Communication barrier-incorporated network modeling for interorganizational opinion formation in emergency events

Abstract

During and after an emergency event, multiple organizations with various specialties are involved in consensus decision-making to reduce the loss of lives and property in a timely manner. However, timely, high-consensus decision-making is challenging due to communication barriers between participating organizations. Thus, this study generalizes a conceptual communication network considering communication barriers by reviewing multiple historical emergencies and proposes a quantitative communication network model by integrating an opinion dynamics model and social network analysis (SNA). An illustrative example is provided by simulating two emergency decision-making scenarios to verify the proposed model. A case study of the 2013 Qingdao oil pipeline explosion is presented to demonstrate the feasibility and applicability of the proposed model. The results of the case study indicate that the proposed model can accurately quantify the impact of communication barriers on the opinion formation time. This research provides a quantitative toolkit for understanding and improving decision-making performance in various emergencies.

Keywords

Interorganizational communication network communication barriers opinion formation emergency decision-making

1 Introduction

Emergency events (e.g., natural and human-made disasters) posing immediate risks to life and property have received increasing attention in recent years due to their destructiveness (e.g., massive casualties and property loss) [2, 11]. The UN 20-year review reported that emergency events have resulted in 1.3 million fatalities and left 4.4 billion people injured, homeless, and displaced, causing $2,908 billion US dollars in direct economic losses [36]. It is crucial for all crisis response organizations (e.g., public security organizations, medical facilities, and transportation departments) to obtain relevant information and expertise in a timely manner to cope with the immediate crisis. After an emergency event, multiple organizations with different types of expertise and resources become part of an interorganizational communication network to provide efficient response and relief. The decision-making time, i.e., the time required for organizations to reach a consensus, significantly influences the effectiveness of the relief actions because the first 72 hours following an emergency event are vital for saving lives

and reducing losses [26].

Unlike conventional decision-making processes, emergency decision-making has unique characteristics: (1) Unpredictability. Emergencies are characterized by uncertainty and sudden occurrence. It is difficult to predict the characteristics, evolution, and destructiveness of emergencies, and it is often impossible to predict which organizations will participate in emergency decision-making. (2) Time pressure. Due to the sudden occurrence, significant harm, and potential secondary disasters, decision-makers must make efficient decisions to reduce losses. Thus, multiple organizations will be involved to achieve efficient and accurate decision-making. It is essential for these organizations to communicate effectively through email, meetings, and reports to prevent communication barriers common in inadequate communication networks [13]. Due to the suddenness of emergency events, various relief organizations may participate temporarily in a communication network. As a result, communication barriers occur, such as a lack of trust and initial communication between organizations, significantly affecting the time to reach a high-consensus decision.

Thus, it is critical to consider communication barriers to determine the opinion formation time in a communication network. This research proposes a quantitative model that considers communication barriers to describe interorganizational decision-making in emergency events. The results provide suggestions for practitioners to quantify the impact of communication barriers on the performance of emergency decision-making. The academic contributions of this study are as follows: (1) a conceptual communication network based on historical emergency events is established. (2) A quantitative communication network model is developed. (3) A quantitative measure to assess the impact of communication barriers on the decision-making time is utilized. Practitioners can use the proposed model to (1) quantify the impact of communication barriers on decision-making performance and (2) perform emergency decision-making involving interorganizational communication and collaboration in various emergency scenarios from the perspective of economics and management.

The remainder of this paper is organized as follows: A literature review is conducted first to describe the research gaps and the necessity of this study. Second, the methodology is presented, including the establishment of the conceptual communication network based on multiple historical emergency events, quantitative communication network modeling using an opinion dynamics model and social network analysis (SNA), and an illustrative example to validate the quantitative model. Subsequently, a case study is employed to demonstrate the feasibility and applicability of the proposed model, and suggestions are provided. Finally, the research contributions, limitations, and future work are discussed.

2 Literature review

Due to the wide range of expertise required in emergencies, decision-making is no longer limited to individual decision-making but requires the participation of experts from multiple professional organizations [41]. Interorganizational communication is essential in emergency decision-making. However, since decision-makers come from different organizations, such as fire and rescue services, medical assistance, government agencies, and public organizations, communication barriers exist between multiple organizations [13]. Organizations prefer internal communications over interorganizational communication during an emergency response due to a large number of participating organizations, communication barriers, time constraints, and a lack of strategic direction. Communication barriers prevent an effective emergency response from multiple organizations, often resulting in decision-making failure [3]. Effective communication among decision-makers is crucial for obtaining relevant information and reaching a decision consensus [7]. Since communication issue is an important part of decision-making, many scholars qualitatively analyzed the impact of communication on decision-making [8 , 28].

