## Manufacturing Cell Design: An Integer Programming Model Employing Genetic Algorithms (1996)

Venue: | IIE Transactions |

Citations: | 15 - 5 self |

### BibTeX

@ARTICLE{Joines96manufacturingcell,

author = {Jeffrey A. Joines and C. Thomas Culbreth and Russell E. King},

title = {Manufacturing Cell Design: An Integer Programming Model Employing Genetic Algorithms},

journal = {IIE Transactions},

year = {1996},

volume = {28},

pages = {69--85}

}

### OpenURL

### Abstract

The design of a cellular manufacturing system requires that a part population, at least minimally described by its use of process technology (part/machine incidence matrix), be partitioned into part families and that the associated plant equipment be partitioned into machine cells. At the highest level, the objective is to form a set of completely autonomous units such that inter-cell movement of parts is minimized. We present an integer program that is solved using a genetic algorithm (GA) to assist in the design of cellular manufacturing systems. The formulation uses a unique representation scheme for individuals (part/machine partitions) that reduces the size of the cell formation problem and increases the scale of problems that can be solved. This approach offers improved design flexibility by allowing a variety of evaluation functions to be employed and by incorporating design constraints during cell formation. The effectiveness of the GA approach is demonstrated on several problems from the literature.

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Citation Context ...of the oldest and most commonly applied array-based methods. Subsequent modifications and improvements of these algorithms have been described by Chan and Milner [10], Chandrasekharan and Rajagopalan =-=[11]-=-, Khator and Irani [30], King and Nakornchai [32], and Kusiak and Chow [38]. In Chu's [17] comprehensive comparison of three array-based clustering techniques, the bond energy algorithm outperformed t... |

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Citation Context ... Kusiak [34], one of the more popular models, minimizes the total sum of distances between each pair of parts (machines). Other integer programming models have been developed by Boctor [5], Choobineh =-=[14]-=-, Gunasingh and Lashkari [20], and Purcheck [49]. Srinivasan et al. [55] developed an assignment model for the cell formation problem, while Steudal and Ballakur [57] applied a dynamic programming mod... |

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Citation Context ...uce a large number of products in small-to-medium lot sizes. One approach used to gain these benefits has been to develop a cellular manufacturing system using the principles of group technology (GT) =-=[24]. The-=- manufacturing system is decomposed into several manageable subsystems, or groups, by aggregating similar parts into part families and dissimilar machines into cells [37]. The ideal cell is "inde... |

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Citation Context ...tures and (2) those that manipulate process sequences or routings to form the corresponding machine cells. Extensive literature (see Joines, King, and Culbreth [27, 28] and Selim, Askin, and Vakharia =-=[53]-=-) has been devoted to various techniques that partition a population of parts, as described by the use of process technology (part/machine incidence matrix), into part families and associate them with... |

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Citation Context ... 4 2 37 680.4 0.7609 6 0.7791 5 9 27 1785.1 6 King (1982)[32] 16x43 126 N.A. 4 0.4926 4 26 77 1134.7 7 Srinivasan(1990), et al. [54] 10x20 40 0.8163 4 0.8163 4 0 9 262.1 8 Askin and Subramanian (1987)=-=[3]-=- 14x23 58 0.6436 N.A. 0.6951 4 2 28 560.1 9 Chandrasekharan and Rajagopalan(1989) [13] 24x40 105 0.8015 7 0.8015 7 0 26 1637.7 10 Carrie(1973)[9] 24x18 88 0.5410 7 0.5701 7 27 19 986.3 11 Chandrasekha... |

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Citation Context ...ted to the part/machine incidence matrix. (iv) Graph theoretic methods: Rajagopalan and Batra [50] used a graph partitioning algorithm that utilizes cliques to group the machines. Lee and Garcia-Diaz =-=[40]-=- transformed the cell formation problem into a network flow formulation and used a primal-dual algorithm developed by Bertsekas and Tseng [4] to solve for the machine cells. This algorithm is more eff... |

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Citation Context ...to merge groups into successively larger partitions until a single cluster contains the whole set. The agglomerative approach has been applied by Carrie [9], McAuley [41], Mosier [47], and Seifoddini =-=[51]-=-. The similarity index used as the basis in the formation of groups by hierarchical clustering methods offers a distinct advantage over array-based methods. It allows information, such as annual part ... |

