**1. Introduction**

Complex projects are a focus of research in project management to meet social demands. For instance, infrastructure projects are being pursued at a breakneck pace in developing countries in water and sewage, electricity, and transportation and communications, while developed countries are improving infrastructure systems to solve outstanding problems [1]. Complex projects refer to construction projects that are large in scale and involve large investments, multiple stakeholders, complex interactions, and a dynamic environment. They thus feature a high level of uncertainty, unknown dependencies, and unpredictability [2]. Uncertainty in complex projects leads to unexpected events, such as incorrect on-site exploration and accidents, while organizations handling such projects need to be flexible because of the unknown dependencies [2]. Unexpected situations often lead to construction delays [3,4]. Therefore, project success is closely related to project complexity, such as the scale and technical difficulty [5,6].

Breaking down project complexity is useful to help practitioners identify complex projects more accurately. It is recognized that project complexity has organizational and technical types [7]. Given the long project life cycle and uncertain final project scope, the dynamic and growth-related traits of projects helped researchers define project complexity from the perspectives of time and space [8]. The composition of project complexity also includes information and targets [9], communication [10], interface management [11], cost

**Citation:** Yang, L.; Hu, X.; Zhao, X. Organization Synchronization in Response to Complex Project Delays: Network-Based Analysis. *Buildings* **2022**, *12*, 662. https://doi.org/ 10.3390/buildings12050662

Academic Editor: Audrius Banaitis

Received: 4 April 2022 Accepted: 13 May 2022 Published: 16 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

performance [12], and a dynamic environment [13]. Hence, it is important to summarize existing interaction ways among complex project organizations [14].

Organizations dynamically interact with each other in complex projects and form the behavior of organization synchronization once an accident, such as a delay, occurs [15,16]. Organization interactions are generally made up of different types, such as written, oral, and technical interactions [17,18]. However, it remains unclear in which interaction ways organizations synchronize effectively and which organizations have strong synchronization capabilities. Therefore, this study aimed to resolve the organization synchronization issue by (1) finding the most key construction delay factors (CDFs); (2) establishing an index system of organization interactions; and (3) determining the synchronizability of important organizations and effective interaction ways. The complex network synchronization (CNS) theory was adopted to analyze the process of organization synchronization and a case study was used to validate the application of the CNS theory. Thus, this study contributes to the theory and practice of organizational synchronization and provides a comprehensive way to evaluate synchronizability and the importance of nodes.

#### **2. Literature Review**

#### *2.1. Construction Delay Factors*

Construction delays in complex projects refer to time extensions that result from multiple causes related to different stakeholders at different project phases. The causes of delays are mainly related to project partners, such as clients, contractors, designers, suppliers, investors, laborers, supervisors, and governments [19–23]. Other researchers indicated that some external factors have a large influence on project performance, such as dangerous environments and terrible weather [21,24], rising prices [20,25,26], and cultural influences [27]. As shown in Table 1, we summarized a total of 27 CDFs gleaned from the literature review and deconstructed the causes of delays from the perspective of stakeholders, including financial institutions, clients, contractors, designers, supervisors, governments, and external factors.

Previous studies indicated that the responsibility for delays should be attributed to contractors and their direct stakeholders, such as suppliers and clients [20,26]. For these organizations, the causes of delays include construction mistakes, site management, delayed payments and other problems with materials, personnel, and equipment [3,20,28]. The coordination of service providers related to project sites and project works was particularly weak [29], and poor communication or coordination problems may lead to rework [3,24,27,30,31]. Therefore, smooth coordination is required in order to successfully remain on schedule to prevent variations in critical activities [26]. However, few previous studies have explained how delay issues are solved by organization synchronization in the context of complex projects, which involve large numbers of organizations and complex organization interactions.


**Table 1.** Summary of construction delay factors.



#### *2.2. Organizational Synchronization in Complex Projects*

Synchronization is a ubiquitous process emerging from many dynamically interacting units in many different areas, such as biological ecology, electronic circuits, social relationships, and economic management [36,37]. Examples include numerous fireflies suddenly flashing at the same time and clocks swinging at the same frequency after some imperceptible movements. Importantly, synchronization not only involves multiple interacting units but also the interaction of several signal units that transmit synchronization signals to the other units [38]. Once a complex system has been disturbed by an external or internal accident, the synchronization phenomenon first occurs in the local community that is formed by the signal units and then spreads to the whole system. When achieving a state of synchrony, all units show a high degree of coordination and the complex system reaches a high level of stability.

