A complexity management approach to servitization: the role of digital platforms

Purpose – This study aims to enhance the theoretical foundations of servitization research by establishing a theoretical connectionwith complexity management. Theauthors developaconceptual framework todescribe complexity management mechanisms in servitization and digital platforms ’ specific role in allowing synergies between complexity reduction and absorption mechanisms. Design/methodology/approach – A theory adaptation approach is used. Theory adaptation introduces new perspectives and conceptualization to the domain theory (servitization, with a focus on the role of digital platforms) by informing it with a method theory (complexity management). Findings – This study provides four key contributions to the servitization literature: (1) connecting the servitization and complexity-management terminologies, (2) identifying and classifying complexity-management mechanisms in servitization, (3) conceptualizing digital platforms ’ role in servitization complexity management and (4) recognizing digital platforms ’ complexity-management synergies. Originality/value – This studyhighlights thatby usingdigital platforms in servitization andunderstanding theplatformapproachmorethoroughly,companiescangainnewcapabilitiesandopportunitiestomanageandleveragecomplexity.


Introduction
In recent decades, a trend of traditional manufacturers increasing their businesses' amount of service offerings has emerged.The literature has referred to this transition using the term "servitization" (Baines et al., 2009;Vandermerwe and Rada, 1988).Companies create more value and make competitive imitation harder by creating more diverse offerings for their customers and forming more interconnected networks with their stakeholders on both the demand and supply sides (Andreassen and Lidestadt, 1998;Gebauer et al., 2013;Kohtam€ aki et al., 2019b).Through this process, they aim to better fit with the increasingly complex business environment, which is characterized by significant multiplicity, diversity, interdependence and variability (Kohtam€ aki et al., 2019b;Kreye et al., 2015;Raja et al., 2018;Zou et al., 2018).
In servitization, increased complexity has emerged from service processes and offerings themselves as businesses consider the needs of many diverse stakeholders, both within and outside of companies (Jovanovic et al., 2019;Raddats et al., 2016;Spring and Santos, 2014).Complexity has also originated from service organizations' increasing embeddedness in networks with many inter-and intra-organizational relationships (Henneberg et al., 2013;Gebauer et al., 2013).Over the last decade, the increasing adoption of digital technologies has also expanded servitization's complexity.Through "smart" connected products (Porter and Heppelmann, 2014), big data and analytics (Opresnik and Taisch, 2015), the internet of things (IoT), digital platforms (Jovanovic et al., 2021), and augmented reality (Mourtzis et al., 2017), service offerings have diversified and service processes have been re-engineered.Service networks' reach has also extended due to the rapidly expanding connectivity between individuals, organizations and machines (Baines and Lightfoot, 2014).
Instead of examining the specific methods or results of increasing or decreasing complexity in servitization, the current study focuses on complexity management: finding the proper balance between complexity reduction and complexity absorption.Through complexity reduction, companies reduce the variety in their responses to environmental stimuli; conversely, through complexity absorption, companies try to represent their environment in multiple ways and pursue diverse responses (Boisot and Child, 1999).The extant servitization research has mainly approached complexity reduction vs absorption as an "either-or" question; we, in contrast, reveal the synergies between these two seemingly opposing methods of complexity management.Also, while the extant analyses of complexity management in servitization and digital servitization have employed the terminology native to servitization, we emphasize a more context-agnostic complexity-management vocabulary.
Thus, this study aims to enhance the theoretical foundations of servitization research by establishing a theoretical connection with complexity management.Methodologically, we adopted a theory-adaptation approach (Jaakkola, 2020) in which servitization, and especially digital platforms, constitutes the domain theory and complexity management constitutes the Complexity management approach to servitization method theory (Jaakkola, 2020) (Figure 1).Through theory adaptation, we develop a conceptual framework to describe complexity management mechanisms in servitization and digital platforms' specific role in allowing synergies between complexity-reduction and -absorption mechanisms.
Additionally, our research addresses more abstract concerns in the servitization domain.The limited theoretical foundations of servitization research have been questioned (Rabetino et al., 2018).Similarly, researchers have highlighted the need to adopt a more integrated perspective in order to understand servitization's underlying logic and mechanisms (Kohtamaki et al., 2019a) and integrate servitization into its adjacent research fields (Rabetino et al., 2018).Furthermore, digital servitizationthe essential new domain of servitization researchremains in its infancy, "requiring thorough definition and conceptualization" (Kohtamaki et al., 2019b, p. 383).
The remainder of the current paper is structured as follows.In the next section, we describe the domain and method theories.Then, we build a conceptual framework using theory adaptation.Next, we illustrate this framework with two example cases.A discussion of the results and implications of our theorizing then follows, and the paper's final section concludes.