Research on interorganizational communication in emergency decision-making essentially belongs to the field of interactive group decision-making. Interactive group decision-making is based on the theory of group decision-making, which considers the participant’s preferences and information exchange in interactive decision-making. Numerous scholars have extended interactive group decision-making to emergency decision-making using fuzzy mathematics [10, 38], Markov method [31, 51], and opinion dynamics models [18, 50]. The opinion dynamics model can describe emergency decision-making because it considers the social environment, individual characteristics, and evolution rules; thus, it has attracted extensive attention [21]. Opinion dynamics models can be classified as discrete and continuous opinion dynamics models. Examples of the classical discrete opinion dynamics model are the Ising model [6] and the voter model [35]. Discrete models utilize discrete binary variables. For example, voters participating in an election are assigned values 0 and 1 to represent their voting choice. The continuous opinion dynamic model has received extensive attention because of its wider application range than the discrete model. Continuous values are used in this model. For example, the values 0.1 and 0.9 can be used to express low and high concerns in a continuous value range. A classic continuous opinion dynamics model is the DeGroot model [8]. This model describes the personal opinions of individuals using weighted averaging and assumes that the interaction relationship between individuals does not evolve over time. Current research extended the DeGroot model to adopt the opinions outside the confidence level [4]. Another classic continuous opinion dynamic model is the Friedkin–Johnsen (F-J) model [15], which evolved from the DeGroot model. The F-J model considers individual psychological factors affecting opinions. It retains some of the initial opinions of interacting individuals and considers the opinions of other individuals.

Group decision-making is carried out in social network scenarios [24]. The social relationship and interaction between decision-makers significantly affect the decision-making results. SNA examines how social structures impact behaviors utilizing a set of links (interactions or relationships) between a defined set of nodes (agents or groups) [27]. The opinion formation in emergency decision-making is a result of the interaction among various organizations after discussing emergency response strategies using various communication networks. An inadequate communication network, indirect communication, or mutual influences between organizations results in communication barriers [13], reducing the efficiency of opinion transfer [17]. Researchers have developed two types of network structures, i.e., formal and informal, to improve the opinion formation time. Formal networks have a hierarchical structure, which is typical in large organizations, such as governments and organized religions [33]. Informal networks (e.g., small-world networks [16], scale-free networks [14], and fully connected networks [19]) are socially accepted and oriented to individual members. Informal networks have better communications than formal ones because less time is required for opinion formation [34]. Although these networks are functional, they are not suitable for practical applications due to their negligence to consider communication barriers occurring between emergency organizations and the lengthy period required for opinion formation.

Existing research tends to quantify the impact of communication barriers on decision-making performance and ignores the quantitative study of communication barriers. In addition, the current opinion dynamics models cannot quantify the influence of communication barriers on the opinion formation time, which is required to improve the performance of group decision-making. Therefore, an opinion formation model that considers communication barriers is needed to describe opinion formation during emergency events accurately.

3 Methodology

The workflow of this study is illustrated in Fig. 1. First, real emergency events are examined to establish a general conceptual network model. Second, an opinion dynamics model and SNA are used to create the conceptual communication network model. The impact of communication barriers on the opinion formation time is assessed by simulating communication barriers of various degrees and changing the communication network structure. Third, illustrative examples are used to validate the quantitative model. The improvement in the opinion formation time is quantified by comparing various communication networks. Finally, the feasibility and applicability of the proposed model are evaluated using a real emergency event: the Qingdao oil pipeline explosion that occurred in China in 2013.

Fig. 1

Workflow of the study.

3.1 Establishment of the conceptual communication network

Emergency decision-making is a non-procedural process because of the unpredictability of emergency events [25]. Informal communication networks are formed according to various emergency tasks to cope with unpredictable emergency tasks. The communication network is the basis for information exchange and opinion formation. After an emergency event, the news is reported on social media, in government reports, and academic research. Information from these sources is used to assess emergency events and discover problems in emergency decision-making. On this basis, communication networks between organizations are created to communicate emergency-related information. According to network connectivity theory, the network is modeled as a graph where the vertices represent the nodes, and the edges represent the links between the nodes [37]. In our communication network, the nodes represent the organizations with various specialties, and the edges denote the communication relationships between the organizations. The communication network depends on the participating organizations and their relationships in real emergency cases rather than a randomly generated network. The details of the conceptual communication network formation using examples from real emergency cases are described as follows.

Specifically, news, reports, and the literature related to the sinking of the cruise ship Dongfang Zhi Xing, the 2015 Tianjian explosion, and the 2008 Sichuan earthquake are analyzed to identify organizations participating in the emergency response to ensure wide applicability of the proposed communication network. The results are summarized in Table 1. One characteristic of emergency response is the formation of a temporary communication network by relevant organizations and an emergency operations center. The emergency operations center takes the lead in the network. It coordinates the tasks of participating organizations and collects information to reach a final consensus decision for emergency response. Notably, some organizations in the network do not communicate directly; instead, they communicate through the emergency operations center, which hinders efficient information sharing, resulting in delayed or failed decision-making.

Table 1
Participating organizations in various emergency events

Emergency events Participating organizations

Sinking of Dongfang Zhi Xing [5, 42, 45] •: Emergency Operations Center; ➀: People’s Liberation Army Navy;

➁: Political Bureau of Central Committee; ➂: Transportation Department;

➃: Public Security Department; ➄: National Health Commission;

➅: Meteorological Administration; ➆: Water Resources Bureau;

➇: Local Government; . . .

2015 Tianjin Explosions [20, 23, 40, 48, 49] •: Emergency Operations Center; ➀: Security Fire Department;

➁: Environmental Protection Department; ➂: Safety Supervision Bureau;

➃: Medical Department; ➄: Academy of Military Medical Sciences;

➅: Tianjin Municipal Public Security Bureau; ➆: Transport Department;

➇: Local Government; . . .

