Toward a service-innovation ecosystem of enterprises in China

Abstract

Service innovation is an important driver of enterprise self-development and growth in the current service-attuned economy. And across economic sectors, the prevalence of self-organized and self-governed ecosystems renders service innovation increasingly crucial to such service ecosystems. Scholars study service innovation from the perspective of service ecosystem, yet little attention is paid to systematically researching service-innovation components within service ecosystems, especially the implementation path of such components. Based on service-oriented logic, this study presents a framework for service innovation in service ecosystems, built upon five elements: actor-to-actor (A2A) networks, value proposition, resource integration, institutionalization processes, and information technology (IT). This might be the first study to use a combination of the Decision-Making Trial and Evaluation Laboratory (DEMATEL) based Analytic Network Process (ANP) method (called DEMATEL based ANP, or DANP) and the NK model to obtain the optimal path of service innovation in China. Despite the study’s limitations, the results show that enterprises must first develop IT capabilities and innovative value propositions, and then enhance their resource-integration capability and enlarge their A2A networks, as they accelerate their institutionalization processes. Future research must investigate service-innovation components and enhances the idea of service ecosystems, and provides guidelines how to implement service innovation in practice.

Keywords

Service innovation service-oriented logic service ecosystem implementation path NK model

Lei Wang is a Ph.D. candidate (management science and engineering) at School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing, China. He has participated in many scientific research including provincial and national projects, and enterprise consulting projects as well. His major research interests include service innovation, big data and ICT development.

Professor Zeng Jianqiu obtained his Ph.D. degree from Cambridge University, UK. He is a professor and a doctoral advisor at School of Economics and Management, Beijing University of Posts and Telecommunications, and also the Director of Information Economy and Competitiveness Research Center.

David Strohmaier is a Ph.D. candidate at School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing, China. His research focuses on social interaction and information systems.

Shafaq Salam earned her Ph.D. degree from Beijing University of Posts and Telecommunications, Beijing, China. She works at Beaconhouse School Network, Peshawar, Pakistan as an education expert. Her areas of interests are education development and advanced technology in education sector.

Khuram shahzad is a Ph.D. candidate at School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing, China. His research interests are Information System, Innovative & Technological practices in Management both Public & Private Sectors.

1 Introduction

With the rapid growth of service economy, the service sector shares about 66.07% of the world’s GDP (the World Bank, 2016), and it represents a significant part of the world economy [1]. As the engine of service economy growth and social renewal [2], service innovation (SI) can help companies to meet the needs of customers [3, 4], gain competitive advantages [5, 6] and promote industrial enhancement [7, 8]. Therefore, the research on SI is of interest to both managers and academics.

Over the last decade, the increasingly complex environment and accelerated information technologies (IT) have brought a radical shift to SI [9]. SI is no longer the independent behavior of one firm, but the close collaborations of actors in various fields [10]. Thus, more and more enterprises try to access resources and provide new services by constructing the societal structures required for societal human systems to emerge by or of themselves, each and every time human beings, with our human intentionality or purposefulness, i.e., customers, suppliers, governments, etc., interact with said requisite societal structures. An example of this phenomenon is Alipay. Using the system which covers about 200 firms, banks and financial administrative departments, Alipay continuously innovates its services to provide extensive service to millions of business and hundreds of millions of private customers and furthermore, extend its business fields.

Vargo and Lusch [11] use “service ecosystem” to identify these systems and defines service ecosystem as “a relatively self-contained, self-adjusting system of resource integrating actors connected by shared institutional arrangements and mutual value creation through service exchange”. Actors can easily participate in service ecosystems, interface with other actors and use their senses to determine how and when to respond or act. With the ascendance of IT the sensing and responding is more and more spontaneous [12]. Every activity of actors, including resource integration, service exchange and value creation, would change the nature and of ecosystem to some degree and thus the context for the next iteration and determination of value creation. So service ecosystems are not just networks, but self-organized and self-governed systems [13]. Service ecosystems provide the organizing logic for participants in SI to mutually exchange service and co-create values [10]. In the complex social and economic environments of and therefore increasingly serve as the venue for SI instead of organizations [13, 14]. Accordingly, the study of SI within service ecosystem becomes a new research stream [15, 16].

The identification of elements of a system is a well-known method for structured system analysis and has been used for the effective management of service [17]. Therefore, many scholars focused on the research of elements of SI from the perspective of service ecosystem. A variety of elements driving SI within the service ecosystem are presented, such as resource integration [18, 19], institutionalization processes [20, 21] and technologies [22 –24]. Moreover, Lusch and Nambisan [10] proposed a conceptual model of SI including three dimensions: service ecosystem, service platform and value co-creation. Hollebeek and Andreassen [25] developed a “hamburger” model of SI to depict the utilization of actors’ engagement and resource integration in the process of SI.

However, most of these articles do research on SI based on one or a few dimensions. There is a lack of a comprehensive framework which covers all elements of SI and connects them as a whole. The fragment findings raise an urgent need for a systematical review of SI [26, 27]. More importantly, mangers need a framework to help them make sense of the practical approaches of SI because adopting the best sequential implementation of creating new services can make enterprises realize the full economic benefits of SI in the fast changing environment [28, 29]. The literature of SI’s sequence, which can guide organizations on how to implement their practice, are limited [26, 30], specifically within a service ecosystem context.

To fill this research gap, this article desires to provide a systematic study of SI in China to broaden the understanding of essential elements and optimize the implementation path of elements of SI within service ecosystem. More specifically, this article focuses on three research purposes:

To present the systematic framework of SI elements within service ecosystem;

To analyze the relations of those elements and identify the weights of them;

To put forward the sequential approach of SI within service ecosystem.

In this study, we use a combination of the Decision-Making Trial and Evaluation Laboratory (DEMATEL) based Analytic Network Process (ANP) method (called DEMATEL based ANP, or DANP) and the NK model to address those purposes. The former is used to extract the mutual relations of different factors and obtain the factors’ weights. Based on that, we use the NK model to find the best implementation path of SI within service ecosystems.

The remainder of this article is organized as follows. Section 2 presents the theoretical framework of the elements of SI within service ecosystem based on the literature review. Section 3 introduces the research methodology and the computational procedure. Section 4 analyzes the relations among elements and presents an implementation path of SI through empirical study in China. Section 5 discusses the research results, followed by conclusion and future work in section 6.

