Anthea Van Der Hoogen

Brenda Scholtz

André Calitz

Using Theories to Design a Value Alignment Model for Smart City Initiatives

Keywords: Dimensions, Factors, Stakeholder Roles, Value, Alignment, Theories

Smart city initiatives are widely becoming part of the world agenda to address crises and to identify new initiatives for countires to manage resources while providing better living conditions for all citizens. The purpose of this study was to design a model to support the alignment of value in Smart City initiatives. To address this purpose, a systematic literature review (SLR) was conducted to find what Smart City initiatives have been addressed in empirical studies, and what dimensions and factors are linked to these initiatives. The SLR also identified the stakeholders in a Smart City, and what their roles should be linked to these initiatives. Six theories were identified and used to undergird the researcher's understanding of the domains of Smart Cities, value and alignment. The concepts from these theories were then used with the SLR findings to design a conceptual model for Smart City initiatives. The proposed Value Alignment Smart City Model (VASC) can be used to plan or assess Smart City initiatives. The main contribution is the alignment of value amongst stakeholders to support the success of such initiatives. Further research is required to investigate adopting the model and empirically evaluate it.

Introduction

Even though there is no consensus by researchers regarding the definition of a Smart City, many agree on certain aspects that can help with the understanding of what Smart City studies are about [START_REF] Neirotti | Current trends in smart city initiatives: Some stylised facts[END_REF]. The common component of Smart Cities reported is ICT solutions that address economic, social and environmental issues to contribute to a better quality of life for the citizens [START_REF] Neirotti | Current trends in smart city initiatives: Some stylised facts[END_REF]- [START_REF] Lu | Technology roadmap for building a smart city: An exploring study on methodology[END_REF]. It is found that addressing Smart City concepts and trends through initiatives can help to reach a cohesive understanding amongst cities in the world who are trying to overcome similar or different problems [START_REF] Neirotti | Current trends in smart city initiatives: Some stylised facts[END_REF], [START_REF] Lu | Technology roadmap for building a smart city: An exploring study on methodology[END_REF]. The feasibility of Smart City initiatives is driven from the point of view that it is depending on Big Data and the Internet of Things (IoT) [START_REF] Neirotti | Current trends in smart city initiatives: Some stylised facts[END_REF], [START_REF] Hashem | The role of big data in smart city[END_REF]. Smart city initiatives should further incorporate technologies such as sensors where data can be collected and analysed [START_REF] Abreu | A resilient Internet of Things architecture for smart cities[END_REF].

Conventional and futuristic Smart City initiatives can still be classified or fit in the six dimensions namely Smart People, Smart Governance, Smart Economy, Smart Environment, Smart Mobility, and Smart Living [START_REF] Giffinger | European Smart Cities : the need for a place related Understanding[END_REF]. These dimensions are said to characterise what a smart city should include and for each dimension there are factors that characterise the dimension's success [START_REF] Albino | Smart cities: Definitions, dimensions, performance, and initiatives[END_REF]. A study on Smart City definitions identified certain factors on the importance of a Smart City and the information flow between the factors [START_REF] Albino | Smart cities: Definitions, dimensions, performance, and initiatives[END_REF]. Their definition will be adopted for this study and states that: "A Smart City is based on intelligent exchanges of information that flow between its many different subsystems. This flow of information is analyzed and translated into citizen and commercial services. The city will act on this information flow to make its wider ecosystem more resource-efficient and sustainable. The information exchange is based on a smart governance operating framework designed to make cities sustainable". Many studies have investigated endless lists of initiatives, factors and technologies in Smart City research fields. Some studies have also addressed instruments for assessing the alignment of value and the practices of creating value [START_REF] Dameri | Smart City and Value Creation[END_REF]- [START_REF] Pellicano | Value Co-Creation Practices in Smart City Ecosystem[END_REF]. However, few studies have assessed the perceived value by stakeholders amongst these initiatives according to the theories found for Smart Cities, theories for value and theories for alignment. The research question this study will investigate is "What appropriate theoretical concepts can be used that will help to build a conceptual model to support the alignment of value in Smart City initiatives?". The data value chain is seen as an important component within the conceptual model to ensure that data for each initiative can be identified for all the stakeholder interest. The rest of the paper starts with the research design (Section 2) followed, by findings from the dimensions and factors of a Smart City (Section 3). The stakeholders are perceived as a critical component in Smart City (Section 3.3). For this reason, it is even more important to identify the value created for each stakeholder that can ensure alignment between all the stakeholders' interests (Section 4). The proposed Value Alignment Smart City model (VASC) includes the components that can form part of a Smart City to achieve success in projects (Section 5). Finally, conclusions and future research are provided (Section 6).

Research Design

The research approach used to answer the research question was a systematic literature review (SLR) [START_REF] Kitchenham | Systematic literature reviews in software engineering -A systematic literature review[END_REF]. The journal articles, conference papers and reports were selected from Google Scholar, Google, and Research Gate. Only studies that cited real examples of Smart City initiatives were considered in the review. White papers and reports were excluded from the SLR. Only papers that were published between 2011 and 2018 were included, since it was shown by [START_REF] Mora | The First Two Decades of Smart-City Research: A Bibliometric Analysis[END_REF] that Smart City research started to boom from 2010 onward. The SLR started with the identification of nine Smart City dimensions from 15 initial studies (Section 3.1). The keywords were derived from the research question of this study and included "smart city framework", "smart city initiative", and "smart city dimension". The second round of the SLR included the identification of 39 related factors across all nine dimensions only from emperical studies included in the first round and the findings are summarized (available on request). The second round eliminated non-empirical studies and the final list of 12 studies was used as part of the analysis (available on request). The third round of the SLR helped to identify 58 stakeholder types across four stakeholder roles namely: Enabler; Provider; Utiliser and User. The final list of stakeholder types was reduced to 30 types after eliminating any duplications across the studies included in the analysis (available on request). Finally, theories from the three domains namely Smart Cities, Value, and Alignment were investigated (Table 1). Six theories were identified as relevant and used together with the SLR findings to guide the selection of the components for the VASC model. A summary of these theories and the related components are listed in Table 1. [START_REF] Allwinkle | Creating Smart-er Cities: An Overview[END_REF] Extra dimensions: Smart Policy; Smart Organisation; and Smart Technology-and-ICT Infrastructure Triple Helix Model Theory [START_REF] Etzkowitz | The Triple Helix-University-Industry-Government Relations: A Laboratory for Knowledge Based Economic Development[END_REF] Stakeholder roles and types