2008 Wenchuan Earthquake [9, 44] •: Emergency Operations Center; ➀: Earthquake Administration;

➁: Security Fire Department; ➂: Medical Department;

➃: People’s Armed Police; ➄: Housing and Urban-Rural Development;

➅: Transport Department; ➆: State Grid;

➇: International Community; . . .

Emergency events	Participating organizations
Sinking of Dongfang Zhi Xing [5, 42, 45]	•: Emergency Operations Center;	➀: People’s Liberation Army Navy;
	➁: Political Bureau of Central Committee;	➂: Transportation Department;
	➃: Public Security Department;	➄: National Health Commission;
	➅: Meteorological Administration;	➆: Water Resources Bureau;
	➇: Local Government;	. . .
2015 Tianjin Explosions [20, 23, 40, 48, 49]	•: Emergency Operations Center;	➀: Security Fire Department;
	➁: Environmental Protection Department;	➂: Safety Supervision Bureau;
	➃: Medical Department;	➄: Academy of Military Medical Sciences;
	➅: Tianjin Municipal Public Security Bureau;	➆: Transport Department;
	➇: Local Government;	. . .
2008 Wenchuan Earthquake [9, 44]	•: Emergency Operations Center;	➀: Earthquake Administration;
	➁: Security Fire Department;	➂: Medical Department;
	➃: People’s Armed Police;	➄: Housing and Urban-Rural Development;
	➅: Transport Department;	➆: State Grid;
	➇: International Community;	. . .

Next, the participating organizations in Table 1 are analyzed to evaluate their communication relationships. Two rules are used to create the edges (i.e., the communication relationships) between the nodes (i.e., the participating organizations) in the communication network: (1) an edge is established between two nodes in the network if direct information exchange occurs between two organizations (e.g., report and cooperation); (2) if direct cooperation or other forms of direct communication between the two organizations is not mentioned in the case materials, it is assumed that communication barriers exist between the two organizations. Thus, no edge is established between these nodes.

The Sinking of Dongfang Zhi Xing is used as an example to illustrate the formation of the communication network using these two rules. According to the reference [42, 45], the participating organizations numbered from ding172 to ➆ in Table 1 were convened by the emergency operations center. Therefore, they have communication relationships with the emergency operations center. reference [5] describes that the “Political Bureau of the Central Committee communicated with the People’s Liberation Army and Navy to participate in the rescue operation of Dongfang Zhi Xing...” implying that the Political Bureau of the Central Committee ding172 and the People’s Liberation Army and Navy ➁ had a communication relationship. The communication network related to the sinking of Dongfang Zhi Xing is shown in Fig. 2(a) . The same rules are used to establish the communication networks of the other two emergency events (Fig. 2 (b) and (c)).

Fig. 2

As illustrated in Fig. 2, communication exists between the organizations and the emergency operations center, whereas communication barriers exist between the organizations. The communication networks in Fig. 2 are generalized into two categories to simplify the analysis of the impact of communication barriers on the opinion formation time. In the first category, all organizations have communication barriers, i.e., there are no edges between the nodes, except for the emergency operations center (Fig. 3(a)). In the second category, some organizations have communication barriers. For illustration purposes, ➂ and ➃, as well as ➄ and ➅, are linked (Fig. 3(b)).

Fig. 3

The generalized interorganizational communication network: (a) Network 1: all organizations have communication barriers, except for the emergency operations center; (b) Network 2: some organizations have communication barriers.

Multiple organizations are involved in emergency responses due to the complexity. After the occurrence of an emergency event, the emergency operations center convenes the related organizations, which are not aware of each other’s involvement. Therefore, the initial communication network is similar to Network 1 (Fig. 3(a)). As communication relationships are being established, the communication network changes to Network 2 (Fig. 3(b)).Network 1 provides a good starting point to study the impact of communication barriers on opinion formation time. Therefore, Network 1 is considered the initial interorganizational communication network. All organizations have communication relationships with the emergency operations center but no communication relationships with other organizations.

3.2 Quantitative communication network modeling

Quantitative communication network modeling aims to measure the impact of communication barriers in the conceptual communication network on the opinion formation time. The process of opinion formation is shown in Fig. 4. After an emergency event, the organizations exchange their opinions on emergency response strategies to minimize losses. A communication network is formed based on their communication relationships, enabling influential organizations to pass on information to other organizations in case of emergencies [43]. The participating organizations update their opinions according to information from other influential organizations in the network until the required consensus degree is reached. However, the network structure and communication barriers affect the efficiency and effectiveness of information transfer between organizations, influencing the opinion consensus [17]. Therefore, communication barriers are evaluated and quantified by changing the structure of the communication networks to study their impact on the opinion formation time.

Fig. 4

Opinion formation process.

The impact of communication barriers in the conceptual communication network on the opinion formation time is analyzed based on opinion dynamics model, which is widely used in conjunction with SNA to construct a quantitative communication network model. In SNA, the influence of the organization’s opinion is represented by weights, which are determined objectively according to the organization’s position in the communication network. Since communication barriers affect the influence of opinions between organizations, the communication barriers are evaluated quantitatively in the SNA. The notations used in the proposed model are listed in Table 2.

