用网络流模型优化制造系统中的工序分组，提升设备利用率。
Solving Generalized Grouping Problems in Cellular Manufacturing Systems Using a Network Flow Model
- 将工序分组建模为最小费用网络流问题，自动确定分组数量。
- 两阶段求解：先分工序族，再分配设备到细胞，目标是最大化设备使用率。
- 相比传统方法更灵活，适合复杂多工艺路线的制造系统。
本文研究细胞制造系统（CMS）中的广义分组问题，其中零件可能拥有多个工艺路线。每个工艺路线列出了对应操作所需的机器。受网络流算法广泛应用的启发，本文将工艺路线族形成问题建模为单位容量最小费用网络流模型，目标是最小化同一族内工艺路线间的机器需求差异。所提模型无需预先指定零件族数量即可最优求解工艺路线族形成问题。该过程是分层流程的第一阶段。第二阶段（设备单元形成）提出两种方法：一种是二次分配规划（QAP）公式，用于在预设数量的细胞中同时分配工艺路线族和机器，以最大化总设备利用率；另一种是层次化启发式方法。测试问题的计算结果表明，QAP与启发式方法得出相同结果。
原文摘要 · Abstract (English)
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.
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