2 Conceptual framework

After Barras [31] published his article about “Reverse Product Cycle”, the research on SI develops steadily and can be roughly divided into three categories [32]: assimilation (using traditional product innovation theories to study SI), demarcation (developing new service-specific theories to analyze SI), and synthesis (supposing the theories of SI should encompass innovation in both services and manufacturing). Synthesis is replacing assimilation and demarcation in research on SI [33]. As a synthesis theory, service-oriented logic supposes that “Service is the fundamental basis of Exchange”, and all product innovations are service innovations because “Goods are distribution mechanisms for service provision” [11]. By nesting services and goods into an integrated service view [34], service-oriented logic transcends the tangible and intangible differences between goods and services, and is increasingly used as a theoretical basis for SI research [4, 35].

Service ecosystem develops from the service-oriented logic theory, and is regarded as “the system of service systems” [22]. A system, according to the Merriam-Webster Dictionary, is “a regularly interacting or interdependent group of units forming an integrated whole”. Usually, the members of the system act collegially for their common purpose within the ecologically societal structure. Similarly, service systems are “value co-creation configurations of people, technology, value propositions connecting internal and external service systems and shared information” [36]. The smallest service system centers on an individual as he or she interacts with others. Besides, businesses, cities, government agencies, nations, and even the global economy are all service systems [37]. As the system of service systems, service ecosystem consists of three levels: micro level (individual and dyadic structures and activities), meso level (midrange structures and activities, such as brand community) and macro level (broader societal structures and activities). Service ecosystem emphasizes the interactions and value co-creation among multiple service systems which are governed by institutions [36] and therefore, provides a view of innovation that enables the oscillation among micro level, meso level and macro level perspectives [38]. In recent years, SI has been positively discussed from service ecosystem perspective and gained considerable insights into this field (as shown in Table 1).

Table 1
Elements of SI within service ecosystem

Authors Elements Conclusions

Edvardsson and Tronvoll [34] Resource integration Interaction of actors SI originates from the integration and configuration of resource and the changes in schemas of interaction of actors in service system.

Akaka and Vargo [22] Technology As an operant resource, technology becomes a critical resource for SI.

Aal et al. [39] Values resonance Innovation of brands Resource integration Collaboration and resource integration between actors based on shared values are crucial for SI.

Lusch and Nambisan [10] A2A network Resource integration Service platform IT SI is a cooperative process occurring in A2A network through resource integration and value co-creation

Skålén et al. [40] Value proposition SI is sourced by the creation of new value propositions through creation or integration or development of practices and resources

Resource integration

Vargo et al. [20] Institutionalization processes Institutionalization- the breaking, making, and maintaining of institutions -is the central activity of service innovation

Åkesson et al. [41] Value proposition, Resource integration SI is a process of resource integration which can generate new value propositions.

Koskela-Huotari et al. [21] Institutionalization processes Resource integration SI is a process of changes in the institutional arrangements that govern resource integration practices in service ecosystems.

Siltaloppi et al. [42] Institutional complexity Institutional complexity (i.e. the multiplicity of institutional arrangements) drives SI

Frey et al. [23] IT IT plays an important role in SI and enables SI in four different ways.

Di Pietro et al. [43] Value propositions Collaboration of actors Resource integration Institutionalization The scaling up of service innovations depends on four drivers: new value propositions; partnering with strategic actors; integration of resources and practices; and institutionalized norms and rules.

Polese et al. [44] Actors Technology Institutions Resource integration SI in smart tourism ecosystem can be driven by the following dimensions: actors, technology, institutions, and resource integration.

Authors	Elements	Conclusions
Edvardsson and Tronvoll [34]	Resource integration Interaction of actors	SI originates from the integration and configuration of resource and the changes in schemas of interaction of actors in service system.
Akaka and Vargo [22]	Technology	As an operant resource, technology becomes a critical resource for SI.
Aal et al. [39]	Values resonance Innovation of brands Resource integration	Collaboration and resource integration between actors based on shared values are crucial for SI.
Lusch and Nambisan [10]	A2A network Resource integration Service platform IT	SI is a cooperative process occurring in A2A network through resource integration and value co-creation
Skålén et al. [40]	Value proposition	SI is sourced by the creation of new value propositions through creation or integration or development of practices and resources
	Resource integration
Vargo et al. [20]	Institutionalization processes	Institutionalization- the breaking, making, and maintaining of institutions -is the central activity of service innovation
Åkesson et al. [41]	Value proposition, Resource integration	SI is a process of resource integration which can generate new value propositions.
Koskela-Huotari et al. [21]	Institutionalization processes Resource integration	SI is a process of changes in the institutional arrangements that govern resource integration practices in service ecosystems.
Siltaloppi et al. [42]	Institutional complexity	Institutional complexity (i.e. the multiplicity of institutional arrangements) drives SI
Frey et al. [23]	IT	IT plays an important role in SI and enables SI in four different ways.
Di Pietro et al. [43]	Value propositions Collaboration of actors Resource integration Institutionalization	The scaling up of service innovations depends on four drivers: new value propositions; partnering with strategic actors; integration of resources and practices; and institutionalized norms and rules.
Polese et al. [44]	Actors Technology Institutions Resource integration	SI in smart tourism ecosystem can be driven by the following dimensions: actors, technology, institutions, and resource integration.

Through the literature review, this article enumerates the following elements of SI: collaboration or interaction of actors, A2A network, resource integration, value proposition, value resonance, technology, information technology, institutions, institutionalization processes, institutional complexity, and brands. In order to obtain the critical elements of SI, 20 experts are invited to attend the process of selecting elements. Ten of them are scholars in the field of SI research; others are senior managers of different service enterprises who have rich experience in SI. The Delphi method is used to conduct three rounds of expert consultation for selecting and supplementing the elements of SI within service ecosystem. Based on the results, we determine five essential elements of SI which include A2A network, value proposition, resource integration, institutionalization processes and IT and propose the conceptual framework (as shown in Fig. 1). This framework generalizes the extant research of SI within service ecosystem and reflects the development trend of SI.

Fig.1

The conceptual framework of service innovation within service ecosystem.