Table 2

Notations of the proposed model

Notations	Explanations
N	The number of emergency response strategies
M	The number of organizations
G _I	The i^th organization
λ_i	The weight of G_i
V _I	Opinion vector of G_i for alternative n, V_i ={ v_il\|l = 1, …, n }
v_il (t)	Opinion value of G_i for the l^th alternative n in stage t
β_i	Degree of stubbornness of G_i regarding a previous opinion
d _ij	Coefficient describing the connection between G_i and G_j
r_ij (t)	The similarity of the opinions between G_i and G_j in stage t
ρ (t)	The consensus degree of the organizations
ρ ^*	The required consensus degree
I	The improvement in the opinion formation time

3.2.1 Influence of the organization based on SNA

An individual’s or organization’s opinion may affect the opinion of others. The influence of the organization depends on its influence in the communication network. In this work, the weight of an organization in the communication network is used to measure its influence. SNA typically utilizes three indicators to measure the weight λ_i of the i^th organization G_i, i.e., degree centrality D_i, betweenness centrality B_i, and closeness centrality C_i. The three indicators measure the importance of an organization in the network regarding the number of connected neighbors, the role of transmitting information, and the distance from other organizations, respectively. Detailed calculation methods have been described in reference [28].

The aggregate weight that incorporates the three indicators is calculated as Eq. (1):

$\begin{matrix} λ_{i} = \frac{w_{i}}{\sum_{i = 1}^{m} w_{i}} \end{matrix}$ (1) where $w_{i} = \frac{1}{3} \sqrt{{\hat{D}}_{i}^{2} {+ \hat{B}}_{i}^{2} {+ \hat{C}}_{i}^{2}}$ , ${\hat{D}}_{i}$ , ${\hat{B}}_{i}$ , and ${\hat{C}}_{i}$ are the normalized weights of D_i, B_i, and C_i, respectively.

3.2.2 Communication barriers modeling using an opinion dynamics model

In the SNA, the F-J model is extended by considering the communication barriers’ effect on opinion formation. It is important to note that d_ij is the coefficient describing the level of the communication barrier between organizations G_i and G_j. The opinion formation of the i^th organization regarding the l^th alternative in stage t + 1 is represented as a quantitative communication network model that considers communication barriers. It is expressed as Eq. (2):

$\begin{matrix} v_{il} (t + 1) \\ = β_{i} \cdot v_{il} (t) + (1 - β_{i}) \cdot \sum_{j = 1, i \neq j}^{m} θ_{j} (t) \cdot v_{jl} (t) \end{matrix}$ (2) where i, j = 1, ⋯ , m, l = 1, ⋯ , n, $θ_{j} = \frac{λ_{j} \cdot d_{ij}}{\sum_{j = 1, i \neq j}^{m} (λ_{j} \cdot d_{ij})}$ , ∃d_ij = 1 . If a communication barrier exists (i.e., no edge) between G_iand G_j, d_ij = 0, indicating that opinions are not shared between G_iand G_j because of their communication barrier. On the other hand, if no communication barrier exists between G_iand G_j, d_ij = 1, indicating that opinions are shared between G_iand G_j. Equation (2) is composed of two parts: one part represents the organization’s stubbornness to its previous opinion, and another part represents the opinion influenced by other organizations’ opinions. When ∀d_ij = 1, Eq. (2) is reduced to the F-J model.

Quantitative communication network modeling is used to simulate the opinion formation process between the organizations for the same emergency response strategy. Since the independence of the opinions on strategies and this study focuses on communication barriers, the opinion on one of the emergency response strategies is taken as a representative to study the impact of communication barriers on opinion formation in the following analysis.

3.2.3 Evaluation indicators of the efficiency of opinion dynamics

The efficiency of opinion dynamics in emergency decision-making affects the loss of life and property; therefore, it is crucial to obtain accurate measurements of the efficiency of the decision-making process in various decision-making scenarios. A consensus is achieved in emergency decision-making through consultation, negotiation, and compromise, the core aspects of the study of group decision-making efficiency. Two evaluation indicators are used to measure the decision-making efficiency: the consensus degree of decision-making and the decision-making time. The definition and calculation of these two evaluation indicators are described as follows.

Consensus degree of decision-making. The consensus degree of decision-making describes the similarity degree of decision-making of multiple organizations. The higher the similarity degree, the higher the consensus degree is. The objective of the interaction between the organizations is to obtain a high degree of consensus in emergency decision-making. For the same conditions, the higher the consensus degree, the higher the efficiency of decision-making is. Therefore, the consensus degree of decision-making is an effective index to measure decision-making efficiency.

The consensus degree in stage t is calculated as Eq. (3):

$\begin{matrix} ρ (t) = \frac{1}{C (m, 2)} \sum_{\begin{matrix} i, j = 1 \\ i > j \end{matrix}}^{m} r_{ij} (t) \end{matrix}$ (3) where C (m, 2) = m · (m - 1)/2, r_ij (t) represents the similarity of the opinions between G_i and G_j in stage t. The Euclidean distance is used as the similarity measure:

$\begin{matrix} r_{ij} (t) = 1 - \sqrt{\frac{\sum_{l = 1}^{n} {(v_{il} (t) - v_{jl} (t))}^{2}}{n}} \end{matrix}$ (4)

Decision-making time. The decision-making time is the period from the start of discussing the options to reaching a satisfactory consensus degree. Since the 72 hours after an emergency are crucial for saving lives and reducing losses, the time required for the decision-making group to reach a consensus significantly affects the emergency response. Thus, this is an important indicator to evaluate decision-making efficiency.

