*3.2. Data Collection*

The preliminary literature review yielded a list of CDFs and interaction ways. To improve data accuracy, a further expert interview was conducted with three experienced project managers from contractor and client organizations. All experts had either more than 15 years of experience in construction projects or participated in complex projects. They were required to assess the results of the literature review, summarize 10 types of common organizations in complex projects, and initially discuss general interaction ways between these organizations. According to the interview results, complex project organizations include financial institutions (F), governments (G), including governmentfunded representatives and departments approving and supervising construction projects, clients (B), contractors (C), supervisors (S), designers (D), operation units (O), the public (P), investors (I), and academic researchers. In addition, some interactions existing only between particular stakeholders and relevant contract relationships were removed according to the suggestions from the expert team. Thus, the 10 refined common interactions were oral task assignments, instructions, oral reports, inspections of work, discussions and studies, meetings, letters, networks, telephone communications, and telegraph communications.

Focusing on the 10 types of organizations, a questionnaire survey was designed to judge the effect of the 27 CDFs on the project period and the four types of relationships mentioned above. The questionnaire consisted of four main sections. The first section was used to obtain a profile of each respondent and collected information such as work experience, geological distribution, and organization types. The second section assessed the influence of the 27 CDFs on complex projects by a five-point Likert scale (1 = very low, 2 = low, 3 = medium, 4 = high, 5 = very high). The third section quantified the above-mentioned four kinds of relationships (inter-organization, organizations and CDFs, organizations and interaction ways before the delay, and organizations and interaction ways after the delay). The last section was used to obtain text solutions to construction delay problems from these experienced respondents.

The specific participants were first selected via the stratified sampling strategy [69]. Then, a total of 175 questionnaires were sent out via paper or electronic files and 173 questionnaires were returned. There were 169 valid questionnaires, meaning a valid response rate of 96.57%. The rate was relatively high compared with other studies and acceptable rates, including 20.13% in [28], 11.1% in [69], 13.02% in [70], and 70% in [71]. The sample size of 169 was adequate for the data analysis and well above the minimum requirement of 30 according to the central limit theorem [35]. Around 59.76% of the respondents had at least 5 years of experience in working with complex projects. A total of 38.46% of the respondents were academic staff from universities, and the other respondents had an even distribution in terms of organizations and geography.

#### *3.3. Statistical Analysis*

Cronbach's alpha (α) is widely adopted to prove the inter-reliability of survey data and its value ranges from 0 to 1 [72,73]. As stated in many studies [74–76], an acceptable α score is generally larger than 0.70. As tested by SPSS 25.0, the α of 0.933 within the entire survey sample indicated that the questionnaire survey had a high degree of reliability and the fact that the α of each CDF was below 0.933 proved the strong inner consistency of all scales. As shown in Table 3, the mean scores of the CDFs range from 3.06 to 4.06. To select the critical CDFs, the normalized values of the mean scores were calculated, as recommended by Xu et al. and Zhao et al. [77,78]. A total of 15 CDFs with normalized values above 0.50 were regarded as critical factors.

Figure 2 shows the proportion of organization interaction ways before and after delays. Whether delays occur or not, the most frequent means of interaction was meetings. After project delays, the ratio of utilization of oral task assignments, networks, and instructions decreased by 41.38%, 33.14%, and 28.17%, respectively. This indicates that inefficiencies in organizational cooperation became evident in cases of accidents, leading to a further loss of control and poor outcomes. Attention needs to be paid to effective interaction ways, such as meetings and discussions, in order to enhance the efficiency of collaboration and information sharing.

#### *3.4. Network Parameters*

According to the literature review, network synchronizability is related to two types of parameters: (1) global network parameters, including average length path, modularity, and clustering coefficient; and (2) node parameters, including degree and betweenness centrality. The latter type is indirectly related to network synchrony by illustrating signal nodes. Hence, we explain network synchronizability in terms of global network parameters and explore signal organizations and key CDFs in light of node parameters. As shown in Table 4, all involved parameters are explained. Both key CDFs and signal organizations are explained by multiple parameters; thus, conflicting results are prone to occur. Therefore, we summed the rank value of the corresponding parameters to obtain a comprehensive rank.


**Table 3.** Ranking of CDFs.

<sup>1</sup> Normalized value (NV) = (mean − minimum mean)/(maximum mean − minimum mean).