2.1 A2A network

Actor-to-actor (A2A) network is a dynamic, self-adjusting network which is formed through the link of various actors in SI [13]. The early SI theories think enterprises are producers of new services and customers are recipient of SI and therefore, focus on the dual relation between them [45]. Yet, the perception of distinction between producers and consumers is flawed [12] because SI has become a value co-creation process of different actors, such as enterprises and customers. A2A orientation eliminates the restriction of enterprises, customers, suppliers and governments through translating them from the pre-designed roles to the more general actors. From the perspective of service ecosystem, all actors in A2A network play the same role in SI: creating value through resource integration and service provision [13]. As the nodes of A2A network, actors shape the micro, meso and macro level [38] of service ecosystem which serves as the platform for SI [46]. By means of the A2A network, actors conduct extensive service exchange and provide their own unique resources to participate in SI. In a word, A2A network enlarges the boundary of service ecosystem and extends the scope of SI.

2.2 Value proposition

Service-oriented logic theory proposes that value proposition is the promise of value co-creation through resource integration of actors [40]. One of the most significant challenges in SI is the interaction of actors. By providing the opportunities for value co-creation, value propositions can eliminate the cognitive distance and increase the trust of actors. So value proposition is crucial to develop the relation network and promote interaction of actors in service ecosystem [47]. In addition, value propositions reflect customers’ needs. According to value propositions, enterprises can identify target customers groups and perceive significant customers’ interests in SI, so that new services developed by the company are more in line with market trends. In a nutshell, developing compelling value propositions is a prerequisite for successful service innovation within service ecosystem [36].

2.3 Resource integration

Resource integration is a series of ongoing process through that actors perform for others’ interests. The service-oriented logic suggests “all social and economic actors are resource integrators” [48]. SI cannot be separated from resource integration [49]. Within service ecosystem, resources include operand resources which are static and tangible (e.g., goods, natural resources and money), and operant resources which are dynamic and intangible (e.g., skills, ability and knowledge) [10]. Actors carry on operand resources to facilitate or enable SI, and apply operant resource to act on other resources to initiate SI and generate effects. That means, the resources of any actor cannot be used in isolation and must be integrated with additional resources to create value and obtain sustained competitive advantages. Therefore, resource integration becomes the central process of SI.

2.4 Institutionalization processes

Institutions include “laws, norms, values, and moral codes that dictate the proper behavior of actors, as well as cultural beliefs, cognitive models, and frameworks that guide social activities” [21]. As an important part of the service ecosystem, institutions exist in all levels of a system, affect the value co-creating actions and service exchange among various actors [20], and play a crucial role in transforming potential resources into available resources. On the one hand, different combinations of institutions lead to unique sets of practices, symbols and organizing principles and form a unique environment. This environment directs actors’ perception of potential resources and gives resources unique natures. On the other hand, actors of service ecosystem are embedded in the institutional network. By providing a collaboration mechanism, institutes enable actors to integrate resources under the common basis of rules and cognition which ensures the effect of resource integration [48]. Hence, institutionalization processes provide the context, coordination mechanism and realization path for SI within service ecosystem.

2.5 IT

Arthur [50] suggests that technology can be considered as (1) a means (e.g., process) to fulfill a human purpose, (2) an assemblage of practices and components, and (3) the entire collection of devices and engineering practices. Based on this opinion, Akaka and Vargo [22] define technology, with a service ecosystem view, as “a collection of practices and processes, as well as symbols that are drawn upon to serve a human purpose”. As the most active part of technology, IT, accordingly, becomes an essential component of the service ecosystem, enable the real interactions among actors and plays a critical role in SI [11]. In particular, the development of recent IT trends, such as big data, cloud computing, and the Internet of Things, offers “always-on connection, ubiquitous data, and powerful computing capabilities” to eliminate the restrictions of time and location on participants and affect the delivery, innovation and management of the service [22]. Nambisan [52] suggested that IT plays a dual role in SI. On the one hand, IT, as an operand resources (static and tangible resources), can provide new avenues for the processing of information and service exchange in services to promote the efficiency of SI. On the other hand, IT can trigger new services by creating value propositions as operant resources (dynamic and intangible resources). Therefore, SI can hardly operate without the support of IT.

To sum up, service ecosystem provides a spatial and temporal A2A structure for actors interacting through institutions, technology and language [12]. All actors in A2A network have their value propositions which arise from the resources possessed by themselves [47]. Value propositions connect one actor with other interested actors and drive resource integration among them. This process, which is governed by institutions of service ecosystem, allows the creation of new resources and value propositions with service potential. Also, the process attracts new actors to join and makes some new institutions of service ecosystem. Through the synergies of elements which support and complement one another, actors, including customers, organizations and institutions, realize self-development, change service ecosystem and promote iterative updating of new services.

3 Methodology

In order to address the questions discussed above, we propose a sequential research model by combining the DEMATEL-based ANP (DANP) method and the NK model. The DANP method is used to gain the interrelation among the components of SI and measure the importance of them. Afterward, the NK model determines the implementation order and path of SI practices within service ecosystem. The concepts and procedures of DANP and NK model are presented briefly as follows.

3.1 DANP

The DANP method is a combination of DEMATEL and ANP. As one of the most rapid development methods in the research of complex Multiple-Attribute Decision Making (MADM) process, the DANP method is widely applied in fields of policy evaluation, risks analysis and factors research [53]. In the DANP method, DEMATEL is used to solve the complicated and intertwined problems in multi-factor interleaving system. By using graph theory and matrix tools, DEMATEL method can calculate the cause and effect against each element, and analyze the relations among them. The steps are as follows [54, 55]:

Generating the direct relation matrix;

Calculating the normalized direct relation matrix;

Deriving the total influence matrix;

Obtaining the cause/effect matrix.

Then, the DANP method adopts the composite influence matrix got from DEMATEL instead of the pairwise comparison matrices in ANP to get the weight of each element. The steps are as follows:

Normalizing the total influence matrix;

Deriving unweighted super matrix;

Constructing weighted super matrix;

Calculating the limited super matrix.

As mentioned above, the elements of SI within service ecosystem are not independent but interactive. The DANP method can solve the dependence and feedback relations of each component in the system and therefore, is suitable for our research. Adopting the DANP method to identify the mutual relations among elements of SI and the weights of them, makes the computational process much simpler and the results more scientific and reasonable. The details of the DANP method are shown in appendix A.

3.2 NK model

The NK model [56] presents a powerful research framework to study the evolution of complex adaptive systems by analyzing the interactions among the internal elements of systems [57]. While the NK model was originally used for the evaluation of biological systems, it has been rapidly expanding into management fields such as innovation management [58], supply chain [57], business model [59] and service innovation [26].