Value

Complex Value Typology Theory [START_REF] Rescher | Introduction to value theory[END_REF] Five phases of benefits realisation for all stakeholders; Data Value Chain: data gathered and converted into beneficial information across all areas within a Smart City Alignment Strategic Perspective of Alignment [START_REF] Avison | Using and validating the strategic alignment model[END_REF]- [START_REF] Burn | A comparison of the views of business and IT management on success factors for strategic alignment[END_REF] Strategic initiatives of Smart City projects aligned to all components of the model Structural Alignment Theory [START_REF] Burn | A comparison of the views of business and IT management on success factors for strategic alignment[END_REF]; [START_REF] Chorn | The 'Alignment' Theory: Creating Strategic Fit[END_REF] Alignment of roles/responsibilities of Smart City structures for all stakeholders The Hexagonal Dimension Theory (HDT) was selected from the Smart City domain and proposes the first six dimensions for the VASC model [START_REF] Giffinger | European Smart Cities : the need for a place related Understanding[END_REF], [START_REF] Kishore | Exploratory Research on Smart Cities: Theory, Policy and Practice[END_REF]. The HDT is based on models discussing the analysis, relationships, and indicators of the six Smart City dimensions from [START_REF] Giffinger | European Smart Cities : the need for a place related Understanding[END_REF]. Indicators that should be used for assessment to help determine how Smart Cities are ranked are proposed by [START_REF] Kishore | Exploratory Research on Smart Cities: Theory, Policy and Practice[END_REF], [START_REF] Giffinger | Smart cities Ranking of European medium-sized cities[END_REF]. Three additional dimensions were selected as part of the VASC model, based on the Strategic Priority Areas Theory (SPAT) [START_REF] Allwinkle | Creating Smart-er Cities: An Overview[END_REF]. The additional dimensions in this study are Smart Policy; Smart Organisation, and Smart Technology-and-ICT Infrastructure [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF]. The Triple Helix Model Theory (THMT) [START_REF] Etzkowitz | The Triple Helix-University-Industry-Government Relations: A Laboratory for Knowledge Based Economic Development[END_REF], emphasises the importance of the core stakeholders roles and types such as academia, industry, and government, which are key component of any national or multi-national innovation strategy and therefore any Smart City initiatives. The Complex Value Typology Theory (CVTT) was used to guide the researcher's understanding of value [START_REF] Rescher | Introduction to value theory[END_REF]. In this theory, value can be viewed as the nature of the benefits incurred by the stakeholders. Therefore the five phases of benefits' realisation [START_REF] Flak | Towards a theoretical model for corealization of IT value in government[END_REF], are important to be able to identify the potential benefits of all stakeholders in a Smart City initiative. Since one of the key elements of all the technologies involved in a Smart City is the data, the data value chain is extremely relevant for providing value to the stakeholders or for assessing where value is realised. The Strategic Perspective of Alignment (SPA) theory was used to guide the researcher's understanding of alignment and the Structural Alignment Type (SAT) theory was incorporated to align performance of Smart City initiatives between IT strategy and the organisational strategy [START_REF] Rose | Unpacking organizational alignment: the view from theory and practice[END_REF]; as reported in [START_REF] Avison | Using and validating the strategic alignment model[END_REF]- [START_REF] Burn | A comparison of the views of business and IT management on success factors for strategic alignment[END_REF]. SAT is a type of alignment based on a systematic view of a structure to ensure that strategic goals are achieved [START_REF] Chorn | The 'Alignment' Theory: Creating Strategic Fit[END_REF], [START_REF] Torraco | The strategic roles of human resource development[END_REF]. The importance of having structures in place for a Smart City is important as well as to achieve the strategic goals within those structures because from these structures clear roles and responsibilities can be aligned between the stakeholders of Smart City initiatives.

Findings: Smart City Dimensions and Factors

In this section, the term dimension(s) will be used to describe the list of dimensions highlighted in Section 3.1. Any other aspects that are further used to describe these dimensions will be referred to as factors and these are described in Section 3.2.

Dimensions

The first round of the SLR resulted in the findings summarised in Table 2 relating to dimensions referred to in the empirical studies reviewed. The importance of considering the dimensions in a Smart City initiative was confirmed and that measures should be in place to ensure that cities continue to find smarter ways of dealing with challenges [START_REF] Albino | Smart cities: Definitions, dimensions, performance, and initiatives[END_REF], [START_REF] Cocchia | Smart and Digital City: A Systematic Literature Review[END_REF]. The studies are listed in chronological order (Table 2). The 'x' in Table 2 represents the dimensions that are applied or mentioned in the relevant empirical study as a contributor in a Smart City and the frequency (f) of citations for each dimension is provided. The first six dimensions (D1-D6) of Smart Cities were identified by [START_REF] Giffinger | Smart cities Ranking of European medium-sized cities[END_REF] and [START_REF] Giffinger | European Smart Cities : the need for a place related Understanding[END_REF] and are Smart People, Smart Governance, Smart Economy, Smart Environment, Smart Mobility, and Smart Living. These were extended by three dimensions (D7-D9) proposed by [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF], namely Smart Policy, Smart Organisation, and Smart Technologyand-ICT Infrastructure. Each dimension in the VASC model (Figure 1) was classified as either a core dimension or a support dimension. Smart People (D1) and Smart Technology-and-ICT Infrastructure (D9) are classified as support dimensions to the other core dimensions (D2-D8). This classification was based on the description of Porter's value chain according to the support activities or functions in an organisation [START_REF] Porter | Competitive Advantage: Creating and Sustaining Superior Performance[END_REF], where the well-known support functions in an organisation include IT and Human Resource Management. The only studies that reported on all nine dimensions were [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF] and [START_REF] Calderón | Smart Cities in Latin America: Realities and Technical Readiness[END_REF]. Smart economy and smart living were the top two dimensions reported on (f = 11). Smart people, smart policy and smart technology-and-ICT infrastructure are the second-highest dimensions reported (f = 10). The dimensions that were least reported on within its context of being applied within Smart Cities are smart mobility and smart organisation. Smart People (D1) is the first important dimension identified by several Smart City studies [START_REF] Giffinger | European Smart Cities : the need for a place related Understanding[END_REF], [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF], [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF]- [START_REF] Manupati | A Multi-Criteria Decision Making Approach for the Urban Renewal in Southern India[END_REF]. This dimension recognises that people who are stakeholders can contribute to a Smart City's success. The second last row in Tabale 2 indicates the total number of studies per dimension where "x" number of factors are found, i.e. not all dimensions have factors linked to each per empirical study. Some of the factors related to people are the level of qualification, affinity to lifelong learning, social and ethnic plurality, creativity, and synergies through partnerships and collaborations. The second dimension is Smart Governance (D2), which was identified as an important dimension that includes factors that drive a Smart City such as participation in decision-making, public and social services transparent governance [START_REF] Giffinger | European Smart Cities : the need for a place related Understanding[END_REF], [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF], [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF]- [START_REF] Huovila | Smart City Performance Measurement System[END_REF], [START_REF] Yadav | The Role of Open Data in Driving Sustainable Mobility in Nine Smart Cities[END_REF]. The third dimension commonly cited in Smart City studies is Smart Economy (D3) [START_REF] Giffinger | European Smart Cities : the need for a place related Understanding[END_REF], [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF], [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF]- [START_REF] Wendt | Co-Creation for Smart City Solutionsa Peer-to-Peer Process[END_REF], [START_REF] Spaans | Building up resilience in cities worldwide -Rotterdam as participant in the 100 Resilient Cities Programme[END_REF], [START_REF] Kassen | Understanding transparency of government from a Nordic perspective: open government and open data movement as a multidimensional collaborative phenomenon in Sweden[END_REF]. This dimension refers to activities that encourage innovation, entrepreneurship spirit, productivity and international embeddedness. Seven studies reported on the importance of Smart Environment (D4) as a dimension [START_REF] Giffinger | European Smart Cities : the need for a place related Understanding[END_REF], [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF], [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF], [START_REF] Calderón | Smart Cities in Latin America: Realities and Technical Readiness[END_REF], [START_REF] Huovila | Smart City Performance Measurement System[END_REF], [START_REF] Manupati | A Multi-Criteria Decision Making Approach for the Urban Renewal in Southern India[END_REF], [START_REF] Spaans | Building up resilience in cities worldwide -Rotterdam as participant in the 100 Resilient Cities Programme[END_REF]. This discussion relates to factors such as: attractiveness of natural conditions, environmental protection policies and being able to have sustainable resource management, and ensuring that a city is future proof (i.e. sustainable) by having a sustainability strategy to address social-economic, political and environmental aspects of a city. Interestingly, sustainable resource management and a future proof city were reported in the same seven studies as important for a Smart City. Smart Mobility (D5) is the dimension that focuses on factors involving sustainable, innovative and safe transport systems that are accessible locally, nationally and internationally [START_REF] Giffinger | European Smart Cities : the need for a place related Understanding[END_REF], [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF]- [START_REF] Nam | Conceptualizing Smart City with Dimensions of Technology, People, and Institutions[END_REF], [START_REF] Yadav | The Role of Open Data in Driving Sustainable Mobility in Nine Smart Cities[END_REF]. The sixth dimension (D6) is Smart Living, which includes factors such as cultural facilities, health conditions, individual safety, housing quality and education facilities. Smart Policy (D7) is the dimension that highlights the importance of a close relationship between a Smart City initiative and the city's policy and the importance of an innovative policy [28]- [START_REF] Nam | Conceptualizing Smart City with Dimensions of Technology, People, and Institutions[END_REF], [START_REF] Wendt | Co-Creation for Smart City Solutionsa Peer-to-Peer Process[END_REF], [START_REF] Yadav | The Role of Open Data in Driving Sustainable Mobility in Nine Smart Cities[END_REF]- [START_REF] Garg | Information Policy Dimension of Emerging Technologies[END_REF].