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Citation Context ...s and Tseng [4] to solve for the machine cells. This algorithm is more efficient computationally than the p-median model by Kusiak [34]. Other graph approaches include the minimum spanning tree by Ng =-=[48]-=-, a heuristic graph partitioning approach by Askin and Chiu [2], and a network flow approach using a modified version of the Gomory-Hu algorithm by Vohra et al. [58]. (v) Mathematical programming meth... |

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Citation Context ...s more efficient computationally than the p-median model by Kusiak [34]. Other graph approaches include the minimum spanning tree by Ng [48], a heuristic graph partitioning approach by Askin and Chiu =-=[2]-=-, and a network flow approach using a modified version of the Gomory-Hu algorithm by Vohra et al. [58]. (v) Mathematical programming methods: Clustering can be treated as an optimization problem and, ... |

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Citation Context ...ter and then proceed to merge groups into successively larger partitions until a single cluster contains the whole set. The agglomerative approach has been applied by Carrie [9], McAuley [41], Mosier =-=[47]-=-, and Seifoddini [51]. The similarity index used as the basis in the formation of groups by hierarchical clustering methods offers a distinct advantage over array-based methods. It allows information,... |

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Citation Context ...on hierarchy, making the choice of the correct solution difficult for large problems. (iii) Non-hierarchical clustering methods: These clustering techniques include GRAPHICS (Srinivasan and Narendran =-=[55]-=-) and ZODIAC (Chandrasekharan and Rajagopalan [12]). ZODIAC is a modified version of MacQueen's clustering method [1]. It has been shown that these methods outperform the array-based methods and the h... |

6 |
Cluster analysis in manufacturing cellular formation
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Citation Context ...plified through the creation of independent cells. Setup times, work-in-progress inventory, throughput time, and material handling can be reduced, and opportunities for improved quality can be gained =-=[10, 15, 24]-=-. In this paper, we first discuss the various approaches to cell design found in the literature. Then, an integer programming formulation of the cell formation problem is presented that uses a unique ... |

6 |
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Citation Context ...improvements of these algorithms have been described by Chan and Milner [10], Chandrasekharan and Rajagopalan [11], Khator and Irani [30], King and Nakornchai [32], and Kusiak and Chow [38]. In Chu's =-=[17]-=- comprehensive comparison of three array-based clustering techniques, the bond energy algorithm outperformed the other array-based clustering techniques. In general, array-based techniques operate onl... |

6 |
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Citation Context ...ods: Recent applications of artificial intelligence (AI) techniques have shown promise as tools for the design of cellular manufacturing systems. The unsupervised artificial neural network model, ART =-=[29]-=-, offers the advantage of not requiring the storage of the part/machine incidence matrix in memory. The fuzzy c-means clustering algorithm by Chu and Hayya [16] presents the designer with a fuzzy solu... |

5 |
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Citation Context ...ons on the same machine while minimizing inter-cell movement. Seifoddini [52] developed a probabilistic model to overcome assumptions of deterministic demand for parts. The closest neighbor algorithm =-=[6]-=-, the branch and bound algorithm, and the minimum spanning tree algorithm [48] are among the best in the literature for forming manufacturing cells using only the part/machine incidence matrix. 3 Gene... |

5 |
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Citation Context ...ma q) P : 4.4 Genetic Operators Reproduction is carried out by the application of genetic operators on the selected parents. Mutation and simple crossover are the two basic types of genetic operators =-=[44]-=-. Mutation operators alter or mutate one parent by changing one or more variables (gene or alphabet) in some way, or by some random amount, to form one offspring. Crossover operators combine informati... |

5 |
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Citation Context ...de the minimum spanning tree by Ng [48], a heuristic graph partitioning approach by Askin and Chiu [2], and a network flow approach using a modified version of the Gomory-Hu algorithm by Vohra et al. =-=[58]-=-. (v) Mathematical programming methods: Clustering can be treated as an optimization problem and, therefore, mathematical programming methods offer several distinct advantages. These methods have the ... |

