Solving Generalized Grouping Problems in Cellular Manufacturing Systems Using a Network Flow Model

TL;DR

This paper introduces a network flow model to optimize process route grouping in cellular manufacturing, improving machine utilization and reducing dissimilarity among process routes.

Contribution

It formulates the process route family formation as a minimum cost network flow problem, enabling optimal grouping without pre-defining the number of families.

Findings

The network flow model effectively minimizes dissimilarity among process routes.

The QAP and heuristic procedures produce identical results in test cases.

The approach enhances machine utilization in cellular manufacturing systems.

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.