The Smart Organisation dimension was identified as the eighth dimension (D8), and is important since organisational culture and innovative leadership and management can influence the success of a Smart City [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF], [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF]- [START_REF] Nam | Conceptualizing Smart City with Dimensions of Technology, People, and Institutions[END_REF], [START_REF] Wendt | Co-Creation for Smart City Solutionsa Peer-to-Peer Process[END_REF], [START_REF] Manupati | A Multi-Criteria Decision Making Approach for the Urban Renewal in Southern India[END_REF], [START_REF] Nam | Smart City as Urban Innovation: Focusing on Management, Policy, and Context[END_REF]. The ninth dimension (D9) is Smart Technology and ICT-infrastructure and includes all the smart technologies that are used in Smart City used for the collection and analysis of all related data. This is only possible when there is easy access and availability in the ICTinfrastructure [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF], [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF]- [START_REF] Nam | Conceptualizing Smart City with Dimensions of Technology, People, and Institutions[END_REF], [START_REF] Wendt | Co-Creation for Smart City Solutionsa Peer-to-Peer Process[END_REF]- [START_REF] Spaans | Building up resilience in cities worldwide -Rotterdam as participant in the 100 Resilient Cities Programme[END_REF], [START_REF] Nam | Smart City as Urban Innovation: Focusing on Management, Policy, and Context[END_REF], [START_REF] Garg | Information Policy Dimension of Emerging Technologies[END_REF].

Factors

Dimensions and factors should be incorporated in studies of Smart Cities, but provision should be made for other factors to be included when gathering data and findings of studies [START_REF] Giffinger | Smart cities Ranking of European medium-sized cities[END_REF]. Each dimension of a Smart City can be categorised and ultimately measured in terms of a number of factors. From the second round of the SLR process, 39 factors (F1 to F39) were identified and the details are provided (available on request). The studies of [START_REF] Balakrishna | Enabling Technologies for Smart City Services and Applications[END_REF] and [START_REF] Hamzah | A Smart City Assessment Framework[END_REF] were excluded from this analysis as they did not provide empirical evidence of the factors. A total of 12 empirical studies were therefore included in the analysis of the 39 factors. The first 31 factors identified for the first six dimensions were proposed by [START_REF] Giffinger | European Smart Cities : the need for a place related Understanding[END_REF] and confirmed by other studies [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF], [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF], [START_REF] Nam | Smart City as Urban Innovation: Focusing on Management, Policy, and Context[END_REF], [START_REF] Garg | Information Policy Dimension of Emerging Technologies[END_REF], [START_REF] Calderón | Smart Cities in Latin America: Realities and Technical Readiness[END_REF]- [START_REF] Kassen | Understanding transparency of government from a Nordic perspective: open government and open data movement as a multidimensional collaborative phenomenon in Sweden[END_REF], and the remaining eight factors were found in other studies (available on request). The first of these fall within the Smart Environment dimension, and is "Future Proof" (F22) [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF], [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF], [START_REF] Calderón | Smart Cities in Latin America: Realities and Technical Readiness[END_REF], [START_REF] Huovila | Smart City Performance Measurement System[END_REF], [START_REF] Manupati | A Multi-Criteria Decision Making Approach for the Urban Renewal in Southern India[END_REF], [START_REF] Spaans | Building up resilience in cities worldwide -Rotterdam as participant in the 100 Resilient Cities Programme[END_REF]. The other seven factors are: relationship between the Smart City initiative and the city's policy; policy integration; organisational culture; innovative leadership and management; smart technologies; smart data; and availability of infrastructure (including Built and ICT).

Stakeholder Roles and Types

Arguments show the utmost importance to involve all stakeholders in Smart City initiatives, to address the challenges of these initiatives [START_REF] Yadav | The Role of Open Data in Driving Sustainable Mobility in Nine Smart Cities[END_REF]; [START_REF] Nam | Smart City as Urban Innovation: Focusing on Management, Policy, and Context[END_REF], and to lead to successful innovative solutions [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF]. Stakeholders such as citizens, end-users, IT experts and policy experts are key to the architecture of a Smart City [START_REF] Nam | Conceptualizing Smart City with Dimensions of Technology, People, and Institutions[END_REF]. Understanding the needs and wants of all stakeholders will improve the citizen-government relationship [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF]. A significant challenge faced by Smart Cities is to efficiently articulate the relationship between these stakeholders and the city management [START_REF] Calderón | Smart Cities in Latin America: Realities and Technical Readiness[END_REF]. Four key roles for stakeholders were identified in [START_REF] Mayangsari | Multi-stakeholder co-creation Analysis in Smart city Management: An Experience from Bandung, Indonesia[END_REF], namely: enablers, providers, utilisers and users. Enablers create a vision, allocate resources, provide strategic leadership, and promote networking. Providers engage academics and professionals as innovators, provide innovative research and design (R&D) methods, augment knowledge and manage knowledge distribution systematically. Utilisers create suitable products and services, set smallscale objectives derived from the vision, learn new practices to produce accessible knowledge and innovate. Users participate in experiments, empower citizens through co-creation and produce place-based experience. The third round of the SLR identified 58 relevant stakeholder types cited in 15 studies (Table 3). In these studies, common stakeholders were recognised, however on occasions different terms were used to refer to similar stakeholder types in Smart Cities. The studies are listed in chronological order in Table 3. Six stakeholders namely, governments in other jurisdictions, non-profits, companies, schools, universities, and citizens were identified by [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF]. Five stakeholder types were identified by [START_REF] Balakrishna | Enabling Technologies for Smart City Services and Applications[END_REF], namely users, the public, administration, vendors and government. One study [START_REF] Monzon | Smart Cities Concept and Challenges: Bases for the Assessment of Smart City Projects[END_REF] argues that all investors (public and private) are important stakeholders. Residents and workers are amongst the stakeholders found in a Smart City [START_REF] Hamzah | A Smart City Assessment Framework[END_REF]. It was evident in [START_REF] Huovila | Smart City Performance Measurement System[END_REF], that citizens are key to be engaged in Smart City projects to establish their needs, but industrial stakeholders are also important as they give the recommendations needed for new businesses. To create a sustainable city, the participation from stakeholders such as public government, NGOs, private companies and individual citizens is required [START_REF] Spaans | Building up resilience in cities worldwide -Rotterdam as participant in the 100 Resilient Cities Programme[END_REF]. Three stakeholder types were reported in [START_REF] Calderón | Smart Cities in Latin America: Realities and Technical Readiness[END_REF], citizens, government, and businesses. The authors in [START_REF] Manupati | A Multi-Criteria Decision Making Approach for the Urban Renewal in Southern India[END_REF], agree that citizens and government are key stakeholders. Stakeholders influencing privacy of Big Data such as data controllers, data processors, and third parties should be considered in a Smart City [START_REF] Garg | Information Policy Dimension of Emerging Technologies[END_REF].