Theoretical background 2.1 Theoretical approach
This study makes a theoretical connection between servitization research and complexity management research, especially within the digital-servitization context.We focus on conceptualizing how servitized companies can both control and accommodate complexity.
We adopted a theory adaptation approach, aiming to "change the scope or perspective of an existing theory by informing it with other theories or perspectives" (Jaakkola, 2020, p. 22).This approach has previously been applied in different fields of management studies, such as environmental sustainability (Hazen et al., 2020;Nylund et al., 2021), marketing (Williams et al., 2020), andmedia (Dal Zotto andOmidi, 2020).Theory adaptation revises a domain theory (the area under study) using a method theory (the theory used for adaptation), and it introduces new perspectives that usually challenge existing constructs, theories and assumptions (Jaakkola, 2020;MacInnis, 2011).In our work, servitizationand especially digital platformsforms the domain theory.Complexity management Figure 1 illustrates our research approach.

Domain theory: servitization
Traditional manufacturers are shifting from transactional, product-based businesses to more co-creationary relationships with their customers (Lightfoot et al., 2013).This transition has been called "servitization" (Baines et al., 2009;Vandermerwe and Rada, 1988).Servitization is motivated by financial, marketing, and strategic reasons, which entail changes to strategic visions and business models (Baines et al., 2009;Adrodegari and Saccani, 2017).
Servitization research has always been conducted close to empirical phenomena, and the related research results have achieved high practical relevance.Servitization research spans the domains of general management, operations management, marketing management and service management (Lightfoot et al., 2013;Raddats et al., 2019).However, despite the steady growth of the servitization-related literature, this research domain remains at a nascent stage of theory-building (Kowalkowski et al., 2017b).Rabetino et al. (2018, p. 361) analyzed a sample consisting of 1,092 articles about servitization and found that 85% "do not build up their theoretical framework from a grounded theory but merely combine arguments from previous servitization-related research."Therefore, researchers have argued that servitization research uses limited theoretical foundations (Rabetino et al., 2018;Kohtamaki et al., 2019b) and that this research would benefit from both the integration and unification of findings from different theoretical perspectives, as well as interplay analysis among different servitization domains (Kohtamaki et al., 2019a).Furthermore, a theoretical analysis of the convergence between servitization and digitalization requires thorough definition and conceptualization (Kohtamaki et al., 2019b).