4 |
me simpljScmon of Material Flow Systems
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Citation Context ...lies and associate them with machine cells. Cell formation techniques that operate on the part/machine incidence matrix are generally referred to as the second phase of Production Flow Analysis (PFA) =-=[8]-=- and involve combinatorial optimization. Cell formation methods based on process routings can be further categorized according to the type of algorithm employed to cluster the data, e.g., array-based ... |

4 |
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Citation Context ...ed artificial neural network model, ART [29], offers the advantage of not requiring the storage of the part/machine incidence matrix in memory. The fuzzy c-means clustering algorithm by Chu and Hayya =-=[16]-=- presents the designer with a fuzzy solution. In fuzzy solutions, the parts have a different membership grade in several different cells. In crisp solutions, parts are either present or absent with re... |

4 |
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Citation Context ...commonly applied array-based methods. Subsequent modifications and improvements of these algorithms have been described by Chan and Milner [10], Chandrasekharan and Rajagopalan [11], Khator and Irani =-=[30]-=-, King and Nakornchai [32], and Kusiak and Chow [38]. In Chu's [17] comprehensive comparison of three array-based clustering techniques, the bond energy algorithm outperformed the other array-based cl... |

4 |
Machine clustering for economic production
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Citation Context ...egories: divisive and agglomerative. Divisive algorithms start with all the machines (or parts) in a single group and then iteratively generate partitions until each machine is in a singleton cluster =-=[56]-=-. Agglomerative algorithms start with each machine as an initial cluster and then proceed to merge groups into successively larger partitions until a single cluster contains the whole set. The agglome... |

3 |
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Citation Context ...imple Chan and Milner (1982)[10] 10x15 3 8:4729x10 11 0.920 189 6728 0.920 97 3184 0.920 Complex Chan and Milner (1982)[10] 10x15 3 8:4729x10 11 0.800 286 9232 0.781 98 3216 0.800 Simple Joines (1993)=-=[25]-=- 20x25 5 2:8422x10 31 0.860 805 25840 0.860 429 13808 0.860 Complex Joines (1993)[25] 20x25 5 2:8422x10 31 0.775 1156 37072 0.757 671 21552 0.775 Burbidge (1969)[7] 20x35 4 1:2981x10 33 0.757 1272 407... |

3 |
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Citation Context ..., and a simulated annealing approach [5]. (vii) Other heuristics: Other heuristics based on branch and bound techniques have also been developed to aid in the design of cellular manufacturing systems =-=[36]-=-. Minis et al. [46] developed a technique that groups machines into cells and parts into families by minimizing the inter-cell traffic subject to capacity constraints. This method has the capability o... |

3 |
Manufacturing cell formation with multiple, functionally identical machines
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(Show Context)
Citation Context ...nnealing approach [5]. (vii) Other heuristics: Other heuristics based on branch and bound techniques have also been developed to aid in the design of cellular manufacturing systems [36]. Minis et al. =-=[46]-=- developed a technique that groups machines into cells and parts into families by minimizing the inter-cell traffic subject to capacity constraints. This method has the capability of including unique,... |

3 |
A probabilistic model for machine cell formation
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(Show Context)
Citation Context ...ovement, was developed by Harhalakis et al. [22]. This procedure can accommodate ordered operations and non-consecutive operations on the same machine while minimizing inter-cell movement. Seifoddini =-=[52]-=- developed a probabilistic model to overcome assumptions of deterministic demand for parts. The closest neighbor algorithm [6], the branch and bound algorithm, and the minimum spanning tree algorithm ... |

3 |
An assignment model for the part-families problem in group technology
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(Show Context)
Citation Context ...48 5 0.7748 5 11 14 800.0 5 Burbidge (1969)[7] 20x35 136 0.7571 4 0.7571 4 2 37 680.4 0.7609 6 0.7791 5 9 27 1785.1 6 King (1982)[32] 16x43 126 N.A. 4 0.4926 4 26 77 1134.7 7 Srinivasan(1990), et al. =-=[54]-=- 10x20 40 0.8163 4 0.8163 4 0 9 262.1 8 Askin and Subramanian (1987)[3] 14x23 58 0.6436 N.A. 0.6951 4 2 28 560.1 9 Chandrasekharan and Rajagopalan(1989) [13] 24x40 105 0.8015 7 0.8015 7 0 26 1637.7 10... |