(173e) Modularity Measures: Concepts, Computation, and Applications to Manufacturing Systems

Modularization is an organization strategy that is used in living, socio-economic, and industrial systems to facilitate learning and evolution and to cope with complexity [1,2]. For instance, biological networks and the human body exhibit high modularity [3,4]. This organization structure facilitates specialization of components (e.g., organs and metabolic cycles) and enables management of large numbers of functions. Modularity concepts have also been recently explored in the context of industrial production (manufacturing) systems such as chemical processes, energy systems, and infrastructures. Industrial production systems can be built from small-scale and standardized equipment modules that perform well-defined tasks and that are coupled together using well-defined and sparse interfaces [5,6].

The concept of modularity is pervasive in science and engineering but, surprisingly, there are few quantifiable measures of modularity. In the metal processing industry, for instance, a module is defined as a technically and organizationally limited area of a facility that fulfills a defined task in terms of company-internal or -external salable goods and services [7]. In the process industry, a module is defined as an unmodifiable element that provides a dedicated function for the process and is reusable during the planning or realization of modular plants [8]. While these definitions are intuitive, they do not provide means to quantify modularity. Specifically, under these definitions, any equipment unit or an entire facility itself can be a module. Moreover, these definitions fail to capture aspects such as transportability and dimensions.

In this work, we propose measures to quantify the modularity of manufacturing systems and optimization formulations to compute them. We claim that, from a manufacturing perspective, a system is deemed modular if: i) the equipment units that compose it form clusters (modules) of dense connectivity (i.e., difficult module construction is performed off-site), ii) connectivity between modules is sparse (i.e., easy module assembly is performed on-site), iii) the number of modules is small, and iv) the module dimensions facilitate transportation. In the proposed framework, a facility has a topology that is modeled as a graph. Then, the proposed measure is computed for a graph by finding the partition that induces the maximum modularity (given a fixed number of modules). We show that this measure can be computed by solving a convex mixed-integer quadratic program. We also show that the mixed-integer representation allows us to impose additional features such as module dimensions and to identify multiple solutions that give the same level of modularity. We compare the proposed measure against existing measures to highlight the advantages and disadvantages from a manufacturing perspective [9]. Moreover, the proposed measure can be used within optimal design formulations and in other applications beyond manufacturing (e.g., design of control architectures and decomposition of large sets of equations).

References

[1] Simon HA. The architecture of complexity. Proceedings of the American philosophical society. 1962; 106(6): 467–482.

[2] Langlois RN. Modularity in technology and organization. Journal of economic behavior & organization. 2002; 49(1): 19–37.

[3] Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabasi AL. Hierarchical organization of modularity in metabolic networks. science. 2002; 297(5586): 1551–1555.

[4] Meunier D, Lambiotte R, Bullmore ET. Modular and hierarchically modular organization of brain networks. Frontiers in neuroscience. 2010; 4: 200.

[5] Seifert T, Sievers S, Bramsiepe C, Schembecker G. Small scale, modular and continuous: a new approach in plant design. Chemical Engineering and Processing: Process Intensification. 2012; 52: 140–150.

[6] Baldea M, Edgar TF, Stanley BL, Kiss AA. Modular Manufacturing Processes: Status, Challenges, and Opportunities. AIChE Journal. 2017; 63(10): 4262–4272.

[7] Wiendahl H-P., Nofen D., Klußmann J.H., and Breitenbach F. Planung Modularer Fabriken. Carl Hanser Verlag GmbH & Co. KG. 2005.

[8] Hohmann L, Kossl K, Kockmann N, Schembecker G, Bramsiepe C. Modules in process industry - A life cycle definition. Chemical Engineering and Processing: Process Intensification. 2017; 111: 115 –126.

[9] Newman MEJ. Modularity and community structure in networks. Proceedings of the National Academy of Sciences. 2006; 103(23): 8577–8582.