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Journal ArticleDOI

Bi-criteria multi facility location problem in fuzzy environment

10 Jun 1993-Fuzzy Sets and Systems (North-Holland)-Vol. 56, Iss: 2, pp 145-153

Abstract: This paper presents a fuzzy goal programming model for locating multiple new facilities on a plane bounded by a convex polygon under the criteria: (1) minimize the sum of all the transportation costs and (2) minimize the maximum distances from the facilities to the demand points. It has also been proved that the methodology given will always give a nondominated solution. Recti-linear distances have been taken as the scenario may be thought of in an urban setting. A numerical example has been given to illustrate the solution methodology.
Topics: Convex polygon (61%), Facility location problem (59%), Fuzzy logic (56%), Bounded function (52%)
Citations
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Journal ArticleDOI
Abstract: This paper provides a review on recent efforts and development in multi-criteria location problems in three categories including bi-objective, multi-objective and multi-attribute problems and their solution methods. Also, it provides an overview on various criteria used. While there are a few chapters or sections in different location books related to this topic, we have not seen any comprehensive review papers or book chapter that can cover it. We believe this paper can be used as a complementary and updated version.

498 citations


Cites background from "Bi-criteria multi facility location..."

  • ...[32] developed a fuzzy goal programming for their convex multi-facility location problem with minisum (transportation cost) and minimax (distance) objectives with rectilinear distances....

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Journal ArticleDOI
Ta-Chung Chu1Institutions (1)
TL;DR: This work presents a fuzzy TOPSIS model under group decisions for solving the facility location selection problem, where the ratings of various alternative locations under different subjective attributes and the importance weights of all attributes are assessed in linguistic values represented by fuzzy numbers.
Abstract: This work presents a fuzzy TOPSIS model under group decisions for solving the facility location selection problem, where the ratings of various alternative locations under different subjective attributes and the importance weights of all attributes are assessed in linguistic values represented by fuzzy numbers. The objective attributes are transformed into dimensionless indices to ensure compatibility with the linguistic ratings of the subjective attributes. Furthermore, the membership function of the aggregation of the ratings and weights for each alternative location versus each attribute can be developed by interval arithmetic and α -cuts of fuzzy numbers. The ranking method of the mean of the integral values is applied to help derive the ideal and negative-ideal fuzzy solutions to complete the proposed fuzzy TOPSIS model. Finally, a numerical example demonstrates the computational process of the proposed model.

265 citations


Journal ArticleDOI
Alfred L. Guiffrida1, Rakesh Nagi1Institutions (1)
TL;DR: This paper provides a survey of the application of fuzzy set theory in production management research, and identifies selected bibliographies on fuzzy sets and applications.
Abstract: Fuzzy set theory has been used to model systems that are hard to define precisely. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into the model formulation and solution process. Fuzzy set theory represents an attractive tool to aid research in production management when the dynamics of the production environment limit the specification of model objectives, constraints and the precise measurement of model parameters. This paper provides a survey of the application of fuzzy set theory in production management research. The literature review that we compiled consists of 73 journal articles and nine books. A classification scheme for fuzzy applications in production management research is defined. We also identify selected bibliographies on fuzzy sets and applications.

165 citations


Cites background from "Bi-criteria multi facility location..."

  • ...Bhattacharya et al. (1993) formulate a fuzzy goal programming model for locating a single facility within a given convex region subject to the simultaneous consideration of two criteria: (1) minimize the sum of all transportation costs; and (2) minimize the maximum distances from the facilities to the demand points....

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Journal ArticleDOI
Jian Zhou1, Baoding Liu1Institutions (1)
TL;DR: Three types of fuzzy programming models – fuzzy expected cost minimization model, fuzzy a-cost minimizationmodel, and credibility maximization model – are proposed according to different decision criteria in order to model capacitated location–allocation problem with fuzzy demands.
Abstract: In order to model capacitated location-allocation problem with fuzzy demands, three types of fuzzy programming models - fuzzy expected cost minimization model, fuzzy @a-cost minimization model, and credibility maximization model - are proposed according to different decision criteria For solving these models, some hybrid intelligent algorithms are also designed Finally, several numerical experiments are presented to illustrate the efficiency of the proposed algorithms

118 citations


Cites background from "Bi-criteria multi facility location..."

  • ...For example, in Bhattacharya, Rao, and Tiwari (1992, 1993) new facilities are considered to be located under multiple fuzzy criteria, and a fuzzy goal programming approach has been developed to deal with the problems....