N and K are two pivotal parameters in the NK model. In the case of SI, N indicates the number of elements within the service ecosystem. The parameter K refers to that one element is affected by other K related elements. In the initial NK model, every variable has the same parameter K. Each element has several states, and all possible state combinations of N elements depict the system. The change of one element’s state will shift the states of the K elements associated with it, which in turn will affect the state of the entire system. In addition, utilizing the concept of fitness landscape, the NK model uses peaks and valleys in a mountain-like topography to represent the fitness value of states of the system.

The range of the value of K, which determines the ruggedness of the landscape, is from 0 to N-1. If the value of K is low (e.g., K = 0), it means all elements of the system are independent. Then the landscape would be smooth where only peak (the global highest fitness) is facilely to arrive. Along with the increase of K value, the landscape becomes more and more cragged with many peaks and valleys. Correspondingly, the highest fitness is difficult to reach. Through the continuous transformation of the elements’ state, the system can get a climb to the highest peak. So, using the NK model can explore how to adapt the path (i.e. climbing path) to achieve higher fitness peaks. The steps are as follows [57, 59]:

Determining the parameters of N and K;

Calculating the overall fitness value for each state in the system;

Obtaining the optimal path for evaluation of the system.

Just like a biological system, service ecosystem is “a relatively self-contained, self-adjusting system”. In this complex system, SI is not a linear process but a random and non-linear procedure of recombining and/or reconfiguring different elements [26]. The alternations of elements would change the state of the whole system and the process of SI. Thus, the NK model, which is usually used to explore the evolution of systems, can be used to obtain the implementation path of SI within service ecosystem.

4 Empirical analysis of evaluation of SI in Chinese enterprises

In line with the same trend of the development of the world economy, China’s service industry has become the main contributor to its GDP (51.6% in 2017). SI is regarded as the catalyst and propulsion for sustainable economic growth and universally valued by China’s government and enterprises [16]. Furthermore, as we indicate in Barrett et al. [4], emerging markets such as China provide novel opportunities for the research on SI. Hence, by using the DANP method and the NK model, we conduct a practical study on SI in China to deepen the understanding of the evolutionary process of SI within service ecosystem. The process is constructed in the following manner:

(1) Applying DEMATEL to analyze interrelation among elements of SI.

Step 1: Generating the direct influence matrix.

First, we construct the direct influence matrix using the DEMATEL method. According to the framework of SI (Fig. 1), there are total five variables: A2A network (v₁), value proposition (v₂), resource integration (v₃), institutionalization processes (v₄) and IT (v₅). An assessment scale of 0–4 indicates the degree of “no”, “very weak”, “weak”, “strong” and “very strong” respectively on account of the degree of influence among different elements. Those experts, who participate in the selection of elements of SI, support the scoring process. For brevity, we only list one direct influence matrix (as shown in Table 2). Then the direct influence matrix V = [v_ij] _n×n is achieved by averaging each expert’s scores. In matrix V, v_ij denotes the degree of impact of the element i on the element j, and n is the number of elements.

Table 2
The direct-relation matrix of SI elements

v ₁ v ₂ v ₃ v ₄ v ₅

v ₁ 0 2 3 3 2

v ₂ 3 0 4 1 2

v ₃ 1 3 0 2 3

v ₄ 2 2 3 0 2

v ₅ 2 2 3 3 0

	v ₁	v ₂	v ₃	v ₄	v ₅
v ₁	0	2	3	3	2
v ₂	3	0	4	1	2
v ₃	1	3	0	2	3
v ₄	2	2	3	0	2
v ₅	2	2	3	3	0

Step 2: Calculating the normalized direct-relation matrix and the total influence matrix.

The normalized matrix G is derived from the matrix V through the equations (1) and (2). $G = kV$ (1) $k = \min {\frac{1}{max_{i} \sum_{j = 1}^{n} v_{ij}}, \frac{1}{max_{j} \sum_{i = 1}^{n} v_{ij}}}$ (2)

Based on matrix G, the total influence matrix T (as shown in Table 3) is produced by using the equation (3), where matrix I represents an identity matrix of order 5. $T = G + G^{2} + G^{3} + \dots = G {(I - G)}^{- 1}$ (3)

(2) Measuring weight of each element by DANP.

Table 3

The total influence matrix of SI elements

	v ₁	v ₂	v ₃	v ₄	v ₅
v ₁	0.5424	0.7487	0.9412	0.7888	0.7490
v ₂	0.7265	0.6162	0.9959	0.7316	0.7024
v ₃	0.5422	0.7156	0.6468	0.6420	0.6646
v ₄	0.6451	0.6483	0.8231	0.5031	0.5542
v ₅	0.6789	0.8029	0.9446	0.7852	0.5586

Step 3: Normalizing the total influence matrix.

Using the equation (4) and (5), the normalized total influence matrix T^α is derived from the matrix T (as shown in Table 4).

Table 4

The normalized total influence matrix of SI elements

	v ₁	v ₂	v ₃	v ₄	v ₅
v ₁	0.1782	0.1930	0.2161	0.2106	0.2022
v ₂	0.2038	0.1840	0.2248	0.2023	0.1850
v ₃	0.1827	0.2081	0.2008	0.2037	0.2047
v ₄	0.2024	0.2077	0.2049	0.1838	0.2011
v ₅	0.1954	0.2036	0.2282	0.1918	0.1810

$T^{α} = {[t^{α ij}]}_{n \times n} = [\begin{matrix} t^{11} / d_{1} & \dots & t^{1 j} / d_{1} & \dots & t^{1 n} / d_{1} \\ ⋮ & ⋮ & ⋮ \\ t^{i 1} / d_{i} & \dots & t^{ij} / & \dots & t^{in} / d_{i} \\ ⋮ & ⋮ & ⋮ \\ t^{n 1} / d_{n} & \dots & t^{nj} / d_{n} & \dots & t^{nn} / d_{n} \end{matrix}]$ (4) $d_{i} = \sum_{j = 1}^{n} t^{ij}, i = 1, 2, \dots, n$ (5)

Step 4: Obtaining the limited matrix

As just one level elements of SI is used, there is no need to calculate the unweighted super matrix and the weighted super matrix. The limited matrix W^* is obtained from the normalized total influence matrix directly by equation (6) and (7). $W^{α} = {(T^{α})}^{'} W = \lim_{h \to \infty} {(W^{α})}^{h}$ (6) $W = lim_{h \to \infty} {(W^{α})}^{h}$ (7)

In the end, the limited matrix W would become a long-term stable matrix and the weight of each element is obtained (Table 5). The weights and rank of the elements are shown as follows: resource integration 0.2429; value proposition 0.2011; institutionalization processes 0.1939; IT 0.1842; A2A network 0.1779. The results show that resource integration is most important to SI since all innovations including SI are results of existing resource integration [50]. The following one is value proposition which gives impetus to resource integration and participation of actors. Certainly, other elements are also significant as evidenced by their resembled weights.

