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ON SOLUTIONS AND DISTRIBUTION PROBLEMS OF THE LINEAR-programming WITH fuzzy RANDOM VARIABLE-COEFFICIENTS

fuzzy SETS AND SYSTEMS 1993年第2期58卷 155-170页

作者： QIAO, Z WANG, GY HARBIN ARCHITECTURAL & CIVIL ENGN INST HARBIN PEOPLES R CHINA

This paper studies the solution method and distribution problems for two kinds of linear programming with fuzzy random variable coefficients. Some concepts of solutions (for example, the fuzzy (pseudo-) random optimization solution) are introduced for these new programming problems. We prove some equivalent theorems that transform the fuzzy random programming problems into a series of random programming problems. By using the simplex method of linear programming with random variable coefficients, we give the solution method of linear programming with fuzzy random variable coefficients. The formulas of probability distribution function, projective distribution function and expectation on these new programmings are presented.

关键词： INTERVAL ANALYSIS fuzzy RANDOM VARIABLE STOCHASTIC programming fuzzy programming fuzzy RANDOM programming

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Design of close-loop supply chain network under uncertainty using hybrid genetic algorithm: A fuzzy and chance-constrained programming model

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COMPUTERS & INDUSTRIAL ENGINEERING 2015年 88卷 444-457页

作者： Dai, Zhuo Zheng, Xiaoting Jiu Jiang Univ Sch Elect Commerce Jiu Jiang City 332005 Jiangxi Peoples R China

The design of closed-loop supply chain network is one of the important issues in supply chain management. This research proposes a multi-period, multi-product, multi-echelon closed-loop supply chain network design model under uncertainty. Because of its complexity, a solution framework which integrates Monte Carlo simulation embedded hybrid genetic algorithm, fuzzy programming and chance-constrained programming jointly deal with the issue. A fuzzy programming and chance-constrained programming approach take up the uncertainty issue. Monte Carlo simulation embedded hybrid genetic algorithm is employed to determine the configuration of CLSC network. Parameters of GA are chosen to balance two aims. One aim is that the best value is global optimum, that is, maximum profit. The other aim is that the computational time is as short as possible. Non-parametric test confirms the advantage of hybrid GA. Then, the validity of Monte Carlo simulation embedded hybrid genetic algorithm is verified. The impacts of uncertainty in disposed rates, demands, and capacities on the overall profit of CLSC network are studied through sensitivity analysis. The proposed model is effective in designing CLSC network under uncertain environment. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Close-loop supply chain Network design Uncertainty Monte Carlo simulation embedded hybrid genetic algorithm fuzzy programming Chance-constrained programming

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Vendor selection and supply quantities determination in a bakery by AHP and fuzzy multi-criteria programming

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INTERNATIONAL JOURNAL OF COMPUTER INTEGRATED MANUFACTURING 2013年第9期26卷 816-829页

作者： Peric, Tunjo Babic, Zoran Veza, Ivica Univ Zagreb Fac Econ & Business Zagreb 10000 Croatia Univ Split Fac Econ Split 21000 Croatia Univ Split Fac Elect Engn Mech Engn & Naval Architecture Split 21000 Croatia

One of the possible conceptions for the survival in a turbulent world market is a chain cooperation among the producer, his suppliers and customers, according to the concept of supply chain management. The problem of vendor selection and determination of material quantities supplied is one of the most important activities in the supply chain. The purpose of this article is to propose a model for vendor selection and determination of supply quotas in the area of flour supply by using the analytic hierarchy process (AHP) and multi-objective linear programming (LP) model solved by fuzzy LP method, based on the decision-making in a fuzzy environment, and to point to the advantages of the proposed model in comparison to some other vendor selection and supply quantity determination models. The proposed model applied in the concrete problem of vendor selection and determination of supply quotas proved to be very efficient in determining the priority of alternatives, taking into account all the criteria and sub-criteria, as well as in defining criteria weights that express the decision-maker's preferences, which allows a simple sensitivity analysis of the obtained solutions.

关键词： vendor selection supply quantity determination multi-criteria AHP fuzzy programming bakery

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A fuzzy multi-objective programming for optimization of fire station locations through genetic algorithms

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第2期181卷 903-915页

作者： Yang, Lili Jones, Bryan F. Yang, Shuang-Hua Univ Loughborough Sch Business Loughborough LE11 3TU Leics England Univ Derby Appl Comp Dept Derby DE22 1GB England Univ Loughborough Dept Comp Sci Loughborough LE11 3TU Leics England

Location of fire stations is an important factor in its fire protection capability. This paper aims to determine the optimal location of fire station facilities. The proposed method is the combination of a fuzzy multi-objective programming and a genetic algorithm. The original fuzzy multiple objectives are appropriately converted to a single unified 'min-max' goal, which makes it easy to apply a genetic algorithm for the problem solving. Compared with the existing methods of fire station location our approach has three distinguish features: (1) considering fuzzy nature of a decision maker (DM) in the location optimization model;(2) fully considering the demands for the facilities from the areas with various fire risk categories;(3) being more understandable and practical to DM. The case study was based on the data collected from the Derbyshire fire and rescue service and used to illustrate the application of the method for the optimization of fire station locations. (c) 2006 Elsevier B.V. All rights reserved.