Open data is part of Smart Cities and the people that are involved with open data projects are stakeholders and can be used to brainstorm innovative ideas [START_REF] Kassen | Understanding transparency of government from a Nordic perspective: open government and open data movement as a multidimensional collaborative phenomenon in Sweden[END_REF].

Table 3. Stakeholder Types (Author's construct)

Study Stakeholder types (n=58) [START_REF] Nam | Smart City as Urban Innovation: Focusing on Management, Policy, and Context[END_REF] Governments; Firms; Non-profits; Citizens [START_REF] Nam | Conceptualizing Smart City with Dimensions of Technology, People, and Institutions[END_REF] End-users; IT experts; Policy/service domain experts; Public managers [START_REF] Alawadhi | Building Understanding of Smart City Initiatives[END_REF] Governments in other jurisdictions; Non-profits; Companies; Schools; Universities; Citizens [START_REF] Balakrishna | Enabling Technologies for Smart City Services and Applications[END_REF] Users; Public administrations; Vendors; Government [START_REF] Monzon | Smart Cities Concept and Challenges: Bases for the Assessment of Smart City Projects[END_REF] Investors (public and private) [START_REF] Hamzah | A Smart City Assessment Framework[END_REF] Residents/Citizens; Workers [START_REF] Huovila | Smart City Performance Measurement System[END_REF] Citizens; Industrial stakeholders [START_REF] Khatoun | Smart Cities: Concepts, Architectures, Research Opportunities[END_REF] Performance evaluators [START_REF] Spaans | Building up resilience in cities worldwide -Rotterdam as participant in the 100 Resilient Cities Programme[END_REF] Public government; Private companies; NGOs; Citizens [START_REF] Calderón | Smart Cities in Latin America: Realities and Technical Readiness[END_REF] Citizens; Government; Businesses [START_REF] Garg | Information Policy Dimension of Emerging Technologies[END_REF] Individuals; Data controllers; Data processors; Third parties [START_REF] Kassen | Understanding transparency of government from a Nordic perspective: open government and open data movement as a multidimensional collaborative phenomenon in Sweden[END_REF] Public officials; Independent developers; Technically savvy citizens; NGOs; Academic communities; Media communities [START_REF] Wendt | Co-Creation for Smart City Solutionsa Peer-to-Peer Process[END_REF] Industrial players; Business players; Dynamic small and medium-sized enterprises (SMEs); Building owners; Universities; Research & technology organisations; Major standardisation institutes; Government; Citizens; Local experts; External domain experts [START_REF] Yadav | The Role of Open Data in Driving Sustainable Mobility in Nine Smart Cities[END_REF] Citizens; City managers; Developers; Governments [START_REF] Manupati | A Multi-Criteria Decision Making Approach for the Urban Renewal in Southern India[END_REF] Citizens; Government They could be independent developers, technically savvy citizens, academic communities or non-governmental organisations. The co-creation process for Smart City solutions, identified by [START_REF] Wendt | Co-Creation for Smart City Solutionsa Peer-to-Peer Process[END_REF], reiterates the importance of the involvement of all stakeholders (industrial and business players to external domain experts) and the alignment of value to achieving Smart City success. City managers and government should provide easy accessibility and interactions for users such as developers and citizens to open datasets [START_REF] Yadav | The Role of Open Data in Driving Sustainable Mobility in Nine Smart Cities[END_REF] since this should help these users to understand the datasets and to identify ways toward sustainable open data systems. An analysis of the definitions taken from [START_REF] Mayangsari | Multi-stakeholder co-creation Analysis in Smart city Management: An Experience from Bandung, Indonesia[END_REF] for each role was used to classify each stakeholder type according to the most relevant role. This analysis resulted in the initial list of 58 stakeholder types being reduced to 30 common types (T1 to T30) across the 15 studies and the four stakeholder roles (available on request). For example company types such as private, public, firms and SMEs were combined into one type. Two stakeholder types (city mayor and think tanks/incubators ) were not identified in the studies in Table 3 but were added to the final list based on the argument of [START_REF] Mayangsari | Multi-stakeholder co-creation Analysis in Smart city Management: An Experience from Bandung, Indonesia[END_REF] that they are equally important stakeholders. Citizens as stakeholders were reported in 11 of the 15 studies, making this the most popular type reported. Six studies reported government and four studies reported companies as important. It is clear that when a city wants to co-create smart solutions, many different types of stakeholders have to be considered.

Alignment of Value for Benefits Realisation

The previous sections related to the SLR findings, it is evident that the dimensions, factors and stakeholders of a Smart City should be used to assess the benefits of a Smart City initiative. However, existing Smart City studies do not explore whether or not the benefits of initiatives are realised or whether stakeholder value is considered or aligned. It is argued that what one stakeholder might view as a successful or valuable initiative may not be considered as successful or valuable to another stakeholder. In order to finalise the model so that value can be considered, the value theory of [START_REF] Etzkowitz | The Triple Helix-University-Industry-Government Relations: A Laboratory for Knowledge Based Economic Development[END_REF] was incorporated, which equates assessment of benefit to the concept of value [START_REF] Rescher | Introduction to value theory[END_REF]. For example, "human wants, needs, and interest that are served by their realisation" [START_REF] Hamzah | A Smart City Assessment Framework[END_REF].

In another study of value, the authors showed the factors influencing value co-creation established by [START_REF] Sarker | Exploring Value Cocreation in Relationships Between an ERP Vendor and its Partners: A Revelatory Case Study[END_REF] and also applied by [START_REF] Flak | Towards a theoretical model for corealization of IT value in government[END_REF]. They proposed an integrated process model for co-realisation of value, and they used a government case study in Norway to validate their approach to co-realisation of IT value in a collaborative setting. In the study of [START_REF] Flak | Towards a theoretical model for corealization of IT value in government[END_REF] the value co-creation process incorporated five phases for benefits realisation to co-create IT value. Their study contributed to value theory and showed that these phases are appropriate for new, major service development in the Norwegian government. This phased approach can be adopted in Smart City initiatives to achieve alignment of stakeholder value. The first phase is Phase 1-Articulate benefits whereby the key benefit areas, Key Performance Indicators (KPI) and goals are identified and articulated amongst all stakeholders. Potential benefit areas for new services in a Smart City were also explored. Based on the THMT and studies, as many stakeholders from the roles and types should be considered and should collaborate on services in a Smart City. The second phase is Phase 2-Plan benefits realisation where the registrar (i.e. Smart City project manager) assists the service owners (i.e. stakeholders) in elaborating their ideas into a detailed benefits plan with action steps to ensure that the benefits will be realised. In Phase 3-Implement plan, the service stakeholder has to implement the plan according to the benefit plan from Phase 2. In Phase 4-Measure benefits realised, the service stakeholder has to measure the benefits according to the measurements from the benefit plan in Phase 2 and report these to the registrar. Lastly, Phase 5-Evaluate benefits gaps and needs is where the registrar evaluates all the reports from all service stakeholders and decides on corrective measures to be taken where delays in services are evident.