Table 5

The limited matrix of SI elements

	v ₁	v ₂	v ₃	v ₄	v ₅
v ₁	0.1779	0.1779	0.1779	0.1779	0.1779
v ₂	0.2011	0.2011	0.2011	0.2011	0.2011
v ₃	0.2429	0.2429	0.2429	0.2429	0.2429
v ₄	0.1939	0.1939	0.1939	0.1939	0.1939
v ₅	0.1842	0.1842	0.1842	0.1842	0.1842

(3) Determining the implementation path of SI in China by the NK model

Step 5: Constructing an NK model for SI

The most significant step in developing the NK model is to determine the parameters N and K. In this article, parameter N represents the elements of SI within service ecosystem, so its value is 5.The parameter K would be decided by the strength of interactional relations amongst those elements.

The total influence matrix T can help us to get a proper value of K because it describes the degree of impact among SI elements. However, t_ij of the total influence matrix T represents the impact of element i on element j. On the contrary, in the NK model, k_ij denotes that element i is affected by element j. So transposing the matrix T is necessary. Through the brainstorming of experts, the threshold value λ (λ = 0.6371) is decided to filter the minor impact level of the matrix T’. Comparing each item in matrix T ‘with λ by using equation (8), the adjacency matrix E is created (Table 6).

Table 6

The adjacency matrix of SI elements

	v ₁	v ₂	v ₃	v ₄	v ₅
v ₁	0	1	0	1	1
v ₂	1	0	1	1	1
v ₃	1	1	1	1	1
v ₄	1	1	1	0	1
v ₅	1	1	1	0	0

$(8) e_{ij} = {\begin{matrix} 1 t_{ij}^{'} ⩾ \\ 0 t_{ij}^{'} < \end{matrix} i, j \in {1, 2, \dots, N}$ (8)

Each element’s correlation k_i is the sum of i^th column. That is: $k_{i} = \sum_{j = 1}^{N} e^{ij}, i = 1, 2, \dots, N$ (9)

Different from the traditional NK model, the value of parameter K is given as (3, 4, 4, 4, 3) that means every element is influenced by different number of elements. The interdependence matrix of the NK model is constructed as shown in Table 7.

Table 7

The interdependence matrix of the NK model

	v ₁	v ₂	v ₃	v ₄	v ₅
v ₁	1	1	0	1	1
v ₂	1	1	1	1	1
v ₃	1	1	1	1	1
v ₄	1	1	1	1	1
v ₅	1	1	1	0	1

Step 6: Calculating the overall fitness value of each state

In this article, the parameter a_i used to express the state of elements of SI. Kauffman [56] pointed out the number of states of elements has no obvious effect on the results of the NK model. For that reason, without loss of generality, a_i takes the value of 0 or 1in this study. Consequently, the state A of SI within service ecosystem can be represented as the binary string of a_i (i.e., A = a₁, a₂, a₃, a₄, a₅) and there are 2⁵ possible configurations of A which include {0, 0, 0, 0, 0}, {1, 0, 0, 0, 0}, ... , {1, 1, 1, 1, 1}.

By the NK model theory, each state of element corresponds to a fitness value f_i. The value of f_i is extracted form (0,1) uniformly distributed random varies when the state of i element or the state of other K elements which can influence i element is changed. The overall fitness value F of the SI performance is the arithmetic mean of the values assigned to each f_i of the N elements (10): $F = \frac{1}{N} \sum_{i = 1}^{N} f_{i}, i = 1, 2, \dots, N$ (10)

In equation (10), the weight of each factor is same by default. However, some elements may be more important than others to SI. By confining the early search to relatively, crucial elements can get the better performance with less search time in the NK model [60, 61]. Hence, we use the weight w_i of each element got by DANP to obtain the overall fitness value (11):

$\begin{matrix} F = \sum_{i = 1}^{N} w_{i} f_{i} = (0.1779 f_{1} + 0.2011 f_{2} \\ + 0.2429 f_{3} + 0.1939 f_{4} + 0.1842 f_{5}) \end{matrix}$ (11)

According to equation (11), MATLAB is used to simulate the evolutionary process of SI and calculate the fitness value of each state. To ensure the stability and credibility of the results, this study performs100,000 ➀ simulations on the fitness matrix.

Step 7: Determining the optimal path for SI within service ecosystem.

From the analysis above, we can see that the process of the search optimal path for SI is the evolution process of the elements. Once the states of all elements of SI are determined, the performance landscape is generated. Then the organization moves on the landscape to search for a higher fitness value by changing the states of elements, which is the process of “climbing” on the fitness landscape map. It should be noted that only one element’s state changes at a time during the climbing process in this study.

Through the statistical analysis of the results getting from step 6, it can be found that selecting the fifth element (i.e., IT) as the first step accounts for 24.1%, far exceeding other elements. It implies that IT is the primary condition for SI within service ecosystem and its state should change from “0” to “1” in this step. Similarly, in those states which choose IT as the first step, the second element (i.e., value proposition) has the largest proportion (33.5%) as the next step, and its state should change from “0” to “1” in the second step. By the same token, the order of changing state of remaining elements is “resource integration ⟶ A2A network ⟶ institutionalization processes”. In Table 8, the fitness values of each state in one climbing process are shown as an example.