The improvement in the decision-making time I is used to evaluate the decision-making efficiency. It is calculated as Eq. (5):

$\begin{matrix} I = \frac{max (t_{a}, t_{b}) - min (t_{a}, t_{b})}{max (t_{a}, t_{b})} \end{matrix}$ (5) where t_a and t_b are the times required to reach the required consensus degree in the communication networks a and b, respectively, t_a, t_b > 0. The communication networks a and b are the two arbitrary communication networks, in which the required consensus degree was not reached initially, i.e., t_a, t_b ≠ 0.

3.2.4 Details of opinion formation for emergency decision-making

As illustrated in Fig. 4, the steps of opinion formation for emergency decision-making are as follows:

Step 1: When t = 0, the number of participating organizations m and their communication relationships are identified according to the specific emergency event. The initial opinion value of G_i regarding the alternatives n, V_i (0) ={ v_il|l = 1, …, n } are given as i = 1, …, m.

Step 2: The communication network is established according to the communication network formation rules in 3.1.

Step 3: The weight of each organization λ_i is calculated using Eq. (1), and the communication coefficient d_ij representing the communication barrier between G_i and G_j is identified.

Step 4: Let t = t + 1, organizations interact with each other. The opinion of G_i is updated to v_il (t + 1) using Eq. (2).

Step 5: The consensus degree ρ (t) is obtained from Eq. (3) and compared to the required consensus degree ρ^*. When ρ (t) ⩾ ρ^*, a consensus has been reached, and the opinion formation time is recorded. Proceed to step 6. If ρ (t) < ρ^*, no consensus has not been reached, and the process goes to step 4 for further interaction until ρ (t) ⩾ ρ^*.

Step 6: When a consensus has been reached, Eq. (3) and (5) are used to calculate the impact of the communication barriers on the opinion formation time for different decision-making scenarios.

3.3 Illustrative example

The validity of the proposed model by simulating the opinion formation time is evaluated by using Python for two extreme communication networks. (1) In the barrier-containing communication network, the organizations only communicate through the emergency operations center (Fig. 5(a)). (2) In the barrier-free communication network, all organization communicates with each other with no barriers (Fig. 5(b)). In the examples presented below, four organizations involved in emergency response with different initial opinions are considered. First, in the barrier-containing communication network, different initial opinions, consensus degrees, and stubbornness degrees are assumed to evaluate whether the consensus degree over time is consistent with common sense. Second, the opinion formation time is simulated for various scenarios by comparing the barrier-containing and the barrier-free communication networks to validate the improvement in the consensus degree. The simulation settings and results are discussed below.

Fig.5

Two interorganizational communication networks: (a) Barrier-containing communication network; (b) Barrier-free communication network.

3.3.1 Trend of consensus degree with different variables

The communication network in Fig. 5 (a) is used as an example to evaluate the consensus degree of the proposed model. The values of the initial opinions and stubbornness degrees are changed to obtain the trends. The simulation results are shown in Fig. 6.

Fig. 6

Trend of consensus degree with (a) different initial consensus degrees and (b) different stubbornness degrees.

As shown in Fig. 6(a), for the same conditions, the lower the initial consensus degree, the longer time it takes to meet the required consensus degree. Groups with many differences in opinions need more time to discuss strategies. It is observed in Fig. 6(b) that the higher the stubbornness degree of an organization, the longer it takes to reach a consensus. The conclusions are the same as for the consensus degree. Since the stubbornness degree represents the organization’s persistence to hold on to an initial opinion, more time is needed for a stubborn agent to accept another’s opinion. The trend obtained from the proposed model is consistent with common sense, indicating the rationality of the model.

3.3.2 Comparison of the opinion formation time

Based on the verified model, the two interorganizational communication networks in Fig. 5 are compared to illustrate the impact of communication barriers on the opinion formation time for the required consensus degree. Different initial consensus degrees and stubbornness degrees of the organizations in the interorganizational communication network are simulated to demonstrate the impact of the barrier-free communication network on the opinion formation time in various emergencies.

Initial consensus degrees: The stubbornness degree of the organizations (β = 0.9) is fixed, and four initial consensus degrees (ρ = 0.4, 0.53, 0.67, and 0.8) are randomly generated. Figure 7 shows the trends of the consensus degrees for the barrier-containing communication network (blue lines) and the barrier-free communication network (orange lines).

Fig. 7

Trend of consensus degree for different initial consensus degrees for the (a) barrier-containing communication network (blue lines) and the (b) barrier-free communication network (orange lines).

Two findings are observed in Fig. 7: (1) it takes fewer iterations of opinion formation to reach the same consensus degree in a barrier-free communication network, regardless of the initial consensus degree. This result implies that barrier-free communication networks are the ideal decision-making mode in emergency decision-making. For the same initial consensus degree, a barrier-free communication network has a lower opinion formation time than a barrier-containing communication network. (2) As the initial consensus degree increases, the improvement in the iteration time in the barrier-free communication network becomes smaller. A high initial consensus degree means that the initial opinions are more consistent, and communication plays a less important role. For instance, when the initial consensus degree is 0.8, the trend line for the barrier-free communication network nearly overlaps with that of the barrier-containing communication network.

The improvement in the opinion formation I to reach the required consensus degree ρ^* (Eq. (5)) for different initial consensus degrees is shown in Fig. 8. At the same initial consensus degree, the improvement in the opinion formation time increases with an increase in ρ^*. In addition, for the same ρ^*, the improvement decreases with an increase in the initial consensus degree. This finding implies that the barrier-free communication network results in a larger improvement in the opinion formation time when the organizations have a low initial consensus degree and a high required consensus degree.