Discussion and Proposed Model

The proposed VASC model is shown in Figure 1 and represents the important components of a Smart City to achieve the success of a Smart City project or initiatives. The model was designed based on the SLR findings and the six theories, relating to the domains of Smart Cities, value, and alignment. The first component is the nine dimensions of a Smart City (see Fig 1). Each dimension has several factors for determining the success of the dimension (available on request). The second component is the four stakeholder roles, which is a key component, since if the stakeholders are not considered no Smart City initiative will be successful. In order to ensure the value or benefits derived from such initiatives, five phases should be followed and are included as the third component of the model. Finally, any Smart City initiative is dependent on the information flow that supports it. Information flow is described as a "series of steps needed to generate value and useful insights from data" [START_REF] Curry | The Big Data Value Chain: Definitions, Concepts, and Theoretical Approaches[END_REF]. To obtain value from a Smart City initiative, the data value chain is therefore a crucial consideration and is the last component in the model. The data value chain includes the entire data life-cycle and involves data acquisition, analysis, curation, storage and usage so it can be used for decision making by relevant stakeholders.

Conclusions

Smart City research has made strides to making it easier to identify smarter ways of addressing real-world problems, especially with regards to the pressures of urbanisation and resource depletion. However, consensus on the definition, required components and value for Smart Cities has yet to be reached. The theoretical perspectives explored in this study can assist researchers to move closer to such consensus. The SLR conducted focused on seeking empirical studies of Smart City projects and reviewed theories that can help to address the gaps in knowledge relating to value in Smart Cities.

The study contributes to showing real-world examples in Smart Cities, and provides a comprehensive lists of factors that can be classified for each dimension. A gap in previous research was evident relating to value alignment for Smart Cities, and this study fills this gap. The contribution is the proposed VASC model, which can be used to address how value can be aligned within a Smart City for all stakeholders and dimensions. The study was limited to secondary data and future research should therefore investigate the adoption of the model in Smart City initiatives.

Fig. 1 .

 1 Fig. 1. VASC model

Table 1 .

 1 Theoretical Concepts informing the VASC model

Domain Theoretical Concepts Component of the VASC model

	Smart	Hexagonal Dimension Theory [6];	Original dimensions: Smart People; Smart Gov-
	Cities	[13]	ernance; Smart Economy; Smart Environment;
	(SLR)		Smart Mobility; and Smart Living
		Strategic Priority Areas Theory

Table 2 .

 2 Comparison of dimensions of Smart Cities (Author's construct)

Acknowledgement

"This work is based on the research supported wholly / in part by the National Research Foundation of South Africa (Grant Numbers: 116779)".


Katja Bley
email: katja.bley@tu-dresden.de

Hendrik Schön
email: hendrik.schoen@tu-dresden.de

Susanne Strahringer
email: susanne.strahringer@tu-dresden.de

Overcoming the Ivory Tower: A Meta Model for Staged Maturity Models

Keywords: Maturity Model Development, Meta Model, Conceptual Modeling

When it comes to the economic and strategic development of companies, maturity models are regarded as silver bullets. However, the existing discrepancy between the large amount of existing, differently developed models and their rare application remains astonishing. We focus on this phenomenon by analyzing the models' interpretability and possible structural and conceptual inconsistencies. By analyzing existing, staged maturity models, we develop a meta model for staged maturity models so different maturity models may share common semantics and syntax. Our meta model can therefore contribute to the conceptual rigor of existing and future maturity models in all domains and can be decisive for the success or failure of a maturity measurement in a company.

Introduction

Economic development, the assumption of growth, and the ongoing transformation of processes increase the competitive pressure on enterprises of all sizes. Hence, they search for tools that can help determine their current benchmarking position or assess their subsequent performance compared to a predefined best-practice performance [START_REF] Bley | A Role-Based Maturity Model for Digital Relevance[END_REF].

One famous example of these benchmarking tools is Maturity Models (MMs). Considering their components, two definitions result: 'maturity' as a "state of being complete, perfect or ready" [START_REF] Simpson | The Oxford English dictionary[END_REF] and 'model' as "an abstraction of a (real or language based) system allowing predictions or inferences to be made" [START_REF] Kühne | Matters of (Meta-) Modeling[END_REF]. Thus, an MM can be regarded as an abstraction of a system that allows predictions or inferences about a complete or perfect state. Its aim is a structured, systematic elaboration of best practices and processes that are related to the functioning and structure of an organization [START_REF] Wendler | The Maturity of Maturity Model Research: A Systematic Mapping Study[END_REF]. The MM is divided into different levels, which are used as benchmarks for the overall maturity of an organization. By application, an object is able to assess its own position in a predefined best-practice approach. An awareness of the maturity level in a particular domain is necessary in order to recognize improvement potentials and stimulate a continuous improvement process [START_REF] Isoherranen | Operational excellence driven by process maturity reviews: A case study of the ABB corporation[END_REF]. Especially when it comes to emerging phenomena like digitalization or the Industrial Internet, MMs became a favored instrument especially for SMEs in order to determine their own digitalization status and corresponding guidelines for improvement. But it is not only in this area that there has been an enormous increase in MM publications in recent years. Due to their general applicability, the rather simple development, and the promising competitive advantages many MMs have emerged in both science and practice over the last decade. They differ in the concepts of maturity, the considered domains, the development approach, or the target group [START_REF] Wendler | The Maturity of Maturity Model Research: A Systematic Mapping Study[END_REF][START_REF] Tarhan | Business Process Maturity Models: A Systematic Literature Review[END_REF].

Although there exist several approaches to the rigorous development (i.e. [START_REF] Pöppelbuß | What makes a useful maturity model? A framework of general design principles for maturity models and its demonstration in business process management[END_REF][START_REF] Becker | Developing maturity models for IT management[END_REF][START_REF] De Bruin | Understanding the Main Phases of Developing a Maturity Assessment Model[END_REF]), and there are MMs that already follow these guidelines and should be considered as complete and thorough, a plethora of developers still see a need for new and different kinds of MMs. A possible reason for this phenomenon may be that current MMs lack in consistency regarding their semantics, syntax, and concepts. This leads to a situation where many different MMs introduce ontologies that are either conceptually the same but are used for different subjects and in different contexts so researchers do not understand or recognize similar models or they try to differentiate from existing approaches by using different terminology (e.g. level vs. stages, maturity vs. assessment, dimension vs. area). This in turn weakens the benefits of MMs for companies, as they are unable to understand, compare, and apply the models due to different terminology or incomprehensible concepts and relationships. As a consequence, a solution is needed that proposes theoretical and practical solutions for the semantic and syntactical pitfalls and difficulties mentioned.

