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.

翻译：本文聚焦于单元制造系统（CMS）中的广义分组问题，其中零件可能具有多条工艺路线。工艺路线列出了对应零件各工序所需的机器。受网络流算法广泛应用的启发，本研究将广义分组的工艺路线族构建问题表述为单位容量最小成本网络流模型，其目标是最小化同一族内各工艺路线之间的差异性（基于所需机器）。所提出的模型能够在不预先指定待构建零件族数量的情况下，最优求解工艺路线族构建问题。工艺路线族构建是分层流程的第一阶段。针对第二阶段（机器单元构建），本文提出了两种方法：二次分配规划（QAP）模型与启发式方法。QAP模型将工艺路线族与机器同时分配到预设数量的单元中，以实现总机器利用率最大化。机器单元构建的启发式方法本质上是分层进行的。部分测试问题的计算结果表明，QAP方法与启发式方法可获得相同的结果。