关键词： location fire stations multi-objective programming genetic algorithm fuzzy programming

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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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An interactive fuzzy satisficing method for multiobjective stochastic linear programming problems through an expectation model

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2003年第3期145卷 665-672页

作者： Sakawa, M Kato, K Nishizaki, I Hiroshima Univ Grad Sch Engn Fac Engn Dept Artificial Complex Syst Engn Higashihiroshima 7398527 Japan

For decision making problems involving uncertainty, both stochastic programming as an optimization method based on the theory of probability and fuzzy programming representing the ambiguity by fuzzy concept have been developing in various,ways. In this paper, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. For such problems, as a fusion of these two approaches, after incorporating fuzzy goals of the decision maker for the objective functions, we propose an interactive fuzzy satisficing method for the expectation model to derive a satisficing solution for the decision maker. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： multicriteria analysis linear programming stochastic programming fuzzy programming interactive programming

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Planning Water Resources Allocation Under Multiple Uncertainties Through a Generalized fuzzy Two-Stage Stochastic programming Method

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IEEE TRANSACTIONS ON fuzzy SYSTEMS 2015年第5期23卷 1488-1504页

作者： Fan, Yurui Huang, Guohe Huang, Kai Baetz, Brian W. Univ Regina Fac Engn Regina SK S4S 0A2 Canada Univ Regina Inst Energy Environm & Sustainabil Res UR NCEPU Regina SK S4S 0A2 Canada North China Elect Power Univ Inst Energy Environm & Sustainabil Res UR NCEPU Beijing 102206 Peoples R China McMaster Univ Dept Civil Engn Hamilton ON L8S 4L8 Canada

In this study, a generalized fuzzy two-stage stochastic programming (GFTSP) method is developed for planning water resources management systems under uncertainty. The developed GFTSP method can deal with uncertainties expressed as probability distributions, fuzzy sets, as well as fuzzy random variables. With the aid of a robust stepwise interactive algorithm, solutions for GFTSP can be generated by solving a set of deterministic submodels. Furthermore, the possibility information (expressed as fuzzy membership functions) can be reflected in the solutions for the objective function value and decision variables. The developed GFTSP approach is also applied to a water resources management and planning problem to demonstrate its applicability. Solutions of decision variables and objective function value are expressed as fuzzy membership functions, reflecting the fluctuating ranges of decision alternatives under different plausibilities. And thus, the water alternatives can be directly derived from the obtained fuzzy membership functions when the preferred a value is predefined by decision makers.

关键词： Decision making dual-uncertainty fuzzy programming planning water resources

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An interactive fuzzy satisficing method for general multiobjective 0-1 programming problems through genetic algorithms with double strings based on a reference solution

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fuzzy SETS AND SYSTEMS 2002年第3期125卷 289-300页

作者： Sakawa, M Kato, K Hiroshima Univ Fac Engn Dept Ind & Syst Engn Higashihiroshima 7398527 Japan

In this paper, focusing on general multiobjective 0-1 programming problems involving positive and negative coefficients, we propose an interactive fuzzy satisficing method by extending our previous genetic algorithms with double strings for multiobjective multidimensional 0-1 knapsack problems. In the extended genetic algorithms, a new decoding algorithm for individuals represented by double strings which maps each individual to a feasible solution is proposed through the introduction of backtracking and individual modification. After examining the feasibility and efficiency of the extended genetic algorithms with double strings using a lot of 0-1 programming problems involving positive and negative coefficients, an illustrative numerical example demonstrated the feasibility and efficiency of the proposed interactive fuzzy satisficing method. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： multicriteria analysis genetic algorithms 0-1 programming fuzzy programming interactive programming

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Dependent-chance programming in fuzzy environments

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fuzzy SETS AND SYSTEMS 2000年第1期109卷 97-106页

作者： Liu, BD Tsinghua Univ Dept Appl Math Beijing 100084 Peoples R China

Dependent-chance programming is a new type of stochastic programming. This paper provides a framework of dependent-chance programming as well as dependent-chance multiobjective programming and dependent-chance goal programming in fuzzy environment as opposed to stochastic environment. We also extend the concepts of uncertain environments, events, chance functions and induced constraints from stochastic to fuzzy cases. Finally, a fuzzy simulation based genetic algorithm is illustrated by some numerical examples of dependent-chance programming models. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： fuzzy programming genetic algorithm fuzzy simulation

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A two-phase approach for multi-objective programming problems with fuzzy coefficients

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INFORMATION SCIENCES 2007年第23期177卷 5191-5202页

作者： Arikan, Feyzan Guengoer, Zuelal Gazi Univ Dept Ind Engn TR-06570 Ankara Turkey

In this study, a two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems. The procedure provides a practical solution approach, which is an integration of fuzzy parametric programming (FPP) and fuzzy linear programming (FLP), for solving real life multiple objective programming problems with all fuzzy coefficients. The interactive concept of the procedure is performed to reach simultaneous optimal solutions for all objective functions for different grades of precision according to the preferences of the decision-maker (DM). The procedure can be also performed to obtain lexicographic optimal and/or additive solutions if it is needed. In the first phase of the procedure, a family of vector optimization models is constructed by using FPP. Then in the second phase, each model is solved by FLP. The solutions are optimal and each one is an alternative decision plan for the DM. (C) 2007 Elsevier Inc. All rights reserved.

关键词： multiple objective programming fuzzy sets fuzzy parameters fuzzy programming

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