We address this problem of conceptual divergence by introducing a UML-based meta model of MMsa formal construct that summarizes the various MM concepts, features, and interdependencies and relates them to each other. We introduce this meta model regarding the different MM concepts, where each MM can be an instance of it as it provides a conceptual template for the rigorous development of new and the evaluation of existing maturity models. We thereby focus on staged MMs, as they have a holistic and cross-organizational structure that is dominant in MM research. Based on the most popular MMs as well as several newly developed MMs, we summarize and discuss already existing MM concepts. We are able to show a valid instantiation of our maturity meta model by classifying different staged MMs in their properties and concepts with our meta model.

2

The Anatomy of Maturity Models

Definition and Application of Maturity Models

According to [START_REF] Fraser | The use of maturity models/grids as a tool in assessing product development capability[END_REF], MMs typically consist of: a) a number of levels (commonly 3-6), b) a generic description of each level, c) a number of dimensions or "process areas," d) a number of elements or activities for each process area, and e) a description of the performance of each activity or element as it might perform or might be performed at each maturity level. The purpose of MM assessment can vary. Depending on its intended aim, the MM focuses on an assessment of the current state of development (descriptive), the identification of improvement potential (prescriptive), or its application as a benchmarking tool (comparative) for an object under study [START_REF] Röglinger | Prozessverbesserung mit Reifegradmodellen[END_REF]. MM development has faced an evolution of around 40 years. The early approaches of these models reach back to the late 1970s, when Crosby and Nolan developed the first preliminaries of today's MM: the five-staged Quality Management Maturity Grid and the stage theory on electronic data processing [START_REF] Crosby | Quality is Free: The Art of Making Quality Certain[END_REF][START_REF] Nolan | Managing Crises of Data Processing[END_REF]. The concept of these models gained more and more attention, and to date, the Capability Maturity Model Integration (CMMI) [14] represents one of the most well-known and applied MMs.

Although there are different types of MMs, we focus on the dominant form, the staged MM. Its basic assumption is that an organization is constantly evolving, interand intra-organizationally, due to learning effects and improvements. This evolution process is represented in a simplified step-by-step approach using a certain number of degrees of maturity (usually 3-6), a combination of key factors that must be given in order to achieve a certain level of maturity. Figure 1 shows a common representation of a staged MM. When using such an MM, the presence of relevant factors is measured via indicators. After conducting this assessment, the results are summarized with corresponding evaluations and a representative maturity level (see Fig. 1).

Fig. 1. Structure of a staged MM

Development of Maturity Models

Researchers who develop an MM have to decide on a research design for model development (i.e., empirical qualitative/quantitative, conceptual, design-oriented or other), specific research methods to be applied (i.e., case studies, surveys, literature reviews, interviews, conceptual developments or no method at all), and the research content that has to be elaborated and described (i.e., conceptual, descriptive, assessment, comparative, or others) [START_REF] Wendler | The Maturity of Maturity Model Research: A Systematic Mapping Study[END_REF]. Considering the long history of MMs, multiple development guidelines evolved over time that focus on these decisive processes and can be regarded as supportive instruments for MM development. [START_REF] De Bruin | Understanding the Main Phases of Developing a Maturity Assessment Model[END_REF] present the most established standard for the development of MMs: a six-step generic phase model comprising scope, design, populate, test, deploy, and maintain. A different procedure model is postulated by [START_REF] Becker | Developing maturity models for IT management[END_REF], who strongly focus on a design science research approach. They suggest an eight-phase development approach, focusing on problem definition, comparison of existing MMs, determination of the development strategy, iterative MM development, the conception of transfer and evaluation, implementation of transfer media, evaluation, and rejection of MM. [START_REF] Pöppelbuß | What makes a useful maturity model? A framework of general design principles for maturity models and its demonstration in business process management[END_REF] set up general design principles (principles of form and function) for the development of useful MMs. A framework for the characterization of existing MMs is presented by [START_REF] Mettler | Maturity assessment models: a design science research approach[END_REF]. In order to create sound and widely accepted MMs, he proposes two "maturity model cycles." Based on a development cycle, focusing on a developer's perspective and an application cycle, focusing on a user's perspective, he identifies different decision parameters MM developers should take into account (Fig. 2) [START_REF] Mettler | Maturity assessment models: a design science research approach[END_REF].

Summarizing, many approaches can support researchers in creating MMs. However, these guidelines are limited in their interpretability and validity, as they do not provide concrete terminology specifications or structural concept models. Consequently, many models were built following these recommendations, but they still differ in the terminology used, their descriptive principles, the extent of provided information about factors, and the factors' influence on the degree of maturity [START_REF] Pöppelbuß | What makes a useful maturity model? A framework of general design principles for maturity models and its demonstration in business process management[END_REF]. [START_REF] Mettler | Maturity assessment models: a design science research approach[END_REF])

Fig. 2. Development and application cycle of maturity models (in accordance with

Criticism and Inconsistencies of Maturity Models

In spite of their salient popularity, there are also critical voices regarding the scientific implications and the practical applicability of MMs. From a scientific point of view, [START_REF] Pöppelbuß | What makes a useful maturity model? A framework of general design principles for maturity models and its demonstration in business process management[END_REF] criticize a lack of empirical research foundation during the development process. This in turn, often leads to a simple copy of existing model structures (i.e., five-staged-MMs) without considering the conceptual suitability for the given context. Furthermore, [START_REF] Lasrado | Maturity Models Development in IS Research: A Literature Review[END_REF] mention the lack of validation when selecting factors or dimensions for the model as well as the linear course of maturation. Another aspect is the missing operationalization of maturity measurements which impedes replication of an evaluation. Similarly, [START_REF] Pfeffer | Knowing "What" to Do Is Not Enough: Turning Knowledge into Action[END_REF] argue that a simple demonstration of a gap (as done in many MMs) is not enough. Only understanding cause and effect can help to guide action. Otherwise these models might convey the impression of "falsified certainty" to their users [START_REF] Lahrmann | Inductive Design of Maturity Models: Applying the Rasch Algorithm for DSR[END_REF]. A common promise of MMs is an increase in competitiveness, effectiveness and efficiency in a specific domain or a general improvement of constitution. However, MMs lack a clear description and definition of these concepts in their conceptual grounding, making them theoretical constructs but not applicable models for users (i.e., SMEs). [START_REF] Jugdev | Project Management Maturity Models: The Silver Bullets of Competitive Advantage?[END_REF] summarize shortcomings of MMs from a practical perspective. They state that MMs are often inflexible, although a high flexibility is required. Similar to [START_REF] Pfeffer | Knowing "What" to Do Is Not Enough: Turning Knowledge into Action[END_REF], they argue that MMs focus on identifying gaps and raising awareness towards a specific topic, but enterprises are in need of concrete recommendations for action. Furthermore, these models are disciplinary, impractical, and overwhelming for many enterprises, especially for SMEs where a corresponding executive management level is missing.

However, not only the application and general structure of models is a topic of criticism. Inconsistent terminology of the models' concepts plays a major role in MM research. When developing new MMs, developers tend to invent new titles for common MM approaches in order to stand out from the plethora of already existing MM terms.