Method theory: complexity management
The complexity concept has been developed in the systems-analysis context to describe multiplicity, diversity, interconnectivity, co-evolution and self-similarity between a system's elements (Kauffman, 1992;Birkinshaw, 2013).Complexity emerges from "partially connected agents whose interaction gives rise to complex behavior that is characteristic of these systems" (Eisenhardt and Piezunka, 2011, p. 508).
While rooted in mathematical and biological systems (Sanger and Giddings, 2012), the social sciences have already investigated complexity for over two decades, especially in economics and organizational analysis (Murray, 1998;Smith, 2005).Herein, the concept of complexity is used when understanding the concept to understand organizations' external environments and organizations' fit with their environments (Zhang, 2017), especially when these environments are characterized by uncertainty and turbulence (Smith, 2005).
Based on the work of McKelvey and Boisot (2009), we can use the variety of environmental stimuli to indicate an environment's complexity.According to Ashby's (1956) concept of requisite variety in biological systems, agents deal appropriately with their environments if they find a fit between their internal variety and their environments' variety.However, while biological systems progress evolutionarily, interpretative systemssuch as organizationsuse intentional and planned behaviors to decode and react to external-environment changes (Beer, 1985).
Organizations have two different ways to manage complexity (Boisot and Child, 1999): (1) complexity reduction, which simplifies interpretations of an environment and keeps the Complexity management approach to servitization variety in an organization's responses low, and (2) complexity absorption, which implies multipleand even opposinginterpretations of an environment.Reduction and absorption strategies address two domains of complexity: cognitive and relational.Cognitive complexity refers to the variety of information that actors exchange, while relational complexity describes the structures of actors' interactions (Ashmos et al., 2000).
The primary complexity-reduction methods are abstracting stimuli (reducing the number of categories that must be considered to comprehend phenomena) and codifying stimuli (assigning data to categories and giving them form) (Boisot and Child, 1999).In the cognitivecomplexity domain, abstraction and codification reduce the number of business goals, simplify strategic activities, and formalize decision-making patterns (Ashmos et al., 2000).In the relational-complexity domain, abstraction and codification instead reduce systems' numbers of interacting elements and interdependencies (Ashmos et al., 2000).
Complexity absorption entails "creating processes or ad hoc structures that facilitate information exchange and allow the generation of multiple interpretations of information" (Ashmos et al., 2000, p. 581).In the cognitive-complexity domain, absorption refers to pursuing multiple goals and strategies, thereby creating options, portfolios, and risk-hedging strategies while avoiding commitments to any single high-risk-vs-high-return path.In relational complexity, absorption implies increasing the number of participants and their interdependencies, thereby enhancing networking, fostering collaborative partnerships and decentralizing decision-making (Ashmos et al., 2000).
(2) Diversity: the variety of units, activities, and actors involved in developing and delivering servitized offeringsfor example, the variety of customer requirements for satisfaction with customized offerings (Raja et al., 2018;Raddats et al., 2016;Song and Sakao, 2017).
(3) Interdependence: dependencies between actors and components in servitized offerings, which inherently relate to both the transition from transactional to relational approaches (Oliva and Kallenberg, 2003;Kreye, 2019) and the development of new services (Kindstr€ om and Kowalkowski, 2009).
When discussing complexity management, the literature has emphasized modularization and standardization paradigms (Pekkarinen and Ulkuniemi, 2008;Brax et al., 2017;Fargnoli et al., 2018;Salonen et al., 2018;Rajala et al., 2019).Modularization is a system's division "into components that are only loosely coupled with other components and, thus, have only limited interdependencies and are mediated by defined interfaces" (Valtakoski, 2017 p. 142).
Standardization refers to commonality of components across different solutions that make them easily repeatable (Salonen et al., 2018).
Leveraging on modularization and standardization, a modular solution design can be achieved, which relies on modular systems of standardized components (Davies et al., 2007), and stands at the basis of solution productization and mass customization (Salonen et al., 2018) according to an industrializer servitization trajectory (Kowalkowski et al., 2015).Kapoor et al. (2021) found through a multiple-case study that manufacturers with wide portfolios of servitized offerings and diverse customer bases emphasized modular offerings, while companies facing rapidly increasing, widespread demand for services focused on standardization.

A specific interest area in theory adaptation: digital servitization platforms
The literature has widely accepted digital platforms' role in complexity management since their organizing systems allow for "maximizing the variety of contributions [to the system] [. ..] while maintaining coherence through a minimum level of hierarchy" (Consoli and Patrucco, 2011, p. 201).However, the literature has approached digital platforms from different disciplinary perspectives.
First, product-innovation research has regarded a platform as a "set of subsystems and interfaces characterized by a common structure from which a company can efficiently develop and manufacture a family of products" (Ardolino et al., 2020, p. 2).Productinnovation platforms help develop new affordances and support generativity (Nambisan, 2017) that is, platforms help embrace complexity.They maintain system structures through modularity, common rules and protocols (Gawer and Cusumano, 2014;Bresnahan and Greenstein, 1999).A platform's complementary elements are integrated among themselves and with the platform's core (Baldwin and Clark, 2000), based on standardized architectures.
Second, economists have studied platform thinking from a marketplace perspective (Hagiu and Wright, 2015).The "multisided market" approach has accentuated platforms' role in matching demand with supply, as well as promoting cross-side network effects (Gawer and Cusumano, 2014;Muzellec et al., 2015).The advent of digital technologies and, above all, the Internet has led to businesses' spreading out, based on digital, multisided platforms (Ardolino et al., 2020).This approach has used marketplace logic to expand the reach and variety of contributions to a system while keeping interactions standardized by defining their mediums of exchange and marketplace ownership (T€ auscher and Laudien, 2018).