**Table 4.** Parameters of complex networks.

#### **4. Case Study**

Phase I of the Hangzhou Metro Line 4 project was selected as a case study for the following reasons. First, it is a typical complex project considering the interacting project complexities due to the organizational structure, technologies, etc. Second, seven delays indeed occurred in the case project and led to a huge final cost of as much as 14.35 billion RMB. It was supposed to be operational on 29 December 2017, but the operational trial was postponed by six months to 6 June 2018. The actual causes of the delay reported by the news included a huge financial risk, prominent problems of land expropriation, an unreasonable timeline for clients, an improper organizational construction design, safety accidents, disharmony with neighbors, and the excavation of aerial bombs. Third, as a completed complex project, ample data could be collected to determine the project organizations. Three official websites (Zhejiang Provincial Development and Reform Commission, Hangzhou City Development and Reform Commission, and Hangzhou Metro) were the major sources of data on project organizations and publish project information such as progress and participants. By a full-text search and the use of Web crawlers on the websites in chronological order, a total of 357 texts were obtained and split into substantial quantities of words. By selecting words with the organization property, more than one hundred organizations were found to have participated in the completion of this project.

#### *4.1. Network Nodes and Links*

According to the research framework, there are three types of network nodes in a theoretical complex project system, including 15 CDFs (Table 3), 10 types of project organizations, and 10 common organization interaction ways. Before the evaluation of network links, a focus group was formed to discuss the suitability of the theoretical nodes in the case study. Seven experts participated in this project and came from various organizations, including the client, two construction units, two supervision units, one material supplier, and the investor. They consistently agreed that the initial selection of 15 CDFs and 10 interaction ways could be applied to the case study. Importantly, the expert team selected 51 major project organizations according to their experience in the case study. As shown in Table 5, the project organizations in the case study consisted of the financial institution, the client, 14 contractors, 10 supervision units, 3 design units, 13 material suppliers, the government, the investor, the operation unit, and 7 public units. The rule used when coding the nodes was that the first number represents the organizational type and the second number represents the numerical reference method.


**Table 5.** Node coding.

Network links refer to the four kinds of relationships between the 15 CDFs, the 51 project organizations, and the 10 interaction ways. The weights of network links were assessed by a questionnaire survey similar to the one described in Section 3.2 (Data Collection), and four corresponding matrices were formed for network visualization. As shown in Table 6, a sample matrix consists of *i* row nodes ( *Nr*<sup>1</sup> ∼ *Nri*) and *j* column nodes ( *Nc*<sup>1</sup> ∼ *Ncj*). The weight of the link between *Nri* and *Ncj* is defined as *wij*. Note that diagonal values such as *w*<sup>11</sup> are 0 in complex network analysis. For example, the 51 project organizations are both row and column nodes in the IO matrix, and 782 links were found and weighted by the questionnaire survey; in the OCDF matrix, the 51 project organizations are row nodes, the 15 CDFs are column nodes, and 66 links exist between these nodes.

**Table 6.** Sample matrix of complex networks.


The tools available for analyzing complex networks include GEPHI, MATLAB [67], NETWORKX, IGRAPH, Python, UCINET [81], NetMiner, and Pajek [82,83]. Among these tools, NetMiner is user-friendly and provides a sufficient parameter analysis. Therefore, the four matrices were input into NetMiner 4.0 and nodes were styled using different colors and types. For instance, Figure 3 shows the inter-organization network visualized by NetMiner 4.0, where nodes are styled as follows: public, red heart; investors/the government, yellow crisscross; operation units, orange star; financial institution, pink pentagon; the client, blue triangles; other construction organizations, rectangles in different degrees of blue. CDFs and interaction ways are styled in purple diamonds and green circles, respectively, in other networks.

**Figure 3.** Inter-organization network.

### *4.2. Parameter Analysis*

4.2.1. Network Synchronizability Analysis

Table 7 summarizes the global features of complex networks based on the four parameters. Network synchronizability is reflected from two perspectives: average path length and modularity. Apart from the IO network, the OCDF network and the OIW network before and after the delay have the same average path length of 1. Thus, the relative synchronizability of the three networks depends on their modularity values. The higher the modularity value is, the better synchronizability the complex network has. As can be seen in Table 6, OCDF ranks first in terms of modularity. Compared with the IO network, the OCDF network has a shorter average path length, showing greater synchronizability. In addition, the organizations interacted more frequently and effectively after the delay because the modularity increased by 47.9%.


**Table 7.** Global features of complex networks.

The IO network has the highest density and clustering coefficient. However, the network performs the best when the values of both parameters are close to 1. This indicates that, in the case study project, organizational relationships were supposed to be enhanced for rapid information flow and effective cooperation.

