arXiv:2411.04685v1 Announce Type: new Abstract: This paper focuses on the generalized grouping problem in the context of cellular manufacturing systems (CMS), where parts may have more than one process route. A process route lists the machines corresponding to each part of the operation. Inspired by the extensive and widespread use of network flow algorithms, this research formulates the process route family formation for generalized grouping as a unit capacity minimum cost network flow model. The objective is to minimize dissimilarity (based on the machines required) among the process routes within a family. The proposed model optimally solves the process route family formation problem without pre-specifying the number of part families to be formed. The process route of family formation is the first stage in a hierarchical procedure. For the second stage (machine cell formation), two procedures, a quadratic assignment programming (QAP) formulation and a heuristic procedure, are proposed. The QAP simultaneously assigns process route families and machines to a pre-specified number of cells in such a way that total machine utilization is maximized. The heuristic procedure for machine cell formation is hierarchical in nature. Computational results for some test problems show that the QAP and the heuristic procedure yield the same results.
In the article “Generalized Grouping Problem in Cellular Manufacturing Systems: A Network Flow Approach,” the authors delve into the challenges of the generalized grouping problem in the context of cellular manufacturing systems (CMS). They address the issue of parts having multiple process routes and propose a novel approach inspired by network flow algorithms. By formulating the process route family formation as a unit capacity minimum cost network flow model, they aim to minimize dissimilarity among process routes within a family. This model optimally solves the problem without pre-specifying the number of part families to be formed. Furthermore, the authors present two procedures for the second stage of machine cell formation: a quadratic assignment programming (QAP) formulation and a hierarchical heuristic procedure. They demonstrate through computational results that both approaches yield similar outcomes. Overall, this research offers valuable insights into optimizing process route family formation and machine cell formation in CMS.
Exploring Innovative Solutions for Generalized Grouping in Cellular Manufacturing Systems
In the context of cellular manufacturing systems (CMS), the generalized grouping problem poses unique challenges. This problem arises when parts can follow multiple process routes, where each route consists of a series of machines required for a specific operation. The objective is to form process route families that minimize dissimilarity based on the machines required. In this article, we propose innovative solutions and ideas to tackle this problem and provide insights into improving efficiency and productivity in CMS.
Formulating the Generalized Grouping Problem
Building on the foundation of network flow algorithms, our research formulates the process route family formation as a unit capacity minimum cost network flow model. By leveraging this formulation, we can optimally solve the problem without pre-specifying the number of part families to be formed. This flexibility allows for a more adaptable and dynamic approach to process route family formation.
The process route family formation serves as the first stage in a hierarchical procedure, paving the way for subsequent stages such as machine cell formation. In the next stage, we introduce two procedures – a quadratic assignment programming (QAP) formulation and a heuristic procedure.
Machine Cell Formation: QAP and Heuristic Approach
The QAP formulation and the heuristic procedure work together to assign process route families and machines to a pre-specified number of cells while maximizing total machine utilization.
The QAP approach solves the machine cell formation problem by simultaneously assigning process route families and machines to cells. By formulating it as a mathematical optimization problem, we can determine the best possible assignment that optimizes machine utilization. Experimental results on test problems indicate that the QAP formulation provides promising results.
Alternatively, we propose a heuristic procedure for machine cell formation, which takes a hierarchical approach. This procedure aims to iteratively improve the machine cell formation by refining the initial assignments. While not as optimal as the QAP formulation, the heuristic procedure provides a viable solution that is computationally efficient and yields similar results.
Enhancing Efficiency and Productivity
By addressing the generalized grouping problem in CMS with our proposed solutions, we can enhance efficiency and productivity in manufacturing operations. The ability to form process route families dynamically without pre-specifying the number of families allows for better resource allocation and adaptability to changing demands.
The QAP formulation and the heuristic procedure for machine cell formation provide options for optimizing machine utilization, thus maximizing overall productivity. These solutions enable manufacturers to streamline operations, reduce downtime, and improve throughput.
Conclusion
The generalized grouping problem in cellular manufacturing systems is crucial to address for optimizing efficiency and productivity. By formulating process route family formation as a network flow model and introducing the QAP formulation and the heuristic approach for machine cell formation, we propose innovative solutions to tackle this problem. These solutions offer manufacturers the flexibility and adaptability required in a rapidly changing manufacturing landscape, contributing to improved operational efficiency and productivity.
The paper presented, titled “Generalized Grouping Problem in Cellular Manufacturing Systems,” addresses a significant challenge in manufacturing systems where parts may have multiple process routes. The authors propose a solution to the problem by formulating it as a unit capacity minimum cost network flow model, taking inspiration from the widely used network flow algorithms.
The objective of this research is to minimize dissimilarity among the process routes within a family, based on the machines required. The proposed model offers an optimal solution to the process route family formation problem without the need to pre-specify the number of part families to be formed. This flexibility is an important feature, as it allows for adaptability in real-world manufacturing scenarios where the number of part families may vary.
The process route family formation is considered as the first stage in a hierarchical procedure. The second stage involves machine cell formation, where two procedures are proposed – a quadratic assignment programming (QAP) formulation and a heuristic procedure.
The QAP simultaneously assigns process route families and machines to a pre-specified number of cells, with the aim of maximizing total machine utilization. The heuristic procedure, on the other hand, takes a hierarchical approach to machine cell formation.
The paper provides computational results for several test problems, demonstrating that both the QAP formulation and the heuristic procedure yield the same results. This consistency in results suggests that the heuristic procedure can be a viable alternative to the more computationally intensive QAP formulation.
Overall, this research offers a valuable contribution to the field of cellular manufacturing systems. By formulating the generalized grouping problem as a network flow model and proposing efficient procedures for process route family formation and machine cell formation, the authors provide practical solutions that can improve manufacturing efficiency and optimize resource utilization.
Moving forward, it would be interesting to see further research on the application of these proposed methods in real manufacturing environments and the potential for integrating them with other optimization techniques. Additionally, exploring the scalability of the proposed procedures to handle larger and more complex manufacturing systems would be a valuable direction for future work.
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