Table 8

The fitness values of each state in SI

a₁	a₂	a₃	a₄	a₅	f₁	f₂	f₃	f₄	f₅	F
0	0	0	0	0	0.6512	0.4456	0.3652	0.1602	0.0170	0.3284	(a)
1	0	0	0	0	0.1358	0.4740	0.7937	0.0250	0.8998	0.4829
0	1	0	0	0	0.7290	0.8231	0.4005	0.6414	0.0170	0.5200
0	0	1	0	0	0.6512	0.2000	0.7061	0.4373	0.3039	0.4684
0	0	0	1	0	0.6785	0.6779	0.1842	0.3588	0.4718	0.4582
0	0	0	0	1	0.9568	0.2843	0.4915	0.3805	0.6974	0.5490	(b)
1	1	0	0	0	0.4559	0.7994	0.2505	0.0686	0.4116	0.3918
1	0	1	0	0	0.9568	0.3233	0.0200	0.6654	0.7451	0.5064
1	0	0	1	0	0.6696	0.5642	0.6180	0.1101	0.6974	0.5325
1	0	0	0	1	0.9098	0.3507	0.9436	0.0174	0.1515	0.4929
0	1	1	0	0	0.6785	0.3112	0.7428	0.9905	0.3203	0.6148
0	1	0	1	0	0.8033	0.5572	0.9787	0.0334	0.4718	0.5861
0	1	0	0	1	0.5964	0.7481	0.5279	0.8187	0.6345	0.6604	(c)
0	0	1	1	0	0.7290	0.3016	0.1037	0.9001	0.3039	0.4460
0	0	1	0	1	0.1358	0.6004	0.9066	0.7808	0.6564	0.6374
0	0	0	1	1	0.3330	0.1044	0.4429	0.1404	0.8998	0.3808
1	1	1	0	0	0.4559	0.9304	0.4007	0.6421	0.6492	0.6096
1	1	0	1	0	0.3935	0.5174	0.3685	0.3192	0.4116	0.4013
1	1	0	0	1	0.7284	0.7929	0.6798	0.7318	0.0892	0.6125
1	0	1	1	0	0.6696	0.1357	0.4255	0.8709	0.7451	0.5559
1	0	1	0	1	0.9098	0.4639	0.9207	0.5267	0.3166	0.6392
1	0	0	1	1	0.1542	0.3329	0.7786	0.8728	0.1515	0.4806
0	1	1	1	0	0.8033	0.4835	0.0544	0.4124	0.3203	0.3923
0	1	1	0	1	0.5964	0.4316	0.7854	0.7945	0.8660	0.6972	(d)
0	1	0	1	1	0.7533	0.4911	0.3381	0.4199	0.6345	0.5132
0	0	1	1	1	0.3330	0.4578	0.3893	0.5825	0.6564	0.4797
1	1	1	1	0	0.3935	0.5042	0.6354	0.9111	0.6492	0.6220
1	1	1	0	1	0.7284	0.7503	0.4328	0.9481	0.8204	0.7205	(e)
1	1	0	1	1	0.9071	0.3212	0.3320	0.5568	0.0892	0.4310
1	0	1	1	1	0.1542	0.4522	0.5325	0.7654	0.3166	0.4544
0	1	1	1	1	0.7533	0.5575	0.4553	0.0567	0.8660	0.5272
1	1	1	1	1	0.9071	0.8298	0.7700	0.8749	0.8204	0.8360	(f)

In order to graph the climbing map in three dimensions, the values of a₁, a₂ and a₃ are set along the X-axis, a₄ and a₅ are set along Y-axis, and the overall fitness value F is set along Z-axis. The optimal path for SI within service ecosystem, that moves from point (a) (0,0,0,0,0) to (b) (0,0,0,0,1) to (c) (0,1,0,0,1) to (d) (0,1,1,0,1)to (e) (1,1,1,0,1) and finally arrive at the highest peak (f) (1,1,1,1,1), is shown in Fig. 2.

Fig.2

The optimal implementation path of SI within service ecosystem for Chinese enterprises.

5 Discussion

By the combination of the DANP method and NK model, this study obtains the optimal path of SI within service ecosystem (Fig. 2). According to the results, China’s companies should first enhance the ability of IT for SI. In the past research of SI, IT plays an active role, but it is not essential. On the contrary, in service ecosystem, IT becomes an indispensable part of SI and affects all other elements: first, IT provides the infrastructure for SI thus, different actors in service ecosystem can connect with each other to shape the A2A network. Second, the development of IT can assist enterprises to separate the useful information from massive data and improve the efficiency of resource integration. More importantly, IT can generate new value proposition, new service attributions and turns into the trigger of SI. Last, IT can accelerate the institutionalization processes of SI. For example, famous China’s bike-sharing enterprise, Mobike, uses IOT technologies to realize bike position to prevent the loss of bikes and maintains the institutions of bike-sharing service.

The second step for SI is the development of value proposition. As the most important organizational principle [62], value proposition is the starting point of SI strategy. Vargo and Lusch [48] pointed out that “the enterprise cannot deliver value, but only offer value propositions”. Thus, enterprises need to provide value propositions to implement value co-creation in the process of SI. Specifically, value propositions propose reciprocal commitments to establish long-lasting, in-depth and extensive links among actors which speeds up the formation of A2A network. Moreover, by describing the potential benefits of SI, value propositions can be an invitation to actors. If actors are attracted to value propositions, they would offer their valuable resources to fill resources gaps in response to the invitation. Therefore, value proposition shapes the resource integration of whole service ecosystem [63].

Improving the capability of resource integration is the third step for SI. Within service ecosystem view, SI can be framed as an iterative process driven by resource integration [22]. As indicated by Peters [18], resource integration can be divided into “homopathic resource integration based on summative relations between resources and heteropathic resource integration based on emergent relations between resources”. While both of them are valuable to SI, heteropathic resource integration is more pivotal because it can result in emergence of new attributions for SI, such as structures, quality, mechanisms, etc. Since value proposition arises from the resources owned by actors [47], the new resources derived from the integration of existing resources are able to generate new value propositions. Moreover, the improvement of enterprises’ IT ability is inseparable from technological resources provided by universities, research institutes, suppliers and consumers.

The next practice for SI is the expansion of A2A network. The A2A network eliminates the restrictions of “producers” and “consumers,” “innovators” and “adoptions” [64], and transforms all of them from pre-defined roles to more general ones - actors. With the expansion of A2A network, more and more actors from various fields participate in SI, share, exchange and reshape their value propositions which promote the formation of same values among different actors. Therefore, they identify the common purposes of SI for guiding resource integration and improving efficiency. In addition, the institutionalization of SI depends on the A2A network. Based on the common values and norms, actors expedite the programs of institutionalization through multiple interactions and practices in the A2A network.

Finally, China’s enterprises should work on the processes of institutionalization (i.e., breaking, making and maintaining the institutions). Innovations of IT, value propositions and the changes in rules of resource integration can produce new services. Nonetheless, there are still a few obstacles between new services and successful SI. One of them is that SI cannot be successful until the new services have been extensively accepted by costumers. Secondly, the new ways of resource integration and service exchange in SI must underlie rules that can be observed by all actors and tracked by institutions. Through breaking the old and unseasonable institutions, making and maintaining the new and more suitable institutions, actors can gradually understand new services, identify those rules and further participate in the institutional process. In the end, all these actions increase the chances that a relatively stable market will be developed and new services will transform into the successful SI.