Complexity management approach to servitization
Third, the meta-organizational approach has combined the previous two major approaches (Gawer, 2014).From this perspective, platform users' cooperation extends to all business processes, enabling (1) the creation of nested structures, including several organizations, and (2) the facilitation of diverse resource combinations.The literature has referred to these platforms as "industry platforms" (Gawer and Cusumano, 2014), "platform organizations" (Gawer, 2014), and also, sometimes, "service platforms" (Chesbrough, 2010) and "engagement platforms" (Breidbach et al., 2013).The scale, reach and embeddedness of these platforms have made structural control challenging.Consequently, in stable environments, meta-organizational platforms may suffer performance problemsbut, in fast-evolving markets, quick adaptation benefits can compensate for probable processperformance losses (Autio et al., 2018).
Servitization research has identified platforms as servitization enablers.Platforms integrate technological components (Cenamor et al., 2017;Pirola et al., 2020) and connect actors within ecosystems (Kohtamaki et al., 2019b).Platforms also allow for coping with integrated solutions' increased complexity as "companies utilize digital platforms to address more complex customer problems by analyzing and combining data about various products in the platform ecosystem" (Gebauer et al., 2020c).
The literature has emphasized platforms' potential in managing service-business complexity, allowing diverse offerings alongside operational efficiency and reducing transaction costs (Cenamor et al., 2017;Kamalaldin et al., 2020;Kohtam€ aki et al., 2019bKohtam€ aki et al., , 2020a;;Sklyar et al., 2019a).However, the related analysis has mainly applied a complexityreduction perspective, as in service-modularization and integrated solution-development discussions (Kapoor et al., 2021).Platforms, however, also contribute to complexity absorptionfor example, through orchestrating service innovation and provision networks in the servitization domain (Eloranta and Turunen, 2016).Moreover, while digital servitization platforms allow for standardization and reduce transaction costs (Kohtamaki et al., 2019b), platforms also constitute relation-specific investments that should foster close relationships among customers and providers (Kamalaldin et al., 2020).
Further digital-servitization research on platforms' role from an ecosystem perspective has been called for (Kohtamaki et al., 2019b).A growing interest has focused on platformbased business models' configuration and evolution (Jovanovic et al., 2021;Tian et al., 2021;Kapoor et al., 2021).However, digital platforms' contribution to servitization complexity management has not yet been conceptualized.

Framework development 3.1 Framework foundations
We summarized our theory-adaptation process and its results in a conceptual framework (Figure 2).The framework's vertical dimension exhibits different approaches to complexity management: reduction and absorption.Complexity reduction means simplifying the interpretation of a complex environment, whereas complexity absorption describes allowing (and purposefully generating) multiple interpretations of an environment.The framework's horizontal dimension represents complexity's two different domains: cognitive and relational.Cognitive complexity refers to the variety of exchanged information, while relational complexity describes the structure of interactions among actors.

A complexity-management perspective on servitization
To continue our theory adaptation, we applied our research framework to our domain theory, servitization, by inserting the complexity-management mechanisms that the servitization literature has identified (Figure 3) to Figure 2.These mechanisms are linked to the core IJOPM 41,5 complexity-reduction methods (abstraction and codification) and to complexity absorption (pursuing multiple goals and strategies, as well as increasing the number of participants and their interdependencies in a system).
In servitization, enhancing customer involvement and meeting individualized needs increase representations of reality (Andreassen and Lindestad, 1998) and uncertainties surrounding the offering and delivery processes (Valtakoski, 2017).From the complexitymanagement perspective, this process involves absorbing complexity in the cognitive domainextending the variety of firms' processes and offerings and pursuing multiple business goals.
In the relational domain, complexity is absorbed by embedding service organizations into large-scale organizational networks and ecosystems, which are characterized by numerous inter-and intra-organizational relationships (Gebauer et al., 2013;Kohtam€ aki et al., 2019b).Service and solution networks can be considered complex systems that continuously develop (Basole and Rouse, 2008).Networking also increases within firms (Jovanovic et al., 2019); Beltagui (2018) revealed that the service business's increasing complexity challenges  Complexity management approach to servitization companies' capability development, necessitating more experimentation and evolutionary learning, which leads firms into more flexible and decentralized structural arrangements.In the complexity-management language, this process involves increasing the number of participants and their interdependencies in business systems.
However, simultaneously, firms try to avoid the challenges of increased complexity.In the cognitive domain, companies simplify their offerings and create productized solutions and mass-customized services (Eloranta and Turunen, 2016;Salonen et al., 2018;Kohtam€ aki et al., 2019a).Firms also standardize their processes of developing and delivering offerings (Kohtam€ aki et al., 2019a).In other words, firms categorize (codify) their offerings and processes and also simplify (abstract) them.
In the relational domain of complexity, firms reduce complexity with modularization techniques (Valtakoski, 2017;Kreye et al., 2015) to manage offerings, processes and organizations; modularization works by simplifying structures and dividing these structures into components.Firms also organize their service networks into stable structures; in large networks of actors that co-create value, manufacturers usually act as integrators (Windahl and Lakemond, 2006) and orchestrators (Paiola et al., 2013).
However, while complexity-reduction mechanisms control complexity, they also entail a risk of forming excessively rigid structures that fail to serve diverse customer needs and may contradict servitization's fundamental aim (Agarwal and Selen, 2009;Kowalkowski et al., 2012).This risk is due to the mechanisms of complexity-absorption and -reduction challenging each other, especially in the cognitive domain.Firms are faced with an either-or decision (Kohtam€ aki et al., 2020a) in seeking optimal complexity levelsfor example, choosing between agile processes and standardized processes or between adding divergent offerings or increasing their standardization.In the relational domain, the counteractive tendency is less prevalent: service networks can be extended and diversified while their structure is sustained by modularization.However, the servitization literature strongly reflects the tendency to integrate (build stable networks around orchestrators); therefore, practically, complexity management is often steered primarily toward reduction mechanisms.