In other words, the synchronization process helps to rebalance and restore a disturbed complex system. In complex project systems, organizations are the actors who interact to positively solve delay issues and achieve a state of synchrony. Thus, analysis of organization synchronization can contribute to our understanding of delays in complex project management. Similar to the definition of synchronization, we assume that 'organization synchronization' means a dynamic process in which project organizations interact with each other to effectively respond to project accidents and restore the stability of complex project systems. After organizations have been synchronized, it is possible to achieve effective cooperation between organizations and faster information transmission in complex systems [39–41].

Moreover, to better understand organization synchronization, studies need to focus on organization interactions and the early interaction behaviors of signal organizations in complex projects. Generally, organization interactions can be generated in many ways, such as by tasks, documents (e.g., contracts), commitments or trust, information technologies, communications, information sharing, knowledge exchanges, and management procedures [42–48]. However, few studies have established an index system of interaction ways and evaluated the frequency of each interaction way in project organizations. As shown in Table 2, we summarized these interactions and classified them into written interactions, oral interactions, technical interactions, and meetings.


**Table 2.** Organization interactions in complex projects.

Organization interactions and related communication issues have been widely studied by using the Social Network Analysis (SNA) theory in the construction field [43,54–57]. For example, Li adopted SNA to study the influence of Building Information Modeling on project organizations and the communication patterns [58]. Admittedly, SNA is a useful method for solving organization interaction problems. However, further theoretical development would be needed if SNA is to be used to deal with synchronization issues.

In contrast, the complex network synchronization (CNS) theory, which was derived from the complex network theory, has specifically been developed to explore the synchro-

nization process. Watts and Strogatz (1998) first introduced the network theory to analyze the synchronization of cricket chirps [59]. According to Li, previous studies on the CNS theory can be divided into four types: synchronization of a chaotic system, synchronization within a network, synchronization between different networks, and synchronization of a multi-layer network [60]. Organization synchronization studies belong to the second type, which refers to the synchronization behavior of internal network nodes. In addition, most of the research concentrates on cumbersome mathematical calculations and theoretical modeling in different areas. Few studies have applied the CNS theory to figure out the organization synchronization process, particularly in complex projects.

Network synchronizability is greatly affected by the structural properties [61,62], which rely on the characteristics of nodes and links in a complex network. In addition, the structural properties of a network are generally evaluated by diverse parameters, many of which have been found to have numeric relationships with network synchronizability. For instance, degree, average path length, heterogeneity in the degree distribution, and node betweenness centrality vary inversely with network synchronizability [63,64], and modularity, which measures the density between different communities, is positively proportional to network synchronizability [38]. However, these studies assessed network synchronizability based on one single parameter. It is important to provide a sound analysis by combining the relationships between network synchronizabilty and as many parameters as possible.

As mentioned above, organization synchronization emerges from a local synchronization initiated by several signal organizations. Some investigations have shown that flows of large amounts of information or intensive interactions between the signal organizations contribute to a faster synchronization process [38,65]. Hence, signal nodes in complex networks have two general traits: (1) a high degree of connection with the other nodes; and (2) initial nodes that perceive disturbance factors in complex networks and transmit synchronization signals. Correspondingly, in complex projects, the first organization to perceive delay factors and its closely related stakeholders may be signal nodes if they can be proved to be highly linked with the other organizations. To find signal organizations, it is critical to evaluate the importance of nodes from the network's perspective. Node importance is generally assessed by two parameters: (1) node degree [66,67]; and (2) node centrality, including degree centrality, closeness centrality, betweenness centrality, and eigenvector centrality [68]. Nevertheless, conflicting results frequently occur because node importance usually ranks differently between the analysis of the five parameters. Hence, we ranked network nodes and found signal organizations by unifying the above-mentioned five node parameters.