6 Conclusion and future work

In the current complicated environment, SI is becoming a non-linear, cooperative and co-creative process by all stakeholders from service ecosystem. Consequently, incorporating a systematic and evolutionary perspective into SI is crucial. Based on this point, we have proposed the optimal path for SI to reveal the development process of SI within service ecosystem. This section highlights the contributions of our research and the managerial implications.

6.1 Research contributions

The first contribution of this article is to identify the elements of SI within service ecosystem and get their weights. Previous articles discussed some aspects of SI but did not provide an integrated view of those elements from service ecosystem perspective. A comprehensive framework is required for the development and operation of SI within service ecosystem. Based on extensive literature review, our study proposed a framework for SI based on five elements, namely, A2A network, value proposition, resource integration, institutionalization processes and IT. The framework illustrates the elements’ changes in SI and provides valuable insights for scholars and managers to understand the full spectrum of SI. In addition, we rank the elements according to their weights calculated by the DANP method. As mentioned before, while all of those elements are essential for SI, resource integration is the most critical one as it is the fundamental way to SI [10].

Second, the core purposefulness of this article was to explore the executing order of SI within service ecosystem. Accordingly, we proposed the optimal implement path for SI through the empirical analysis in China. Based on an improved NK model, this study applies MATLAB to perform 100,000 simulations on the climbing process of SI, and generate the best sequential process: IT ⟶ value proposition ⟶ resource integration ⟶ A2A network ⟶ institutionalization processes. Based on the result, we elaborated the interrelation among those elements, how they act on the establishment of the optimal path and what roles they play in the evolutionary process. The conclusion can serve as a reference for future research of SI and help enterprises to implement the practices of SI.

Finally, this article is the pioneer of combining DANP method and NK model to examine the path of SI within service ecosystem. Methodologically we contribute to the NK model by integrating the DANP method. By using the DANP method, we construct the interdependence matrix with the different parameter k_i replacing the same K of each element, which reflects the independence among elements with more details and approaches the fact in a better way. In traditional NK model, all of the variables have the same weight by default, but they usually have different degrees of importance in the real world. Thus, this study measures overall fitness values by adding the corresponding weight to each element. In this way, the effectiveness of the search process for the execution order in SI is improved. To sum up, integration of the DANP method addresses the NK model limitations and makes the “climbing” process more reasonable and efficient.

6.2 Managerial implications

Several managerial implications can be gleaned from our study. First, firms must pay attention to the improvement of IT. In the digital economical era, IT has become an essential element for service enterprises, as it is not only the carrier of other elements acting on SI but also the booster and trigger of SI. Second, the opinion, which regards enterprises as the innovator of service and customer as the accepter of SI, should be changed. In service ecosystem, enterprises, customers, suppliers, researchers and government officers are all actors in SI. A successful SI requires the participant and interaction of all actors. Third, while value proposition is very important for SI, there are few enterprises developing value propositions from the strategic point of view [63]. If enterprises can provide a variety of value propositions to match the needs of different actors, it will stimulate the enthusiasm of actors to participate in SI. Fourth, enterprises need to go beyond their original boundaries and cooperate with actors in “non-obvious” areas to acquire, configure, and integrate heterogeneous resources required by enterprises, which can promote the emergence of new attributes of SI. Fifth, as Vargo and Lusch [13] remarked, acknowledgement of the role of institutions is essential to understand value co-creation of SI. Enterprises should fully consider the existing institutional environment. Thus, they can implement SI, design cooperative mechanisms, maintain and cultivate rules, and accelerate the institutionalization processes of SI. Finally, all of the five elements interact and restrict each other, whereby their synergy constructs the fabric of SI. Therefore, enterprises should recognize the status quo, correct deficiencies and exert the synergistic effects of elements. Generally, our research can be used to guide SI cooperation as well as making the sequential steps to acquire a high performance of SI in the background of service ecosystem.

6.3 Limitations and future work

Although this article provides several contributions, there are still a few limitations that pave the way for future research directions. First, in terms of broader SI and service ecosystem issues, this study constructed a theoretical framework of SI within service ecosystem including just five elements. Although some initial interesting insights can be developed from our research, is there any other important element of SI should be considered. Thus, a deeper study through other methodologies to identify more elements of SI and enhance the idea of service ecosystem is still needed. Second, the implementation path of SI within service ecosystem did not occur in practice. How and how much do the implementation activities of SI influence the enterprises performance should be analyzed by following up with actual practices. Therefore, further research could investigate how to select a set of SI practices based on the actual situation of enterprises and then allocating the resources investment quantities among them to maximize performance outcome. Finally, the current study was conducted in a single country with specific characteristics that may differ from others and can not be representative of all SI contexts. The contextual characteristics may influence SI practices implementation order. Thus, replications of our study under different geographical contexts represent an important next step. The comparison among different contexts will be important in ascertaining the validity of our research and make the results more general applicability and explanatory power.

Footnotes

Appendix A

The DANP method can be summarized as follows [54, 55]:

(1) Application of DEMATEL for a network relation map

Step 1: Calculating the direct relation matrix

The DEMATEL method first constructs the direct influence matrix A according to the logical relations among the factors. The scale of 0–4 indicates the degree of “no”, “very weak”, “weak”, “strong” and “very strong” respectively based on the degree of influence among the factors. Then the direct influence matrix A = [a_ij] _n×n can be achieved. In matrix A, a_ij denotes the degree of impact of the element i on the element j, and n is the number of factors. (12) $A = [\begin{matrix} a_{11} & \dots & a_{1 j} & \dots & a_{1 n} \\ ⋮ & ⋮ & ⋮ \\ a_{i 1} & \dots & a_{ij} & \dots & a_{in} \\ ⋮ & ⋮ & ⋮ \\ a_{n 1} & \dots & a_{nj} & \dots & a_{nn} \end{matrix}]$

Step 2: Calculating the normalized direct-relation matrix

Using the normalization equations (a.1), (a.2) to deal with the direct matrix A, we get the normalized matrix G. (13) $G = kA$

(14) $k = \min {\frac{1}{max_{i} \sum_{j = 1}^{n} a_{ij}}, \frac{1}{max_{j} \sum_{i = 1}^{n} a_{ij}}$

Step 3: Calculating the total influence matrix

The total influence matrix can be derived from the equation (a.3), where I represents the identity matrix. (15) $T = G + G^{2} + G^{3} + \dots = G {(I - G)}^{- 1}$

Step 4: Obtaining the cause/effect matrix

The row sum d_i of the ith row elements t_ij of matrix T denotes the factor i that influence others. Similarly, the column sum r_j of the jth column elements t_ij of matrix T denotes the factor j that is influenced by others. When i = j, c_i = d_i + r_i represents the degree of the central role that factor i plays in the problem. If h_i = d_i - r_i is positive, factor i influences others. On the contrary, if h_i is negative factor, i is affected by others.