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Journal ArticleDOI
Meilin Wen1, Kakuzo Iwamura2Institutions (2)
TL;DR: In this paper, a new model named α-cost model under the Hurwicz criterion is presented with fuzzy demands, and the simplex algorithm, fuzzy simulations and a genetic algorithm are integrated to produce a hybrid intelligent algorithm.
Abstract: Facility location-allocation (FLA) problem has been widely studied by operational researchers due to its many practical applications. Many researchers have studied the FLA problem in a deterministic environment. However, the models they proposed cannot accommodate satisfactorily various customer demands in the real world. Thus, we consider the FLA problem with uncertainties. In this paper, a new model named α-cost model under the Hurwicz criterion is presented with fuzzy demands. In order to solve this model, the simplex algorithm, fuzzy simulations and a genetic algorithm are integrated to produce a hybrid intelligent algorithm. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed algorithm.

93 citations


References
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Journal ArticleDOI
E. T. Jaynes1Institutions (1)
15 Oct 1957-Physical Review
Abstract: Information theory provides a constructive criterion for setting up probability distributions on the basis of partial knowledge, and leads to a type of statistical inference which is called the maximum-entropy estimate. It is the least biased estimate possible on the given information; i.e., it is maximally noncommittal with regard to missing information. If one considers statistical mechanics as a form of statistical inference rather than as a physical theory, it is found that the usual computational rules, starting with the determination of the partition function, are an immediate consequence of the maximum-entropy principle. In the resulting "subjective statistical mechanics," the usual rules are thus justified independently of any physical argument, and in particular independently of experimental verification; whether or not the results agree with experiment, they still represent the best estimates that could have been made on the basis of the information available.It is concluded that statistical mechanics need not be regarded as a physical theory dependent for its validity on the truth of additional assumptions not contained in the laws of mechanics (such as ergodicity, metric transitivity, equal a priori probabilities, etc.). Furthermore, it is possible to maintain a sharp distinction between its physical and statistical aspects. The former consists only of the correct enumeration of the states of a system and their properties; the latter is a straightforward example of statistical inference.

11,158 citations


Journal ArticleDOI
Hans-Jürgen Zimmermann1Institutions (1)
TL;DR: It is shown that solutions obtained by fuzzy linear programming are always efficient solutions and the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution are shown.
Abstract: In the recent past numerous models and methods have been suggested to solve the vectormaximum problem. Most of these approaches center their attention on linear programming problems with several objective functions. Apart from these approaches the theory of fuzzy sets has been employed to formulate and solve fuzzy linear programming problems. This paper presents the application of fuzzy linear programming approaches to the linear vectormaximum problem. It shows that solutions obtained by fuzzy linear programming are always efficient solutions. It also shows the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution.

3,117 citations


Journal ArticleDOI
Arthur M. Geoffrion1Institutions (1)
Abstract: : The concept of efficiency in problems with multiple criterion functions--sometimes under an alias such as 'admissibility' or 'Pareto optimality'--has long played an important role in economics, game theory, statistical decision theory, and in all optimal decision problems with noncomparable criteria. Here we propose a slightly restricted definition of efficiency that eliminates efficient points of a certain anomalous nature. This new definition, which we call proper efficiency, is related in spirit to the notion of 'proper' efficiency introduced by Kuhn and Tucker in their celebrated paper of 1950; but the present definition avoids certain drawbacks inherent in the earlier one. A comprehensive theory of vector maximization is constructed using the new definition, with and without various constraint qualification, convexity, and differentiability assumptions. The theory includes as a special case the standard theory of nonlinear programming.

1,233 citations


Journal ArticleDOI
01 Dec 1972-Management Science
TL;DR: An interactive mathematical programming approach to multi-criterion optimization is developed, and then illustrated by an application to the aggregated operating problem of an academic department.
Abstract: An interactive mathematical programming approach to multi-criterion optimization is developed, and then illustrated by an application to the aggregated operating problem of an academic department.

828 citations


Journal ArticleDOI
01 Jan 1973-
TL;DR: The main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh.
Abstract: In problems of system analysis, it is customary to treat imprecision by the use of probability theory. It is becoming increasingly clear, however, that in the case of many real world problems involving large scale systems such as economic systems, social systems, mass service systems, etc., the major source of imprecision should more properly be labeled ‘fuzziness’ rather than ‘randomness.’ By fuzziness, we mean the type of imprecision which is associated with the lack of sharp transition from membership to nonmembership, as in tall men, small numbers, likely events, etc. In this paper our main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh [1]. However, in our approach, the emphasis is on mathematical programming and the use of the concept of a level set to extend some of the classical results to problems involving fuzzy constraints and objective functions.

578 citations


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