Augmenting our framework from a platform perspective
To highlight digital platforms' potential in servitization from a complexity-management perspective, we further developed Figure 2, this time including the complexity management mechanisms that the platform literature has identified (Figure 4).

Mechanisms for relational complexity reduction
Mechanisms for relational complexity absorption

Mechanisms for cognitive complexity reduction
Mechanisms for cognitive complexity absorption  The complexity of platforms' interactions is reduced through common rules and protocols (Constantiou et al., 2017), such as platforms' application programming interfaces (APIs) and device interoperability protocols, which refer to the theoretical construct of codification.Platforms also reduce complexity by organizing themselves as marketplaces (Hagiu and Wright, 2015), a specific abstraction-driven way to simplify actor-to-actor interrelations and divide labor across platforms.These methodscommon rules and protocols, as well as market logicreduce complexity in the cognitive domain.In turn, as a platform-related complexity-reducing mechanism, modularity (Boudreau, 2010;Cenamor et al., 2017) operates in the relational domain.It uses codification's theoretical approaches to divide system architecture, and it uses abstraction to simplify system architecture.Platforms exhibit modularization by dividing independent components based on their core functionality.
For complexity absorption, digital platforms have deployed tools that allow platform users to self-develop solutions.Practically, these tools include software development kits and customization wizards for users and developers.Platforms also offer collaboration tools to facilitate users' interactions.These approaches drive experimentation and adaptation on platforms; self-development and collaboration push platforms to evolve continuously.In complexity management, these mechanisms pursue multiple goals and strategies.
There are also complexity absorption mechanisms in platforms.Platforms can be open, promoting networking (Choi et al., 2019;Abhari et al., 2017;Broekhuizen et al., 2019); that is, they increase the number of participants and their interdependencies.Also, platforms can specifically facilitate the formation of diverse resource combinations (Wei et al., 2019;Abhari et al., 2017).Practically, this facilitation entails allowing the mutual exposure of platform users' selected resource and capability pools through interfaces, thereby flexibly forming novel resource-and-capability combinations.Also, the recent platform literature has included case studies on platforms that have decentralized their governance and ownership (Chen et al., 2020), which has further empowered these platforms' users while increasing and diversifying the number of interdependencies between them.
In analyzing the complexity-absorption and -reduction mechanisms, we see that in platforms, these mechanisms work in synergy (Figure 4).Platforms seem able to maximize a system's variety while maintaining coherence (Consoli and Patrucco, 2011, p. 201).The related decision is not to define an "optimal" level of complexity but, rather, to manage complexity via some complexity-absorbing mechanisms (and domains) and then mitigate potential issues with complexity-reducing mechanisms (and domains).
Specifically, the mechanisms meant to maintain cognitive stability (complexity reduction) and relational diversity (complexity absorption) seem to have notable synergies.The mechanisms for common rules and protocolsas well as marketplace creationstandardize interactions in a system.These mechanisms allow more degrees of freedom to grow and diversify the relational domain.A platform's scale and reach can, thereby, expand without the significant risk of resource depletion.Also, increasing relational stability has synergies with growing cognitive diversity.Practically, reducing the number of parts in a system's architecture through a modularization mechanism seems to allow for interpretative flexibility regarding interactive content, driven by the mechanisms of self-development solution tools and enhanced collaboration between platform stakeholders.
This quest for synergy between complexity mechanisms and domains contrasts with how the servitization literature has approached complexity, as we noted earlier.The servitization literature has regarded complexity management mostly as either-or decisionsselecting desired levels of complexity (Kohtamaki et al., 2020a).Therefore, our complete framework highlights the following argument: by using digital platforms in servitization and understanding the platform approach more thoroughly, companies can gain new capabilities and opportunities to manage and leverage complexity.