(2) Measuring weights by DANP

Step 5: Normalizing the total influence matrix

The total influence matrix include T_D based on dimensions and T_C based on criteria. Normalizing T_D and T_C by equations (a.4) ∼ (a.8), $T_{D}^{α}$ and $T_{C}^{α}$ can be derived. (16) $T_{D}^{α} = {[t_{D}^{α ij}]}_{m \times m} = [\begin{matrix} t_{D}^{11} / d_{1} & \dots & t_{D}^{1 j} / d_{1} & \dots & t_{D}^{1 m} / d_{1} \\ ⋮ & ⋮ & ⋮ \\ t_{D}^{i 1} / d_{i} & \dots & t_{D}^{ij} / d_{i} & \dots & t_{D}^{im} / d_{i} \\ ⋮ & ⋮ & ⋮ \\ t_{D}^{m 1} / d_{m} & \dots & t_{D}^{mj} / d_{m} & \dots & t_{D}^{mm} / d_{m} \end{matrix}]$ (17) $d_{i} = \sum_{j = 1}^{m} t_{D}^{ij}, i = 1, 2, \dots, m$ (18) $T_{C}^{α} = [\begin{matrix} T_{C}^{α 11} & \dots & T_{C}^{α 1 j} & \dots & T_{C}^{α 1 m} \\ ⋮ & ⋮ & ⋮ \\ T_{C}^{α i 1} & \dots & T_{C}^{α ij} & \dots & T_{C}^{α im} \\ ⋮ & ⋮ & ⋮ \\ T_{C}^{α m 1} & \dots & T_{C}^{α mj} & \dots & T_{C}^{α mm} \end{matrix}]$

In the normalized matrix $T_{C}^{α}$ , $T_{C}^{α ij}$ is a m_i × m_j sub-matrix. We take an example sub-matrix $T_{C}^{α 12}$ to show the process of normalization.

(19) $\begin{matrix} \begin{matrix} C_{21} & \dots & C_{2 j} & \dots & C_{2 m_{2}} \end{matrix} \\ T_{c}^{α 12} = \begin{matrix} C_{11} \\ ⋮ \\ C_{1 i} \\ ⋮ \\ C_{1 m_{1}} \end{matrix} [\begin{matrix} t_{11}^{11} / t_{1}^{12} & \dots & t_{1 j}^{12} / t_{1}^{12} & \dots & t_{1 m_{2}}^{12} / t_{1}^{12} \\ ⋮ & ⋮ & ⋮ \\ t_{i 1}^{12} / t_{i}^{12} & \dots & t_{ij}^{12} / t_{i}^{12} & \dots & t_{{im}_{2}}^{12} / t_{i}^{12} \\ ⋮ & ⋮ & ⋮ \\ t_{m_{1} 1}^{12} / t_{m_{1}}^{12} & \dots & t_{m_{1} j}^{12} / t_{m_{1}}^{12} & \dots & t_{m_{1} m_{2}}^{12} / t_{m_{1}}^{12} \end{matrix}] \end{matrix}$

(20) $t_{i}^{12} = \sum_{j = 1}^{m_{2}} t_{ij}^{12}$

Step 6: Deriving unweighted super matrix

The unweighted super matrix W can be obtained using equation (a.9). (21) $W^{*} = {(T_{C}^{α})}^{'}$

Step 7: Constructing weighted super matrix

$T_{D}^{α}$ is adopted along with the unweighted matrix W^* using equation (a.10) to derive the weighted matrix W^α. (22) $\begin{matrix} W^{α} = T_{D}^{α} W^{*} = \\ [\begin{matrix} t_{D}^{α 11} \times W_{11}^{*} & \dots & t_{D}^{α 1 i} \times W_{i 1}^{*} & \dots & t_{D}^{α 1 n} \times W_{n 1}^{*} \\ ⋮ & ⋮ & ⋮ \\ t_{D}^{α j 1} \times W_{1 j}^{*} & \dots & t_{D}^{α ji} \times W_{ij}^{*} & \dots & t_{D}^{α jn} \times W_{nj}^{*} \\ ⋮ & ⋮ & ⋮ \\ t_{D}^{α n 1} \times W_{1 n}^{*} & \dots & t_{D}^{α ni} \times W_{in}^{*} & \dots & t_{D}^{α nn} \times W_{nn}^{*} \end{matrix}] \end{matrix}$

Step 8: Calculating the limited super matrix

By multiple productions of the weighted super matrix W^α as $lim_{h \to \infty} {(W^{α})}^{h}$ , the limited supermatrix W and influential weights of each criterion can be obtained until it has converged and become a long-term stable super matrix. (23) $W = lim_{h \to \infty} {(W^{α})}^{h}$

A large number of experimental results show that the simulation results are relatively stable when the number of simulations reaches 50,000.

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Toward a service-innovation ecosystem of enterprises in China

Abstract

Keywords

1 Introduction

2 Conceptual framework

2.2 Value proposition

2.3 Resource integration

2.4 Institutionalization processes

2.5 IT

3 Methodology

3.1 DANP

3.2 NK model

4 Empirical analysis of evaluation of SI in Chinese enterprises

Table 2 The direct-relation matrix of SI elements v 1 v 2 v 3 v 4 v 5 v 1 0 2 3 3 2 v 2 3 0 4 1 2 v 3 1 3 0 2 3 v 4 2 2 3 0 2 v 5 2 2 3 3 0

6 Conclusion and future work

6.1 Research contributions

6.2 Managerial implications

6.3 Limitations and future work

Footnotes

Appendix A

References

Table 2
The direct-relation matrix of SI elements

v ₁ v ₂ v ₃ v ₄ v ₅

v ₁ 0 2 3 3 2

v ₂ 3 0 4 1 2

v ₃ 1 3 0 2 3

v ₄ 2 2 3 0 2

v ₅ 2 2 3 3 0