Fig. 8

Improvement in the opinion formation time for different initial consensus degrees.

Due to the uniqueness and unpredictability of emergencies, the participating organizations are temporally convened by the emergency operations center. More communication barriers exist in communication networks with fewer communication relationships. Therefore, the opinion formation time is shorter in the barrier-free than the barrier-containing communication network. The improvements in Fig. 8 are all positive, indicating that the opinion formation time is faster in the barrier-free communication network than the barrier-containing communication network. The trends in Fig. 8 are consistent with common sense.

Stubbornness degrees: Besides the initial consensus degree, the stubbornness degree of the organizations affects the opinion formation time of the given communication networks. The trend of the consensus degree over time is simulated for different stubbornness degrees (i.e., β = 0 . 3, 0 . 5, 0 . 7, and 0.9). The results are shown in Fig. 9.

Fig. 9

Trend of the consensus degree for different initial stubbornness degrees for the (a) barrier-containing communication network (blue lines) and (b) the barrier-free communication network (orange lines).

Two findings are observed in Fig. 9: (1) the barrier-free communication network requires less opinion formation time than the barrier-containing communication network (i.e., it requires fewer iteration times to reach the required consensus degree) for all four stubbornness degrees. The result implies that the barrier-free communication network is the ideal decision-making mode in emergency decision-making. (2) The margin of improvement increases with an increase in the stubbornness degrees of the organizations.

Similarly, the improvement in the opinion formation time I is used to quantify the impact of different stubbornness degrees. The results are shown in Fig. 10. For the same stubbornness degree, I increases proportionally to the required consensus degree ρ^*. For the same required consensus degree ρ^*, I increases proportional with an increase in the stubbornness degree. This result implies that the barrier-free communication network results in larger improvements in the opinion formation time when the organizations have a high stubbornness degree and a high required consensus degree.

Fig. 10

Improvement in the opinion formation time for different stubbornness degrees.

In practice, the stubbornness of an organization represents its persistence to hold on to its opinion due to various reasons, such as confidence in its opinion, an openness to others’ opinions, or a conflict of interest. It takes a longer time to reach a consensus for organizations with a high degree of stubbornness. The proposed model is validated from this perspective.

Number of organizations: The above parameters are changed to compare the effects of communication barriers on the opinion formation time based on a fixed number of participating organizations, as shown in Fig. 5. The number of participating organizations depends on the type of emergency. The impact of the number of participating organizations on the opinion formation time in different decision-making situations is further evaluated as follows.

The initial consensus and stubbornness degrees are fixed to ensure comparability. Since there are many possibilities for organizations to form a communication network, the barrier-containing and barrier-free communication networks are used as examples for comparison. As the number of organizations increases, the number of edges increases accordingly to ensure consistency of the network structure. The numbers of organizations (nodes) m are selected as 3, 6, and 9 for illustration. The results are shown in Fig. 11.

Fig. 11

Trend of consensus degree for different numbers of organizations for barrier-containing and barrier-free communication networks.

Figure 11 shows that in the barrier-containing communication network, there is no significant difference in the time to reach the consensus for different numbers of organizations. The nodes must communicate with other nodes through the central node in the barrier-containing communication network. Therefore, the addition of nodes and edges does not change the communication mode of the other nodes. However, the situation is different in the barrier-free communication network. As the number of nodes increases, it will take a longer time to reach the required consensus degree. This result indicates that the number of organizations affects the opinion formation time in the barrier-free communication network. For each additional node, (m-1) edges are added to connect with the other nodes to maintain a barrier-free communication network. There are many options to connect nodes besides the central node. An increase in the number of nodes disperses the communication efficiency between nodes and increases the opinion formation time. When barrier-containing communication network changes to a barrier-free communication network, an increase in the number of nodes has a more significant impact on the opinion formation time.

4 Case study

Due to the uniqueness of emergency events (different numbers of participating organizations and communication relationships), a fact-based communication network with communication barriers differs from the two extreme communication networks (barrier-containing and barrier-free communication networks) in the illustrative example. Typically, the structure of a fact-based communication network depends on the communication barriers (e.g., lack of communication relationships and insufficient information-sharing) between the organizations in a real emergency event. This section aims to create (1) a fact-based interorganizational communication network based on a real emergency event and (2) compare the quantified impact of communication barriers on the opinion formation time for the fact-based and barrier-free communication networks. The results are used to validate the feasibility and applicability of the proposed methodology.

The 2013 Qingdao oil pipeline explosion in China is selected to demonstrate the implementation of the proposed methodology. This particular case is chosen for three reasons. (1) It is a recent major emergency event that killed 62 people, injured 136 people, and caused direct economic losses of 751 million Chinese yuan [47]; (2) According to information extracted from multiple data sources (i.e., news, literature, and reports), 2013 Qingdao oil pipeline explosion involved multiple organizations and complex communication relationships which is consistent with the research objectives. (3) Communication barriers between the participating organizations in the decision-making process were one reason for the deterioration of the events because the organizations did not comply with Article 40 in the “Emergency Response Law of the People’s Republic of China” [22]. In the following, the establishment of the fact-based communication network and the impact of communication barriers on the opinion formation time for the 2013 Qingdao oil pipeline explosion are discussed in detail.