Illustrating our framework
Although this study remains conceptual, we use two illustrative examples of IoT platforms to show a practical application of the complexity management approach through digital platforms in the servitization context.We also highlight the interplay between complexitymanagement mechanisms.
The first example is ThingWorx by Parametric Technology Corporation, a digital platform meant to provide manufacturers advanced services that are integrated into tangible assets in the domains of remote monitoring, asset optimization, and workforce efficiency.The second example is Siemens's MindSphere, a platform-based solution that has extended Siemens's offering portfolio to industrial services for own and third-party assets.Table 1 summarizes the complexity-management mechanisms that these illustrative companies have adopted.
For complexity absorption, in the cognitive domain, both platforms provide tools and specific development environments that enable customers to build and then integrate their applications and services.Developers can, thus, create applications, connect assets, collect data, and provide IoT services to industrial customers.
The two example platforms are also characterized by mechanisms to absorb complexity in the relational domain.Both platforms promote open, collaborative approaches among developers.ThingWorx enhances collaborative hosting sessions in specific online communities, while MindSphere uses an open-source tool for developer communities to share resource and libraries.
ThingWorx has also created a worldwide vendor and service-provider ecosystem, as well as an application-enablement platform where participants can learn how to build their own IoT applications.Similarly, MindSphere has built an ecosystem comprising application developers, system integrators, technology partners, and infrastructure providers.Thus, these platforms allow users to combine different resources in order to create advanced solutions.
Moreover, the platforms have deployed complexity-reduction mechanisms in both the relational and cognitive domains.Both platforms provide alternative ways to connect with any device, including edge agents, protocol adapters, native device clouds, third-party device cloud support, and application APIs.Therefore, connected-product providers have a set of standards and rules that helps them work with an entire IoT ecosystem's interoperability.
In addition, both platforms provide marketplaces, allowing users to build and sell their own IoT applications and find market-ready solutions.As these marketplaces grow, developers have more opportunities to build their solutions using comprehensive catalogs of prebuilt and tested components.Marketplace-logic simplifies the interactions between different parties, and thereby reduces complexity.
Finally, both example platforms use modular IoT application-platform architecture.Through interchangeable modules and easily configurable native functionalities, users can benefit from the platforms' flexibility and customized functionality while receiving costefficient, timely updates and carrying out agile development paradigms.
These two examples also help us discuss the interplay between complexity-reduction and -absorption mechanisms (Figure 5).The synergy between cognitive-complexity reduction and relational-complexity absorption (relationship 1 in Figure 5) is visible in the platforms' adoption of common rules and protocols, as well as their creation of marketplaces, allowing stable interactions.This synergy allows more complexity to be absorbed in the relational domainfor example, by growing developer communities.
Second, relational-complexity reduction seems synergetic with cognitive-complexity absorption (relationship 2 in Figure 5).Practically, reducing the number of parts in a system's architecture through the modularization mechanism allows for interpretative flexibility visa-vis interactive content, allowing advanced self-development solution tools between Complexity management approach to servitization platforms' stakeholders.On ThingWorx, this effect is visible in customers' ability to combine their resources with resources from the ThingWorx community, using the platform's modular architecture.Correspondingly, MindSphere customers can leverage modularization by self-developing apps and connecting them with Siemens's apps, as well as third-party suppliers' apps.

