Models and solution methodologies for the generalized grouping problem in cellular manufacturing

In the present work, a generalized framework of machine-part grouping is considered where an operation can be performed on more than one machine. For group formation, both hierarchical and non-hierarchical approaches are proposed that use non-binary part-operation-machine incidence matrix. The grouping objective is to maximize the association of part operations with machines. For the non-hierarchical methods, heuristics based on Lagrangian relaxation are proposed to solve the resulting NP-complete problems. The relative suitability of the proposed approach for the various grouping scenarios is discussed. Numerical examples presented illustrate the issues related to the generalized grouping and various solution methodologies.