4.1 Establishment of the fact-based interorganizational communication network

The 2013 Qingdao oil pipeline explosion was a complex emergency and consisted of multiple sub-events. The complex event is broken down into sub-events to determine the participating organizations, their communication relationships, and the emergency response. The details are summarized in Table 3, and the participating organizations are listed in Table 4.

Table 3
Sub-events in the 2013 Qingdao oil pipeline explosion

Sub -events Sub-event description

Sub-event 1 [22, 47] The 110-command center of the Public Security Bureau was notified of an alarm by the alarm company. According to the company’s report, the local government classified the accident as a four-level general oil spill and launched an emergency plan. The experts from the relevant organizations could not verify the authenticity of the company’s report.

Sub-event 2 [1, 30] The amount, type, and concentration of the leaked gas were not obtained by the repair personnel from the accident company and the Public Security Bureau, violating the regulations by using non-explosion-proof electrical appliances. As a result, massive explosions occurred.

Sub-event 3 [30] After the explosion, the local government and the company reported the emergency to an upper-level department. An on-site emergency operations center was established by the State Councillor with the help of the provincial government. The Urban Council, Safety Supervision Bureau, Environmental Protection Department, and Meteorological Administration were convened by the emergency operations center to participate in the emergency response.

Sub-event 4 [30, 46] The company dealt with this emergency situation as a general field leakage accident without considering the urban environmental conditions, resulting in serious environmental impacts.

Sub-event 5 [32] When the leakage accident expanded, the surrounding enterprises and residents were not notified in time.

Sub-event 6 [32] The on-site rescue personnel did not realize the importance of the wind direction when choosing an evacuation route for the surrounding crowd. They did not extinguish the fire sources and turn off the power because the wind direction was not considered early enough.

Sub -events	Sub-event description
Sub-event 1 [22, 47]	The 110-command center of the Public Security Bureau was notified of an alarm by the alarm company. According to the company’s report, the local government classified the accident as a four-level general oil spill and launched an emergency plan. The experts from the relevant organizations could not verify the authenticity of the company’s report.
Sub-event 2 [1, 30]	The amount, type, and concentration of the leaked gas were not obtained by the repair personnel from the accident company and the Public Security Bureau, violating the regulations by using non-explosion-proof electrical appliances. As a result, massive explosions occurred.
Sub-event 3 [30]	After the explosion, the local government and the company reported the emergency to an upper-level department. An on-site emergency operations center was established by the State Councillor with the help of the provincial government. The Urban Council, Safety Supervision Bureau, Environmental Protection Department, and Meteorological Administration were convened by the emergency operations center to participate in the emergency response.
Sub-event 4 [30, 46]	The company dealt with this emergency situation as a general field leakage accident without considering the urban environmental conditions, resulting in serious environmental impacts.
Sub-event 5 [32]	When the leakage accident expanded, the surrounding enterprises and residents were not notified in time.
Sub-event 6 [32]	The on-site rescue personnel did not realize the importance of the wind direction when choosing an evacuation route for the surrounding crowd. They did not extinguish the fire sources and turn off the power because the wind direction was not considered early enough.

Table 4

Participating organizations in sub-events of the 2013 Qingdao oil pipeline explosion

Notations	Organizations
•	Emergency Operations Center
➀	Public Security Bureau
➁	Company
➂	Local Government
➃	Safety Supervision Bureau
➄	Urban Council
➅	Meteorological Administration
➆	Environmental Protection Department

According to the description of the sub-events in Table 3, the communication relationships between the participating organizations in Table 4 are contextually analyzed to evaluate the information exchange between the organizations, such as reports and cooperation. Then, the two rules of the communication network formation described above are used to establish the fact-based interorganizational communication network shown in Fig. 12. The following examples are used to describe the creation of the communication network: (1) the 110-command center of the Public Security Bureau received an alarm from the alarm company (sub-event 1), indicating that the participating organizations are the Public Security Bureau (ding172 in Table 4) and the company (➁ in Table 4). The Public Security Bureau received a report from the company showing a communication relationship between the Public Security Bureau and the Company. In the communication network, an edge exists between nodes ding172 and node ➁ in Fig. 12. (2) The company dealt with this emergency as a general field leakage accident without considering the urban environmental conditions, resulting in serious environmental impacts (sub-event 4). The participating organizations are the company (➁ in Table 4) and the Environmental Protection Department (➆ in Table 4). The information from the Environmental Protection Department was not passed on to the company in time, resulting in inadequate emergency responses, indicating communication barriers between these two organizations. There is no edge between nodes ➁ and node ➆in this communication network. Communication networks are formed according to the sub-events, resulting in the formation of the interorganizational communication network.

Fig. 12

Interorganizational communication network based on the 2013 Qingdao oil pipeline explosion.

Next, the impact of communication barriers on the opinion formation time in a real emergency event is analyzed. The barrier-free communication network is considered the optimal decision-making mode as verified in 3.3, and is therefore used for comparison. The barrier-free communication network has the same number of participating organizations as the fact-based interorganizational communication network, in which all organizations communicate freely with each other. The structures of the fact-based and barrier-free communication networks are compared in Fig. 13.

Fig. 13

Two communication networks: (a) fact-based communication network; (b) barrier-free communication network.

