept Business Informat Technol Pamplin Coll Business Blacksburg VA 24061 USA

One strategy for alleviating excess latency (delay) in the Internet is the caching of web content at multiple locations. This reduces the number of hops necessary to reach the desired content. This strategy is used for web content such as html pages, images, streaming video, and Internet radio. The network of servers which store this content, and the collections of objects stored on each server, is called a content distribution network (CDN). In order to optimally design a CDN, given a network topology with available server storage capacity at various points in the network, one must decide which object collections to place on each server in order to achieve performance or cost objectives. The placements must be within the storage limits of the servers and must reflect the request patterns for each collection of objects to be cached. Researchers have suggested formulations for the CDN problem which address performance by minimizing latency (the average number of hops is a commonly accepted measure of latency) from client to content, or formulations that focus on minimizing cost of storage and/or bandwidth. In this research, we develop a model which allows for the simultaneous treatment of performance and cost, present examples to illustrate the application of the model and perform a detailed designed experiment to gain insights into cost/hops tradeoff for a variety of network parameters.

关键词： Content distribution networks multiobjective programming Integer programming Fuzzy sets

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