#### 4.2.2. Key Construction Delay Factors

Table 8 presents a comprehensive ranking of the 15 CDFs based on the analysis of the five parameters. Delay 2 (safety accidents) was recognized as the most influential factor in the case study project. This result is highly consistent with the case study because a total of seven safety accidents occurred from April 2014 to July 2016 and resulted in a project delay as well as four deaths and one injury. The second-ranked CDF is Delay 1 (Prominent problems of land expropriation). It also postponed the project because neighbors around the construction site (Lianzhuang Station) were afraid of damage to the environment. Another four key CDFs include Delay 5 (Unreasonable timelines by clients), Delay 6 (Improper construction design), Delay 7 (Delayed payments), and Delay 9 (High financial risk). After comparing the theoretical key CDFs and the actual reasons for delays, we found five 'overlapping' factors among the seven actual causes of delay, proving the applicability of the CNS theory to complex projects.


**Table 8.** Node parameters of construction delay factors.

#### 4.2.3. Signal Organizations in Synchronization

Signal organizations are closely connected to other units and are usually the first ones to identify delays. In this study, five parameters (degree, degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality) were analyzed to find critical organizations in the IO network. Figure 4a, Figure 4b, and Figure 4c represent the degree, degree centrality, and betweenness centrality in the IO network, respectively. The other two-parameter analysis yielded consistent results and had similar graphs to those shown in Figure 4. As shown in Figure 4, the signal organizations consist of the client,

investors/governments, the operation unit, two design units (D1 and D3), one public unit (P7), one supervision unit (S1), and one contractor (C12).

**Figure 4.** IO network: (**a**) degree; (**b**) degree centrality; (**c**) betweenness centrality.

Figure 5 presents the visualization of the OCDF network, revealing the relationships between organizations and CDFs. One can easily observe that those signal organizations are close to the seven key CDFs. S1 and C12 are the supervisors and contractors, respectively, in the southern project section who were the parties responsible for safety accidents that occurred in this section. P7 represents the community protesting the construction of Lianzhuang Station; the construction design supplied by D1 and D3 had several mistakes and led to rework. In addition, the government and the client failed to solve the problems of land expropriation and proposed an unreasonable project period due to an underestimation of the construction project's difficulty. The consistency of signal organizations and responsible units also proves the feasibility of the CNS theory's application. Thus, it is possible to predict the specific organizations responsible for delays in complex projects.

**Figure 5.** OCDF network.

4.2.4. Effective Interactions in Organization Synchronization

The above-described research results show that the network synchronizability after the delay increased, and seven key CDFs and related signal organizations were accurately identified. In other words, when faced with the key CDFs, signal organizations interacted with each other to achieve better cooperation. Hence, we determined the variations in organization interaction ways. Figure 6 illustrates the degree distribution of the OIW network before and after the delay. As can be intuitively seen in Figure 6, the values for Inf 6 (Meetings), Inf 3 (Oral reports), Inf 5 (Discussions and studies), and Inf 2 (Giving instructions) are large; thus, they possibly play leading roles in organization synchronization.

Further comprehensive studies were conducted to determine the importance of interaction ways in organizations and make a comparison before and after the delay. Tables 9 and 10 present the parameter values and rankings of the 10 interaction ways. We found that discussions and studies, meetings, and the Internet were used more frequently after the delay, indicating the effectiveness of these three interaction ways in organization synchronization.

**Figure 6.** Degree distribution: (**a**) OIW network before the delay; (**b**) OIW network after the delay. **Table 9.** Ranking of interaction ways before the delay.


**Table 10.** Ranking of interaction ways after the delay.


#### **5. Discussion**

The application of the CNS theory lends credence to the study of organization synchronization in complex projects. To achieve our research objectives, this study involved network synchronizability analysis, six key CDFs, specific signal organizations, and effective interaction ways in the synchronization process.

Network synchronizability was tested in four kinds of networks by two global parameters (average path length and modularity). Results show that the network synchronizability was improved because the modularity increased by 47.9%, while the average path length

remained the same after the project delay. However, it is not clear whether the synchronizability after the delay reached a level that is sufficient for complex projects since there is little similar research. Thus, to discuss the reasonableness of the results, a further review of the literature was used to check whether the case study project had met the boundary conditions. This study was based on a rule that states that network synchronizability is inversely proportional to average path length and positively proportional to modularity [38]. However, studies have proved that the rule related to average path length is useful when the number of all nodes and new nodes remains the same during the project period [84]. The case study involved a static network analysis focusing on the entire project life cycle, meaning that there was no variation in the number of nodes.

