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On the application of uncertainty models in copying machine maintenance

INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE AND ENGINEERING MANAGEMENT 2012年第2期7卷 148-152页

作者： Abass, Samir A. Elsayed, Marwa Sh. Atom Energy Author Cairo Egypt Inst Culture & Sci Cairo 13759 Egypt

A maintenance system is necessary to maintain an efficient production system and reduce the possibility of work being suspended due to machine breakdown. For every manufacturing company the objective is to produce goods at a profit and this is only achieved using an effective maintenance system. Maintenance is required for all types of machinery. The copying machine is one of the most important inventions of the 20th century. In this paper, the maintenance of copying machines is focused on. For this purpose, a multi-objective nonlinear programming model with uncertainty is introduced. Data in many real life engineering and economic problems suffers from inexactness. And uncertainty also exists. In order to deal with uncertain optimization problems, fuzzy and stochastic approaches are commonly used to describe these imprecise characteristics. Here three different approaches to uncertainty are compare;the fuzzy programming approach, the interval number programming approach and the stochastic programming approach. A numerical example is introduced to clarify the proposed method.

关键词： maintenance copying machine multiobjective nonlinear programming fuzzy programming stochastic programming interval number programming

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An optimum multivariate-multiobjective stratified sampling design

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METRON-INTERNATIONAL JOURNAL OF STATISTICS 2011年第3期69卷 227-250页

作者： Ansari, Athar Varshney, Rahul Najmussehar Ahsan, Mohammad Kejriwal Inst Management & Dev Studies Ranchi Bihar India Aligarh Muslim Univ Dept Stat & Operat Res Aligarh Uttar Pradesh India

It is well known that in stratified sampling design when the measurement cost does not vary from stratum to stratum, an estimate of population mean or total constructed from a sample selected according to Neyman allocation is the most precise estimate. But unfortunately the practical use of Neyman allocation suffers from a number of limitations. The most serious of all is the absence of the true values of the stratum standard deviations. When the strata standard deviations are unknown but we have additional information about the equality of standard deviations between some of the strata, we can use this information to increase the precision of the estimate by pooling the strata with equal standard deviations as a single stratum and using Neyman and proportional allocations together. This paper studies the case of multiple pooling of the standard deviations in a multivariate stratified sampling when the number of strata is more than three. The problem is formulated as a multiobjective nonlinear programming Problem. A solution procedure is developed using Goal programming approach. For computation purpose, the software LINGO is used.

关键词： Multivariate stratified sampling Compromise allocation Pooled standard deviations Multiple pooling multiobjective nonlinear programming Goal programming

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Interactive stability of multiobjective integer nonlinear programming problems

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期176卷 230-236页

作者： ElShafel, Mervat Mohamed Kamel Helwan Univ Fac Sci Dept Math Cairo Egypt

In this paper we present a solution method for fuzzy multiobjective integer nonlinear programming (FMOINLP) problems and the stability of this solution. An interactive stability compromise programming method for solving (FMOINLP) problems by using the compromise weights from the pay-off table of membership function for each objective function is presented. (c) 2005 Elsevier Inc. All rights reserved.

关键词： integer programming multiobjective nonlinear programming fuzzy parameters fuzzy number membership functions branch-and bound method stability set of the first kind interactive decision making parametric programming interactive decision making compromise weights interactive compromise programming

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Stability of vector optimization problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints

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INFORMATION SCIENCES 2008年第6期178卷 1663-1679页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Dept Math Tanta Egypt

The aim of this paper is to investigate the stability of multiobjective nonlinear programming problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints and represent, in addition, the related dual problems for which the set of feasible parameters and the solvability set are studied. These fuzzy weights and fuzzy matrix parameters are characterized by fuzzy numbers. The existing results concerning the basic notions parametric space in convex programs are redefined and analyzed qualitatively under the concept of alpha-Pareto optimality. An illustrative example is given to clarify the obtained results. (c) 2007 Elsevier Inc. All rights reserved.

关键词： multiobjective nonlinear programming parametric programming stability fuzzy parameters fuzzy numbers alpha-Pareto optimality

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IT-CEMOP: An iterative co-evolutionary algorithm for multiobjective optimization problem with nonlinear constraints

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期183卷 373-389页

作者： Osman, M. S. Abo-Sinna, Mahmoud A. Mousa, A. A. Menoufia Univ Fac Engn Dept Basic Engn Sci Shibin Al Kawm Egypt High Inst Technol Ramadan Egypt

Over the past few years, researchers have developed a number of multiobjective evolutionary algorithms (MOEAs). Although most studies concentrate on solving unconstrained optimization problems, there exit a few studies where MOEAs have been extended to solve constrained optimization problems. Most of them were based on penalty functions for handling nonlinear constraints by genetic algorithms. However the performance of these methods is highly problem-dependent, many methods require additional tuning of several parameters. In this paper, we present a new optimization algorithm, which is based on concept of co-evolution and repair algorithm for handling nonlinear constraints. The algorithm maintains a finite-sized archive of nondominated solutions which gets iteratively updated in the presence of new solutions based on the concept of epsilon-dominance. The use of epsilon-dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto set approximation by choosing an appropriate e value, which guarantees convergence and diversity. The results, provided by the proposed algorithm for six benchmark problems, are promising when compared with exiting well-known algorithms. Also, our results suggest that our algorithm is better applicable for solving real-world application problems. (c) 2006 Elsevier Inc. All rights reserved.

