• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.44
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• pp.297-309
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• 1997

Exceptional Elements(E.E) are generally eliminated by a machine duplication or a subcontract in cellular manufacturing system. One of the advantages in FMS consists of machines capable of multi-processing. This paper presents a method that eliminates E.Es by tool duplication. First, we develop the exceptional operation similarity(EOS) by machine cell-operation incidence matrix and part-operation incidence matrix. The EOS indicates a similarity of unperformable operations in each part when two exceptional parts are assigned to a machine cell. Secondly, a mathematical model to minimize tool duplication is developed by the EOS. Finally, a heuristic algorithm is developed to reflect dynamic situation in process of elimination of exceptional elements by the EOS and the mathematical model. A numerical example is provided to illustrate the algorithm.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.45
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• pp.329-332
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• 1998

This Paper proposes a mathematical model to solve the cell formation problem with exceptional elements, Exceptional elements are bottleneck machines and exceptional parts that span two or more manufacturing cells. The model suggests whether it is cost-effective to eliminate an EE (by machine duplication or part subcontracting), or whether the intercellular transfer caused by the EE should remain in the cell formation. It provides an optimal solution for resolving the interaction created by EE in the initial cell formation solution. In addition, the model recognizes potentially advantageous mixed strategies ignored by previous approaches.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.1031-1038
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• 2021

The main aim of this article is to study quantitative structure of finite simple exceptional groups F₄(2ⁿ) with n > 1. Here, we prove that the finite simple exceptional groups F₄(2ⁿ), where 2⁴ⁿ + 1 is a prime number with n > 1 a power of 2, can be uniquely determined by their orders and the set of the number of elements with the same order. In conclusion, we give a positive answer to J. G. Thompson's problem for finite simple exceptional groups F₄(2ⁿ).

• IE interfaces
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• v.12 no.1
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• pp.10-18
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• 1999

Job shop manufacturing environments are using the concept of cellular manufacturing systems(CMS) which has several advantages in reducing production lead times, setup times, work-in-process, etc. Utilizing the similarities between cell-machine, part-machine, and the shape/size of parts, CMS can group machines and parts resulting in improved efficiency of this system. However, when grouping machines and parts in machine cells, there inevitably occurs exceptional elements(EEs), which can not operate in the same machine cell. Minimizing these EEs in CMS is a critical point that improving production efficiency. Constraints in machine duplication cost, machining process technology, machining capability, and factory space limitations are main problems that prevent achiving the goal of maintaining an ideal CMS environment. This paper presents an algorithm that minimizes EEs under the constraints of machine duplication cost and factory space limitation. Developing exceptional operation similarity(EOS) by cell-machine incidence matrix and part-machine incidence matrix, it brings the machine cells that operate the parts or not. A mathematical model to minimize machine duplication is developed by EOS, followed by a heuristic algorithm in order to reflect dynamic situation resulting from minimizing exceptional elements process and the mathematical model. A numerical example is provided to illustrate the algorithm.

• Journal of Korean Institute of Industrial Engineers
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• v.20 no.2
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• pp.51-64
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• 1994

Cellular manufacturing requires formation of machine cells that can produce families of parts with similar processing requirement. The purpose of cell formation is to create separable machine clusters and part families simultaneously. However, the cell formation process often includes the identification of exceptional elements. This paper presents cell formation method under consideration of alternative routings in FMS which consists of machines capable of multi-processing and parts which require more than one operation. We suggest theorems to calculate the maximum number of machine cell and part family which have no exceptional elements. We also develop a cell formation algorithm which is based on the suggested theorem. A numerical example is provided to illustrate the proposed theorem and algorithm.

• Journal of Korean Institute of Industrial Engineers
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• v.17 no.1
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• pp.75-82
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• 1991

This research is concerned with Machine-Part Group Formation(MPGF) methodology for Flexible Manufacturing Systems(FMS). The purpose of the research is to develop a new heuristic algorithm for effectively solving MPGF problem. The new algorithm is proposed and evaluated by 100 machine-part incidence matrices generated. The performance measures are (1) grouping ability of mutually exclusive block-diagonal form. (2) number of unit group and exceptional elements, and (3) grouping time. The new heuristic algorithm has the following characteristics to effectively conduct MPGF : (a) The mathematical model is presented for rapid forming the proper number of unit groups and grouping mutually exclusive block-diagonal form, (b) The simple and effective mathematical analysis method of Rank Order Clustering(ROC) algorithm is applied to minimize intra-group journeys in each group and exceptional elements in the whole group. The results are compared with those from Expert System(ES) algorithm and ROC algorithm. The results show that the new algorithm always gives the group of mutually exclusive block-diagonal form and better results(85%) than ES algorithm and ROC algorithm.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.40-43
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• 2000

This paper is concerned with development of an efficient Ρ-median approach applicable to large cell formation(CF) problems. A two-phase methodology that seeks to minimize the number of exceptional elements is proposed. In phase I, two efficient Ρ-median formulations which contain fewer binary variables than existing Ρ-median formulations are constructed. These make it possible to implement large CF problem within reasonable computer runtime with commercially available linear integer programming codes. Given the initial cell configuration found with the new p-median formulations, in phase II bottleneck machines and parts are reassigned to reduce the number of exceptional elements. This procedure has the flexibility to provide the cell designer with alternative solutions. Test results on large CF problems show a substantial efficiency of the new Ρ-median formulations.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.61
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• pp.41-50
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• 2000

Cell formation(CF) Is to group parts with similar geometry, function, material and process into part families, and the corresponding machines into machine cells. Cell formation solutions often contain exceptional elements(EEs). Also, the following objective functions - minimizing the total costs of dealing with exceptional elements and maximizing total similarity coefficients between parts - have been used in CF modeling. Thus, multiobjective programming approach can be developed to model cell formation problems with two conflicting objective functions. This paper presents an effective cell formation method with fuzzy multiobjective nonlinear mixed-integer programming simultaneously to form machine cells and to minimize the cost of eliminating EEs.

• IE interfaces
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• v.2 no.2
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• pp.15-24
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• 1989

When we design, plan, and schedule for group technology, the limitation on the machine cells and cell size may occur. The purpose of this study is to find machine cells and part families to minimize the exceptional elements, constraining both the number of machine cells and the cell size. To solve this problem, the algorithm extending Kusiak's p-median method is proposed. In the proposed algorithm, the method finding initial solution and reducing the number of constraints is presented for computational efficiency. The proposed algorithm is evaluated and compared with well-known algorithms for machine-part group formation in terms of the exceptional elements. An example is shown to illustrate the proposed algorithm.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.54
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• pp.65-75
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• 2000

Cellular manufacturing(CM) is a philosophy and innovation to improve manufacturing productivity and flexibility. Cell formation(CF), the first and key problem faced in designing an effective CM system, is a process whereby parts with similar design features or Processing requirements are grouped into part families, and the corresponding machines into machine cells. Cell formation solutions often contain exceptional elements(EEs). EE create interactions between two manufacturing cells. A policy dealing with EEs considers minimizing the total costs of three important costs; (1)intercellular transfer (2)machine duplication and (3)subcontracting. This paper presents an effective cell formation method with fuzzy nonlinear mixed-integer programming simultaneously to form manufacturing cells and to minimize the total costs of eliminating exceptional elements.