Discussion
Our study provides four key contributions to the servitization literature: (1) connecting the servitization and complexity-management terminologies, (2) identifying and classifying complexity-management mechanisms in servitization, (3) conceptualizing digital platforms' role in servitization complexity management, and (4) recognizing digital platforms' complexity-management synergies.

Connecting complexity-management and servitization terminologies
Servitization researchers have addressed complexity management but their analysis has cleaved closely to the servitization context, using servitization-specific terminology.Our conceptual framework connects the servitization-research terminology with the contextagnostic terminology of the complexity-management literature.The four-field framework we presented in Figure 3 categorizes servitization-related actions into mechanisms that reduce complexity and mechanisms that absorb complexity.Furthermore, these mechanisms were also divided into the domains of cognitive complexity and relational complexity.Our terminological classification provides a direct link between the servitization and complexity-management research domains, thereby allowing servitization scholars to build more precise theoretical and empirical links between studies across the two literature streams.Thus, our research clarifies servitization research and helps develop complexitymanagement research.
The current study contributes to complexity-management servitization research by addressing both complexity-reduction and complexity-absorption.We have identified 11 complexity-management mechanisms in servitization, described and classified according to their aims (to reduce or absorb complexity) and complexity domain (cognitive or relational), as Figure 3 shows.This study's results offer a lens through which to understand how servitizing companies can balance complexity-reduction and -absorption to achieve their desired servitization outcomes.Increased complexity must be accommodated to intensify co-creation with customers and suppliers and to decrease the competitive threat of imitation (Valtakoski, 2017).Complexity-reduction, meanwhile, is needed to maintain efficiency and companies' focus; however, excessive complexity-reduction mitigates servitization's competitive advantages (Valtakoski, 2017).Our framework provides an improved structure to analyze the tension between complexity reduction and absorption.

Conceptualizing digital platforms' role in servitization complexity management
Digitalization and technology adoption in servitization have provided unique possibilities and posed significant risks to servitizing companies (Kohtam€ aki et al., 2019b;Sj€ odin et al., 2020).Digital servitization increases service systems' complexity and challenges traditional complexity-management methods (Kohtam€ aki et al., 2019b).Adaptable organizational forms are needed for companies to benefit from digital servitization (Valtakoski, 2017;Raja et al., 2018).Thus, in this study, we have specifically investigated the complexity-management opportunities that platforms offer for digital servitization.
Our study provides a structural characterization of how complexity-management mechanisms are deployed on digital platforms.We identified nine different complexitymanagement mechanisms, which we described and classified according to their complexity management action (absorption or reduction) and domain (cognitive or relational), as Figure 4 illustrates.Thus, we offer a novel approach to investigating platforms' role in complexity management.Since our analysis has covered both complexity-absorption and -reduction approaches, our results particularly complement the works of, for example, Eloranta and Turunen (2016) and Cenamor et al. (2017).

Recognizing digital platforms' complexity-management synergies
This study also contributes to the servitization literature by extending complexitymanagement opportunities involving the synergetic interplay between complexity-reduction and -absorption mechanisms.Thus far, the literature has aimed to seek a compromise between complexity-reduction and -absorption; however, the complexity-management framework that we have applied to digital platforms (Figure 4) suggests that platforms can help achieve not only a compromise but also a synergy between complexity-reduction and -absorption.This argument aligns with Sj€ odin et al. (2020) and Gebauer et al. (2020a, b), but we have more precisely elaborated on this topic in the complexity-management field.
Figure 4 shows how standardizing interactions through marketplace logic, common rules, and protocols on platforms (complexity reduction in the cognitive domain) accommodates a greater reach and broader networks on platforms (complexity absorption in the relational domain).Similarly, complexity reduction in the relational domain, through modularization, accommodates greater complexity (e.g., richer interactive content between platform users) in the cognitive domain.By highlighting this interplay, we have responded to a specific call for more research on platform-based business models' relation to customized solutions, Complexity management approach to servitization particularly from studies on service modularity and "how to determine best approaches and combinations of service elements in different service settings in order to combine modular elements, customize and personalize the service offering effectively" (Brax et al., 2017, pp. 691).We have also discussed how modularity can reduce complexity in synergy with complexity-absorption mechanisms.
This synergetic enforcement of opposing complexity-management mechanisms constitutes an advancement in the servitization literature.Particularly, this finding suggests that digital platforms provide servitizing companies opportunities to overcome a typical challenge of servitizationthat is, the need to compromise between customization and efficiency.The servitization literature has shown, with empirical research, how firms have sought a level of complexity that seeks the compromise between the costs of increasing complexity with the opportunity costs of limiting complexity.Our study has shown that platforms allow greater flexibility since they can accommodate a greater variety of outcomes while, at the same time, keep complexity under control.
This finding may be especially important to digital servitization: when technological possibilities are adopted, their success is not linear but, rather, forms a U-curve (Kohtam€ aki et al., 2020b), so companies should be able to rapidly increase added technological complexities' value in order to overcome the lower part of this U-shape.Also, the technological investments' value is difficult to know beforehand, companies need platforms' flexibility and scale to explore opportunities, pivot in new directions, and learn during this process (Kohtam€ aki et al., 2020b;Valtakoski, 2017;Sj€ odin et al., 2020).

