## 2 Related Work  
Modular design, in a wider sense, results in such benefits as simplicity, because it reduces the size of the problem that needs to be solved, and velocity, since by solving smaller problems in a parallel way, the time needed to solve the overall problem can be mitigated [13]. [PERSON] and [PERSON] [14] assert that an ad hoc division of a process into modules means to create a hierarchical structure of subprocesses which can only help to better understand a process model. [PERSON] et al. [15] argue that process modularity has significant potential to impact new product introduction performance and point out that product and/or process modularity are important design principles for addressing the challenges associated with rapidly changing technologies. [PERSON] et al. [16] studied the theoretical relationship between product and process modularity and how these system properties affect manufacturing agility and the firm growth performance. Several authors [17; 18; 19; 20] agree that there are certain linkages between product and process modularity, since, like product modules, process modules are characterized by clusters of locally connected elements [21] that have few strong organizational ties [22]. According to [PERSON] and [PERSON] [23], modularity of product design stimulates the creation of a job family in manufacturing and assembly processes, whereas in the next phases, this leads to modifying the number of operations in workstations. [PERSON] et al. [24] provided evidence of the cause-effect trend between modularity and reduction in manufacturing lead time for the orders received by a bus manufacturing company. [PERSON] et al. [25] stated that modularity positively impacts manufacturing time, but without enumeration proof. The manuscript [26] provided the example where time is minimized by modularity; other authors [24] studied modularity in relation to delivery time, while delivery time variables were minimized for this purpose. In the latest years, some articles investigated the positive modularity impacts on manufacturing lead time and throughput rate, but only marginally in other related domains (e.g., Refs. [27; 28; 29; 30; 31]).  
Experiences from Danish manufacturing companies showed that modularity principles are mostly applied in complex manufacturing processes, and that high levels of implementation of JIT shorten lead times, as might be expected [32]. The authors of [33] provided evidence that lower levels of process modularity can cause a higher number of errors than the same process with higher modularity. Moreover, in the case of under-modularization, there are difficulties in maintaining the large modules, while in terms of overmodularization, the disadvantage is that there is a large number of connections that need to be managed. A possible solution to overcome this issue is to identify the optimum number of product/process modules. The modularity optimization problem includes several methods for detecting clusters in complex networks to estimate the optimal number of clusters for a given network [34]. In this context, [PERSON] and [PERSON] [35; 36] proposed the optimal modularity indicator (Qd), which is defined as the fraction of connections within a group in the actual network minus expected fraction of connections in a random network. [PERSON] et al. [37] explored optimization issues in reconfigurable manufacturing systems with the aims to maximize the system modularity and throughput rate, and to minimize system completion time and system cost. Also, it is worth mentioning other related research works, such as by [PERSON] et al. [38], [PERSON] et al. [39], and [PERSON] et al. [40], that deal with manufacturing modularity in the context of throughput rate.  
The results of this survey, from which the selected publications are mentioned above, revealed that the relationships between modularity and manufacturing lead time and between modularity and throughput rate have not been treated and solved previously.