关键词： multiobjective nonlinear programming multiobjective evolutionary algorithms genetic algorithms epsilon-dominance

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Symmetric and self duality in vector optimization problem

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APPLIED MATHEMATICS AND COMPUTATION 2006年第2期183卷 1121-1126页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Dept Math Tanta Egypt

In this paper, we present the first-order symmetric and self duality programs in multiobjective nonlinear programming problems. For these first-order symmetric and dual programs, we introduce the weak, strong, and converse duality theorems under convexity and concavity conditions, where the pair of the symmetric dual multiobjective nonlinear programming problems in this paper different which in [D.S. Kim, Y.B. Yun, H. Kuk, Second-order symmetric and self duality in multiobjective programming. Appl. Math. Lett. 10(2) (1997) 17-22]. Also, we prove the self duality theorem for these first-order self dual programs and illustrate its example. (c) 2006 Elsevier Inc. All rights reserved.

关键词： multiobjective nonlinear programming first-order symmetric duality self duality Pareto optimal solution

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Stability of multiobjective nonlinear programming problems with random variables in the objective functions

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FUZZY SETS AND SYSTEMS 1999年第2期102卷 247-252页

作者： Kassem, MAEH Tanta Univ Fac Sci Dept Math Tanta Egypt

This paper deals with multiobjective nonlinear programming problems with random variables in the objective functions. These random variables are characterized by possibility density functions. The existing results concerning the qualitative analysis of basic notions in parametric nonlinear programming problems are reformulated to study the stability sets of the first, second, third and fourth kind for multiobjective nonlinear programming problems under the concept of a-possibility efficient. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： multiobjective nonlinear programming random variables stability parametric programming

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Stability of multiciteria nonlinear programming problems using fuzziness

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FUZZY SETS AND SYSTEMS 2002年第3期125卷 343-354页

作者： Badra, NM Ain Shams Univ Fac Engn Dept Engn Math Cairo Egypt

This paper presents a generalized fuzzy approach for determining the stability of multicriteria nonlinear programming problems. The proposed approach refers to an ideal, equivalent, single objective representation for the whole objectives. The membership functions for each objective function are constructed and, by the proposed formulation, the multicriteria programming problem will be transformed to an ideal equivalent single problem. By the proposed approach, the crisp intervals for the stability could be determined for the multicriteria nonlinear programming problems after solving two single nonlinear problems. Two illustrative examples are presented to verify the idea of the proposed stability approach. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： multiobjective nonlinear programming decision making membership functions pareto-optimal solutions stability set

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STABILITY OF multiobjective nonlinear-programming PROBLEMS WITH FUZZY PARAMETERS IN THE CONSTRAINTS

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FUZZY SETS AND SYSTEMS 1995年第3期74卷 343-351页

作者： KASSEM, MAE AMMAR, EI Department of Mathematics Faculty of Science Tanta University Tanta Egypt

This paper deals with the stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraint functions. These fuzzy parameters are characterized by fuzzy numbers. Qualitative and quantitative analysis of the basic notions like the set of feasible parameters, the solvability set, the stability sets of the first kind and of the second kind, will be reformulated under the concept of alpha-pareto optimality. An illustrative example is given to clarify the obtained results.

关键词： multiobjective nonlinear programming STABILITY PARAMETRIC ANALYSIS FUZZY programming FUZZY NUMBERS ALPHA-PARETO OPTIMALITY

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A FUZZY DUAL DECOMPOSITION METHOD FOR LARGE-SCALE multiobjective nonlinear-programming PROBLEMS

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FUZZY SETS AND SYSTEMS 1994年第1期67卷 19-27页

作者： SAKAWA, M YANO, H NAGOYA MUNICIPAL WOMENS COLL NAGOYA 464JAPAN

In this paper, we propose a fuzzy dual decomposition method for large-scale multiobjective nonlinear programming problems (LS-MONLPs) with the block angular structure. By considering the vague nature of human judgements, we assume that the decision maker (DM) may have a fuzzy goal for each of the objective functions in the LS-MONLP. After eliciting the corresponding membership function for each of the objective functions through the interaction with the DM, an extended primal problem and the corresponding extended dual problem are formulated. Then a two-level optimization algorithm for the extended dual problem is proposed for deriving the compromise solution for the DM to the LS-MONLP. Based on the proposed algorithm, FORTRAN programs are developed and an illustrative numerical example is demonstrated.

关键词： multiobjective nonlinear programming DECISION MAKING LARGE-SCALE programming DECOMPOSITION METHODS BLOCK ANGULAR STRUCTURE

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