Solving generalized grouping problems in cellular manufacturing systems using a network flow model

Purpose This study addresses the generalized grouping problem in cellular manufacturing systems (CMS) where parts may have multiple alternative process routes. The objective is to optimally form process route families by minimizing dissimilarity based on required machines, without pre-specifying the number of families and to subsequently form machine cells that maximize machine utilization. Design/methodology/approach The process route family formation problem is formulated as a unit-capacity minimum-cost network flow model, exploiting the structure and efficiency of network flow algorithms. This constitutes the first stage of a hierarchical solution framework. In the second stage, machine cell formation is addressed using two approaches: a quadratic assignment programming (QAP) formulation and a hierarchical heuristic procedure. Both approaches assign process route families and machines to a fixed number of cells. Findings Computational experiments on test problems demonstrate that the proposed network flow model effectively forms process route families optimally. Results further show that the QAP formulation and the heuristic procedure for machine cell formation produce identical solutions, indicating the effectiveness of the heuristic as a computationally efficient alternative. Research limitations/implications The study assumes deterministic process routes and machine requirements, which may not fully capture variability in real manufacturing environments. Future research may extend the model to incorporate stochastic processing times, dynamic routing or scalability to large industrial systems. Practical implications The proposed framework provides manufacturing planners with an exact and structured approach to forming process route families and machine cells. By eliminating the need to predefine the number of families and offering an efficient heuristic alternative, the method enhances practical applicability in CMS design. Social implications Improved efficiency in cellular manufacturing can contribute to reduced waste, better resource utilization and more sustainable industrial operations, indirectly supporting environmental and economic sustainability goals. Originality/value This research introduces a novel application of unit-capacity minimum-cost network flow modeling to process route family formation in generalized CMS. The integrated hierarchical framework, combining exact optimization and heuristic methods, offers both theoretical rigor and practical efficiency, extending existing CMS grouping methodologies.