We propose a measure to quantify the modularity of industrial production (manufacturing) systems and optimization formulations to compute it. From a manufacturing perspective, we argue that a system is deemed modular if: (a) the equipment units that comprise it form clusters (modules) of dense connectivity (i.e., difficult module assembly tasks are performed off‐site), (b) connectivity between modules is sparse (i.e., easy assembly tasks are performed on‐site), (c) the number of modules is small, and (d) the module dimensions facilitate transportation. We show that the measure proposed satisfies these requirements and that it can be computed by solving a convex mixed‐integer quadratic program. We provide a discussion on advantages and disadvantages of alternative modularity measures used in different scientific and engineering communities. Our results seek to highlight conceptual and computational challenges that arise from the need to define and quantify modularity in a manufacturing context.

中文翻译：

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模块化度量：概念，计算和在制造系统中的应用

我们提出一种措施来量化工业生产（制造）系统的模块性，并通过优化公式对其进行计算。从制造角度来看，我们认为，在以下情况下，系统被认为是模块化的：（a）组成该系统的设备单元形成密集连接的集群（模块）（即，困难的模块组装任务在现场执行），（b）连通性模块之间稀疏（即，可以在现场执行简单的组装任务），（c）模块数量少，并且（d）模块尺寸便于运输。我们表明，提出的度量满足了这些要求，并且可以通过求解凸混合整数二次程序来计算。我们讨论了在不同的科学和工程界使用替代模块化措施的优缺点。