Six key CDFs were identified by statistical and network analysis (Delay 2 (Safety accidents), Delay 1 (Prominent problems of land expropriation), Delay 5 (Unreasonable timelines by clients), Delay 6 (Improper construction designs), Delay 7 (Delayed payments), and Delay 9 (High financial risk)). Previous studies also recognized the effect of these factors, and they generally pointed out that delays are most related to clients, contractors, and designers [20,25,32,85,86]. In green buildings, the delivery of materials by suppliers was found to play an important role in the construction process [35]. In contrast, we developed an OCDF network to identify the critical organizations that perceived delays the earliest and transmitted signals the fastest.

Specific signal organizations were found in the case study, including the client, investors/governments, the operation unit, two design units (D1 and D3), one public unit (P7), one supervision unit (S1), and one contractor (C12). Compared with previous studies, we achieved a relatively accurate identification of organizations who are responsible for coping with project delays. It is worth noting that supervisors could play a mediating role in complex projects and contribute to the safety of workers [87,88]. Regarding the frequent safety accidents in complex projects, both contractors and supervisors should be cared for, particularly in terms of psychological needs [89].

Researchers also suggest that organizations are supposed to enhance communication and cooperation, but few have proposed specific strategies. As reviewed above, organization interactions had a positive influence on project performance [90]. Therefore, in the case study, effective interactions, such as discussions and studies, meetings, and the Internet, were recognized as ways to enhance organization synchronization after a delay. In addition to the interaction ways presented in Table 2, invisible ways such as organizational culture and national culture affect decision-making performance and the quality of organization interactions [91,92]. Therefore, it is necessary to perfect the index system of interactions, advance methods for measuring the indices, and understand the mechanisms underlying organization interactions and organization synchronization.

Regarding future research, we recommend that further pilot studies be conducted on diverse complex projects, such as road and bridge construction projects and hydraulic projects. Cross-sectional analysis of these typical projects would contribute to perfecting the index system of interactions and determining the range of good synchronizability levels. In addition, the dimensions of interactions can be broadened to social effects such as communication skills and the degree of truth between two organizations. With a combination of information transmission and social effects, a more comprehensive understanding of organization synchronization can be obtained and implemented to cope with delays or other accidents in complex projects.

#### **6. Conclusions**

Organization synchronization is the dynamic process of recovering a complex project system from a disturbed state to an efficient state and can be used to deal with delays in complex projects. In this study, we adopted the CNS theory to break down the synchronization process by assessing network synchronizability, identifying key CDFs, and finding signal organizations and productive interactions after delays. To address these points, we

established a research framework involving multiple methods and validated the feasibility of applying the CNS theory through a case study.

Our research results can be summarized as follows. First, the network synchronizability was enhanced after the delay in the case study. Second, the six key CDFs in complex projects are Delay 2 (Safety accidents), Delay 1 (Prominent problems of land expropriation), Delay 5 (Unreasonable timelines by clients), Delay 6 (Improper construction designs), Delay 7 (Delayed payments), and Delay 9 (High financial risk). The theoretical CDFs were also found to be commensurate with the actual causes of delay in the case study project. Third, a broad range of signal organizations were accurately identified in the complex project and effective interaction ways (meetings, discussions and studies, and the Internet) can contribute to organization synchronization.

Therefore, this study contributes to both the theory and practice of organization synchronization in complex projects. First, it provides an innovative application of the CNS theory to the field of complex project management. Second, this study offers a comprehensive way to assess network synchronziability and node importance by considering multiple parameters simultaneously. Third, the case study based on a complex project may help researchers implement the research framework and provide useful strategies and practical guidance.

This study has some limitations. There was only one case project in China that was suitable for use in the application of the CNS theory. This brought about the limitation on generalization, which is a common problem when a case study method is used. Nonetheless, Yin argues that the aim of multiple case studies is analytical generalization using the theoretical framework of a study to establish a logic that might apply to other situations rather than statistical generalization as in surveys [93].

**Author Contributions:** Conceptualization, L.Y. and X.Z.; methodology, L.Y. and X.H.; software, X.H.; validation, L.Y. and X.H.; formal analysis, X.H.; investigation, L.Y. and X.H.; resources, L.Y. and X.H.; data curation, L.Y. and X.H.; writing—original draft preparation, L.Y. and X.H.; writing—review and editing, L.Y., X.H. and X.Z.; visualization, L.Y. and X.H.; supervision, L.Y. and X.Z.; project administration, L.Y.; funding acquisition, L.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Science Foundation of China, grant number 71702136.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All the data used in this study are presented in Sections 3 and 4.

**Conflicts of Interest:** The authors declare no conflict of interest.