4.2 Impact of communication barriers on the opinion formation time

Various decision-making scenarios with different stubbornness degrees of the participating organizations are simulated to compare the impact of communication barriers on the opinion formation time for the fact-based and barrier-free communication networks. All other variables remain fixed, and different stubbornness degrees are evaluated (β = 0 . 3, 0 . 5, 0 . 7, and0 . 9). Figure 14 shows the trends of the consensus degree over time for the different stubbornness degrees for the fact-based communication network (blue lines) and the barrier-free communication network (orange lines).

Fig. 14

Comparison of opinion formation time for different stubbornness degrees between two communication networks for the (a) fact-based communication network and the (b) barrier-free communication network.

As indicated in Fig. 14, the performances of the barrier-free communication network are better than those of the fact-based communication network for different stubbornness degrees. This result shows that a barrier-free communication network is more conducive to decision-making, and eliminating communication barriers reduces the decision-making time in an actual emergency. In addition, for the required consensus degree of 1, the advantage of the barrier-free communication network increases with an increase in the stubbornness degree, indicating that the greater the stubbornness degree, the more favorable the barrier-free communication network is for decision-making.

To further quantitively compare the impact of communication barriers on opinion formation time, the improvement in the opinion formation time for different stubbornness degrees is shown in Fig. 15.

Fig. 15

Improvement in the opinion formation time for different stubbornness degrees for the fact-based and barrier-free communication networks.

Figure 15 shows the extent of the communication barriers affects opinion formation time. The improvement in the opinion formation time I represents the percentage of time improvement by changing from a fact-based communication network to a barrier-free communication network. For example, when β = 0 . 7 and ρ^* = 0 . 8, I = 11%. This result indicates that if 10 units of time are required for decision-making in the fact-based communication network, 1.1 units of time can be saved to reach a consensus after removing the communication barriers. In addition, the higher the required consensus degree ρ^*, the higher the improvement in the time I is by removing communication barriers. For example, when β = 0 . 9, the time efficiency can be improved by 12% when ρ^* = 0 . 8 compared with I = 8% when ρ^* = 0 . 6.

Figures 14 and 15 show the following: (1) communication barriers in the fact-based communication network during a real emergency event can be accurately estimated by the proposed quantitative communication network model. (2) The opinion formation time in the fact-based communication network can be improved by removing communication barriers or building communication relationships between the participating organizations. (3) The margin of improvement depends on the level of communication barriers in two communication networks and the value of the variables (i.e., stubbornness degree). When the initial consensus degrees have different values, the trends of the fact-based and barrier-free communication networks are similar to the results in the illustrative example. Due to space constraints, the trends with different initial consensus degrees are not shown.

The results of the illustrative example and the case study demonstrate that the proposed methodology can quantify the impact of communication barriers in conceptual and fact-based communication networks and determine the opinion formation time for different emergencies. Practitioners can quantify the improvement in the opinion formation time by removing communication barriers. As shown in the case study, when the stubbornness degree (β = 0 . 9) and the required consensus degree (ρ^* = 0 . 8) are fixed, the improvement in the opinion formation time by removing communication barriers is 12% (e.g., the iteration time) (Fig. 15. green line). A larger improvement is achieved in groups with a low initial consensus degree and a high stubbornness degree (e.g., 33% and 32% time improvement, as shown in Figs. 8 10). The time improvement is encouraging because high-consensus decision-making is crucial in emergency events to save property and lives.

The quantitative results also have implications for management, demonstrating the impact of communication barriers on decision-making performance. The following suggestions are provided to remove communication barriers according to our results. (1) Establishing a permanent interorganizational emergency decision-making center composed of experts from participating organizations typically involved in emergencies to improve communication. (2) Developing an interorganizational communication system to share information in a common language. This system should have sufficient authority, the members should understand the responsibilities of different organizations, and a responsible person should ensure that the organizations stay in touch and understand each other’s rules during emergencies. If mutual understanding exists, initial conflicts will be reduced, and the deep-seated reasons for stubborn organizations adhering to their opinions can be determined to achieve reasonable and timely decision-making. In actual emergency decision-making, practitioners need to balance the benefits of time improvement and the cost of removing communication barriers from the perspective of economics to maximize the benefits in emergency events.

5 Conclusion

This study proposed a method to form a conceptual communication network for emergency events and obtain the quantitative impact of communication barriers on emergency decision-making performance. SNA, opinion dynamics models, and decision-making theory are used in this study. The results of an illustrative example and case study showed that communication barriers had different effects on the decision-making time in various emergency decision-making scenarios, demonstrating the applicability and feasibility of the proposed method.

This research fills the gap in quantitative modeling of the impact of communication barriers on emergency decision-making by exploring new approaches in economics and management. Some limitations exist in internal and external relationships between the participating organizations because of different levels of communications between them during real emergency events. The role of the organizations can be determined by subjectively determining the weights of the organizations according to the types of emergency events.

In a future study, multiple data sources of emergency events will be explored to develop a comprehensive conceptual communication network. The functional weights of the organizations will be considered to assess how communication barriers affect the decision-making performance in communication networks for different emergency events.

Footnotes

Acknowledgments

This research is supported by grants from the National Natural Science Foundation of China (71971217, 72073041), the Major Project of the National Natural Science Foundation of China (72091515), the Independent Exploration and Innovation Project of Graduate Students of Central South University (2017zzts046), and the China Scholarship Council (201706370105).

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