For instance, designations like "Maturity Model," "Assessment Model," "Roadmap," "Maturity Framework," "Maturity Matrix," "Guide to Maturity," and "Excellence Model" are synonyms for the concept of an MM. Inconsistent terminology used within MMs, indirectly results in an inflation of similar MMs, as these models will not be identified as identical or at least similar approaches. This inconsistent terminology may cause, among other problems, two different semantic-syntax errors between MMs: a) developers use the same terminology for maturity concepts, but each concept has a different interpretation (e.g., homonyms), and b) developers address the same concept but label it in a different way (e.g., synonyms). For instance, to describe the field of interest an MM is applied to, MMs use different terms: "domain," "area," or "dimension." But not only the terminology, also the relationships between these concepts remain unclear. There rarely is a standardized definition framework of concepts and relationships. Although there exists a meta model for project management competence models, it is only available in German and focuses on the broader application context, not on the maturity model itself [START_REF] Ahlemann | Kompetenz-und Reifegradmodelle für das Projektmanagement: Grundlagen, Vergleich und Einsatz[END_REF]. In conclusion, these inconsistencies represent a research gap as they lead to a situation where a comparison of existing MMs is almost impossible due to a lack of understanding what is actually provided.

A Meta Model for Staged Maturity Models

A recent study revealed that almost all scientific and many consultancy MMs (in the field of Industrial Internet) are still not being used or are even unknown in business practice, although potential applicants stated a need for and interest in these models in general [START_REF] Felch | Maturity Models in the Age of Industry 4.0 -Do the Available Models Correspond to the Needs of Business Practice?[END_REF]. As this discrepancy comes as a surprise, we assume a weak point either in the development or application of MMs (Fig. 2); otherwise, the reluctant use in praxis is not explicable. A possible explanation for this phenomenon may be located in the different interpretations of MMs' concepts on both sides of stakeholders. Developers may use concepts and relationships that are interpreted differently by model applicants and by other developers in the same field of research. As a result, possible applicants as well as researchers misinterpret an MM's structure and concepts. In other words, syntax and semantics vary across MMs, which is why, on the one hand, companies (as applicants) do not use or apply the models, as they simply do not understand their structure and effects. On the other hand, researchers tend to develop even more and new MMs, as they do not recognize existing models as similar or comparable MM approaches (i.e., from 2016 to 2018, 18 new MMs had been developed in the domain of Industry 4.0 [START_REF] Felch | Maturity Models in the Age of Industry 4.0 -Do the Available Models Correspond to the Needs of Business Practice?[END_REF]). What is needed is an overarching, holistic conceptual framework that can unify and standardize the individual objectives and goals. By focusing on the developer's perspective in this paper, the consistency of existing models can be validated, and future models can be developed in a rigorous way, which will then be the foundation for a sound assessment of models later on. A Meta Model, as "a model of models" [START_REF][END_REF], is an approach that is able to meet the above-mentioned requirements.

Originating from software engineering, it can be understood as a model specifying underlying models that are considered instantiations of the meta model. The meta model itself is instantiated from a meta meta model [START_REF]Object Management Group: UML Infrastructure Specification[END_REF]. In many cases, the meta meta model specifies a subset of the modeling language UML. A meta model typically represents the language (linguistic) and/or structure (ontological) of the underlying (that is, the subordinate) models [START_REF] Strahringer | Metamodellierung als Instrument des Methodenvergleichs: eine Evaluierung am Beispiel objektorientierter Analysemethoden[END_REF]. It is used as an abstract description of (1) the unification of concepts that are part of the model, (2) the specifications and definition of concepts, and (3) the specifications and definition of concepts. Thus, multiple valid models can be instances from the same meta model. The schematic meta-modeling approach for MMs is shown in Fig. 3. On the top layer (M2), the developed meta model is located.

It specifies the underlying MM on M1. Every concept on M1 has to adhere to a type concept specified on M2. Please note that the MM on M1 is, in principle, generally valid for all enterprises. It specifies the ranges and used concepts for a later assessment.

The developer creates an MM type on M1 (according to the meta model on M2), which is "instantiated" on M0. On the M0 level, the "instantiated" and applied MM characterizes a concrete enterprise. This can be done by the user (the person who applies a constructed MM onto an enterprise).

With a detailed meta model for MMs, different MMs can be regarded as instances of it, leading to common semantics and syntaxes between those models. Only by providing a unified meta model ("specification" in Fig. 3), that reveals concepts, relations and entities, will the developer be able to develop a rigorous and logical MM through instantiation ("structure" in Fig. 3). Our research can therefore contribute fundamentally to the development of future staged MMs in all areas, as its structure on the M1 level and its instantiation on the M0 level are directly interdependent and thus decisive for the success or failure of a maturity measurement in a company.

Fig. 3. Schematic overview of a meta model for MMs (own illustration)

However, compared to classical meta-modeling, where the M1 model concepts serve as types for M0 level instances, here, the instantiation of M0 from M1 must be interpreted differently. During assessment (the process that creates the M0 instances), only some of the concepts from the M1 level are instantiated with "values" that ultimately (typically by calculation) yield the resulting maturity level for the assessed enterprise.

Meta Model Development and Concepts

The development of the Meta Model for Maturity Models (4M) was based on a study of the most common and representative staged MMs. In order to elaborate sufficient meta model elements that are valid for a broad class of staged MMs, an analysis of different staged MMs, their development and their structure was conducted to summarize and analyze existing concepts, their relationships as well as their multiplicities and instantiations. As a result, universally applicable meta concepts were found and related to each other. For that, we followed an opportunistic approach: we identified the necessary meta model concepts (and their relations) by reduction and selection via decision criteria based on the available content of the investigated MMs. The resulting meta model in Fig. 4 and Table 1 show the M2 level structure as a conceptual and formal description of an MM, whose instances (on M1 level) reflect the actual concepts and interrelations within various staged MMs investigated in our study (see also Section 5).

Fig. 4. Meta Model for Maturity Models: 4M

The staged structure of MMs is built on common assumptions, which influenced the meta model's design:

1. A maturity model is typically developed within a domain, as it represents a path of growth for a specific field of interest. 2. An MM consists of several maturity levels (i.e., L1-L5), which have an ascending order and are intended to represent the improvement path of an object's ability. 3. The MM can (but does not have to) be divided into dimensions (i.e., D1-D5). These dimensions divide the object of study into fields of interest, mostly depending on the domain in which the model is applied. This subdivision serves the possibility of an incremental measurement of maturity in a certain area.

4.

Factors are properties of the maturity level and (if available) are grouped in dimensions. There are two possible ways of maturity determination by factors: a. In the first approach, the respective maturity level is specified by checking the threshold of certain (related) factors that are applied. Due to the fact that a factor could be used on several levels (however, with different values per level), the factor specification, which assigns the concrete expected value of a factor per maturity level, is used between both. Thus, e.g., level L1 could use factor f with the factor specification fL1 while level L2 is still able to use f as well (then with its own factor specification fL2). This is used to express evolving enterprise maturity via growing requirements per level of the same factor. b. Second, there is the possibility that the maturity level can be determined per dimension instead of "requirements per level." For this purpose, the factors need to be assigned to the respective dimensions and calculated by using a dimensionspecific aggregation formula (e.g., sum, average, median). In contrast to the approach (a), the dimensions do not use any threshold as intermediate value. Thus, a factor can only be assigned to one dimension, and the dimension maturity is calculated by its set of factors (and their current value). A factor cannot be used twice, and the dimension maturity is always a representation of the current state of the enterprise (within this dimension). The MM can make use of both, several dimensions of maturity and an overall level maturity since maturity levels and dimensions are modeled orthogonally in the meta model. However, the specification of the maturity level is still mandatory. 5. Although a factor represents a measurable part of a maturity level and a dimension within an MM, its value is still abstract and not directly transferable into an object under study. This transfer is done by using indicators. Indicators are measurable properties of one or more factors and are directly retrievable (measurable) for an object under study. As a factor can have many indicators, and each indicator can be relevant for multiple factors, the factors retrieve their values from their indicators by using an indicator aggregation. This is a pure technical construct to allow the shared usage of indicators by different factors. However, the aggregation functions (e.g., sum, average, median) are assigned to the factor to yield its value. 6. The indicator measurement is done on the basis of indicator types. This could be, e.g., Likert, ordinal, or cardinal scales, counting or index values.

