Cell formation problem - A Lagrangean relaxation to mathematical programming approach and a linear performance measure

Two topics in the part-machine cell formation problem are discussed: In the first part, a Lagrangean relaxation in a mathematical programming model is proposed to simultaneously set machines into groups and parts into families in a cellular manufacturing system. The objective of this model is to find the optimal number of cells while minimizing inter-cellular part moves and increasing utilization of machines within the cells. The method uses a 0-1 integer programming model. The Lagrangean relaxation relaxes the model through an iterative search. In the second part, we introduce a new performance measure and compare it to some known performance measures. The new measure preserved some important features of previous performance measures and overcomes a number of drawbacks. Both the measure and the model are applied to benchmark problems as well as randomly generated problems. The new measure and model are comparable to the existing models and measures

Cell formation using sequence information and neural networks

Most neural network approaches to the cell formation problem have been based on Competitive Learning-based algorithms such as ART (Adaptive Resonance Theory), Fuzzy Min- Max or Self-Organizing Feature Maps. These approaches do not use information on the sequence of operations on part types. They only use as input the binary part-machine incidence matrix. There are other neural network approaches such as the Hopfield model and Harmony Theory that have also been used to form manufacturing cells but again without considering the sequence of operations. In this paper we propose a sequence-based neural network approach for cell formation. The objective function considered is the minimization of transportation costs (including both intracellular and intercellular movements). Soft constraints on the minimum and maximum on the number of machines per cell can be imposed. The problem is formulated mathematically and shown to be equivalent to a quadratic programming integer program that uses symmetric, sequence-based similarity coefficients between each pair of machines. To solve such a problem two energy-based neural network approaches (Hopfield model and Potts Mean Field Annealing) are proposed

Variant-oriented Planning Models for Parts/Products Grouping, Sequencing and Operations

This research aims at developing novel methods for utilizing the commonality between part/product variants to make modern manufacturing systems more flexible, adaptable, and agile for dealing with less volume per variant and minimizing total changes in the setup between variants. Four models are developed for use in four important domains of manufacturing systems: production sequencing, product family formation, production flow, and products operations sequences retrieval. In all these domains, capitalizing on commonality between the part/product variants has a pivotal role. For production sequencing; a new policy based on setup similarity between product variants is proposed and its results are compared with a developed mathematical model in a permutation flow shop. The results show the proposed algorithm is capable of finding solutions in less than 0.02 seconds with an average error of 1.2%. For product family formation; a novel operation flow based similarity coefficient is developed for variants having networked structures and integrated with two other similarity coefficients, operation and volume similarity, to provide a more comprehensive similarity coefficient. Grouping variants based on the proposed integrated similarity coefficient improves changeover time and utilization of the system. A sequencing method, as a secondary application of this approach, is also developed. For production flow; a new mixed integer programing (MIP) model is developed to assign operations of a family of product variants to candidate machines and also to select the best place for each machine among the candidate locations. The final sequence of performing operations for each variant having networked structures is also determined. The objective is to minimize the total backtracking distance leading to an improvement in total throughput of the system (7.79% in the case study of three engine blocks). For operations sequences retrieval; two mathematical models and an algorithm are developed to construct a master operation sequence from the information of the existing variants belonging to a family of parts/products. This master operation sequence is used to develop the operation sequences for new variants which are sufficiently similar to existing variants. Using the proposed algorithm decreases time of developing the operations sequences of new variants to the seconds

Component grouping for GT applications - a fuzzy clustering approach with validity measure

The variety of the currently available component grouping methodologies and algorithms provide a good theoretical basis for implementing GT principles in cellular manufacturing environments. However, the practical application of the grouping approaches can be further enhanced through extensions to the widely used grouping algorithms and the development of criteria for partitioning components into an 'optimum' number of groups. Extensions to the fuzzy clustering algorithm and a definition of a new validity measure are proposed in this paper. These are aimed at improving the practical applicability of the fuzzy clustering approach for family formation in cellular manufacturing environments. Component partitioning is based upon assessing the compactness of components within a group and overlapping between the component groups. The developed grouping methodology is experimentally demonstrated using an industrial case study and several well known component grouping examples from the published literature