Meta Model Application and Discussion

The final meta model with its concepts can be used to develop the initial-staged MM. The defined elements (concepts) and their relationships are regarded as best practices in MM development and are practically needed concepts in order to build a functioning staged MM. Although one could decide for several variations, the already discovered concepts in the meta model are the sum of (extracted) expert knowledge from previous MMs. Thus, the non-existence of any part of the meta model in an actual MM is neither considered as an issue in the meta model nor is the MM regarded as incorrect. Rather, the interpretation is that the actual MM lacks a feature that is typically used by other MMs, and it could potentially be improved with such. Further, the relatively small amount of meta concepts is not necessarily a drawback, since the meta model only contains the most powerful concepts found. Despite the few concepts, it provides a strong, defined, and universal framework for a whole class of staged MMs.

Maturity Model ⬛ ⬛ ⬛ ⬛ ⬛ ⬛ Domain ⬛ ⬛ ⬛ ⬛ ⬛ ⬛ Maturity Level ⬛ ⬛ ⬛ ⬛ - ⬛ Dimension - ⬛ ⬛ ⬛ ⬛ ⬛ Factor ⬛ ⬛ ⬜ ⬕ ⬛ ⬛ Indicator ⬛ ⬛ ⬕ - ⬕ - Indicator Type ⬜ ⬜ ⬕ - ⬛ ⬛ Factor Specification - - ⬛ ⬜ ⬛ -
Table 2 summarizes an analysis of currently existing and applicable staged MMs regarding the mapping between the developed meta model and the concepts used. The selected MMs represent a sample from different domains, years, and development approaches. The BPMM and CMMI are representatives of the most famous MMs developed [14,[START_REF]Object Management Group: Business Process Maturity Model[END_REF]. Leyh et al. [START_REF] Leyh | The Application of the Maturity Model SIMMI 4.0 in Selected Enterprises[END_REF], Gökalp et al. [START_REF] Gökalp | Development of an Assessment Model for Industry 4.0: Industry 4.0-MM[END_REF], Schumacher et al. [START_REF] Schumacher | A Maturity Model for Assessing Industry 4.0 Readiness and Maturity of Manufacturing Enterprises[END_REF], and Luftman [START_REF] Luftman | Assessing Business-IT Alignment Maturity[END_REF] are representatives of scientific MM approaches from different years.

From the analysis of existing MMs, we conclude that very few models have in-depth explanations of all the concepts and relationships used. However, almost every examined model fulfills common concepts like the MM's name, the domain in which it is located, as well as a description of its respective maturity levels (except one). The concepts' names "factor" and "indicator" are not used within the models. Although [START_REF] Gökalp | Development of an Assessment Model for Industry 4.0: Industry 4.0-MM[END_REF] use the term "indicators," the definition matches the 4M-concept of a factor. The 4Mconcept of "indicator" is not further described in their model. In general, the low-level concepts (like, e.g., indicator) are rarely specified, possibly due to abstraction from the actual calculation of a maturity level. When it comes to the interpretation of the examined concepts and relationships of factors, indicators, and requirements, no MM can be regarded as an exact instantiation of our meta model, as not every concept is present. There is often a lack of information in the available publications about factors and indicators, which are subject to further calculations, or information on which requirements can be used to derive the maturity level. The mere mentioning of concepts allows conclusions to be drawn about the fact that the authors have basically dealt with the respective concepts, but the relationships between them remain undefined.

Possible, general reasons for this phenomenon could be the length of the publications in which the MMs are presented. Conference papers are often too short to describe a comprehensive presentation of all underlying assumptions. Another reason could be that papers do not describe MMs for application purposes, but rather focus on their contribution. However, we do not consider existing staged MMs that do not match the meta model as incorrect. The meta model, as a conceptual orientation, could help other researchers or developers to understand and interpret the respective intention and improves the developer's cycle of MM development. We claim that this will help these models to overcome their ivory tower. The rather few but strong concepts defined in the meta model are a core skeleton of staged MMs that may lead both the development as well as the understanding of MMs.

Although we have built our meta model on a broad analysis of existing models, our research has limitations. Thus, our meta model approach is only valid for staged models and therefore cannot explain other types of MMs (continuous or focus area MMs). In addition, the meta model initially only considers the development cycle and must be further developed for the application cycle. However, as [START_REF] Mettler | Maturity assessment models: a design science research approach[END_REF] proposed, both cycles should not be analyzed concurrently anyway, as they differ in their requirements. To this point, we have been able to show with the current approach that the consistency and concepts of existing MMs are often not entirely described in the development cycle. It will be the focus of our future work to concentrate on the application cycle and to compare concepts of assessment with provided concepts in existing MMs.

Conclusions

In this paper, a meta model for MMs was introduced, which can be used for a standardized and consistent development of MMs. The related concepts, elements, and their relationships were explained and specified in detail. This was done by the analysis of relevant literature that introduces staged MMs and by extracting their core concepts, including their syntax and semantics. Further, the final 4M was evaluated against several MMs from the research literature showing that the majority of MMs lack in the exact specification of their elements and relationships. This uncertainty and divergence in MM specifications often lead to inconsistent applications and implications derived from their application. The presented 4M is therefore beneficial regarding consistent MM development and comparison. The 4M, together with its defined concepts and relationships, is a compact but powerful tool for MM developers for initial development and evaluation of their work, as well as to be consistent with related work and the staged MM semantics in general. However, the 4M only covers the structural part of an instantiated MM. Consideration of the assessment part as an integrated aspect of the 4M would be valuable for the MM user. We therefore intend to develop the assessment aspect in the next research step. Also, we do not claim completeness regarding the concepts in the 4M since we only introduced the concepts that are used by many different MMs. Additional concepts could be introduced; however, we strived for simplicity and usability instead of a complex and over specified meta model. The 4M is only applicable for staged MMs; thus, a meta model for other MM types (e.g., continuous MMs) has to be constructed separately.

Table 1 .

 1 Definition of the meta model's concepts

	Concept	Definition
	Maturity Model	Model for the assessment of the relative fulfillment or ability (maturity)
		of an organizational in a domain; can be specified by dimensions and
		consists of several maturity levels
	Domain	Field of interest on which the maturity model is developed
	Dimension	Subdivision of an organizational structure into areas of interest and re-
		sults from the context of a maturity model applied; can aggregate factors
		related to it

Table 2 .

 2 Comparison of existing MMs with the meta model concepts (⬛ concept defined; ⬕ concept mentioned; ⬜ concept mentioned implicitly;concept not available)

	Meta Model Concept	[25]	[14]	[26]	[27]	[28]	[29]