Limitations and avenues for future research
A limitation we face is that our study is purely conceptualdespite our use of illustrative cases to practically show our conceptual findings.Therefore, further empirical research is needed.The complexity-management synergies we have proposed through our theorizing should be further investigated since they could offer relevant advancements in the analysis of fundamental servitization paradoxes (including the infamous service paradox; Gebauer et al., 2005).
Among digital platforms' complexity-management mechanisms that we have discussed, "decentralizing governance" (Figure 4) deserves particular attention in future research.In recent years, the platform literature has explored the possibilities of increased decentralization and democratic governance to build more engagement among platform users and resilience among platforms (Chen et al., 2020).The servitization literature has been mixed in this regard.Eloranta and Turunen (2016) have provided hints of governance decentralization intertwined with complexity benefits.Kohtam€ aki et al. (2019b) and Jovanovic et al. (2021) have also observed complexity-management benefits in promoting service ecosystems' openness.However, Skylar et al. (2019a) emphasized the importance of centralized decision-making in service networks.Large-scale empirical support for each argument is lacking, and subsequent studies are needed.
Furthermore, while a qualitative research approach is the dominant modus operandi in servitization research, we highly recommended addressing complexity management quantitatively as well to assess complexity levels in servitized contexts and, consequently, quantitatively evaluate the identified complexity-management mechanisms' impact.Indeed, the literature has provided methods to measure complexity in manufacturing contexts (e.g., Vrabic and Butala, 2012;Isik, 2010;Jenab and Liu, 2010).Our study did not conduct any quantitative analysis of the analyzed mechanisms' levels of complexity or effects.
Finally, the theoretical framework that we have developed should also be confronted to identify potential additions vis-a-vis mechanisms and their interplay.While complexity management has been explored in servitization research for over a decade, in-depth IJOPM 41,5 theorizing has only recently entered these discussions.The framework we have introduced in this study provides a solid foundation, but more analysis is needed.

Managerial implications
While this study has focused on theoretical development, our findings offer several implications for practitioners in servitized businesses, especially in the platform-development field.Despite the growing interest in digital technologies and platforms, awareness of platforms' impact on service processesespecially in the industrial B2B domainremains low.
This study has identified and analyzed complexity-management mechanisms that can be implemented on platforms.Therefore, managers can more consciously develop digital platforms to support servitization strategies and develop suitable portfolios of complexitymanagement mechanisms.For instance, managers should know that the larger a platform's users community (e.g., the number of parties engaged in providing services to a global community of customers and third-party service providers), the greater the need to seek synergies with complexity-reduction mechanisms that simplify transactions (marketplaces) and standardize interactions between parties.On the other hand, scale and diversity within platforms' user communities call for absorption mechanisms to accommodate parties' customized needs in the cognitive-complexity domain.This accommodation, in turn, will require the adoption of complexity-reduction mechanisms to control systems' structures (modularity).
Our study's more abstract contributions are also informative for practitioners.Servitization remains challenged by the "service paradox," which reflects the difficulty of providing customized solutions to customers' needs in a cost-effective manner (Gebauer et al., 2005).Digital servitization is also challenged by the "digitalization trap" (Gebauer et al., 2020b) that is, the risk of inadequate revenue increases from digitalization investments.Our conceptual framework offers practitioners tools to (1) analyze and navigate the complexities of (digitally) servitized businesses and (2) design their desired complexity-management actions.Our framework also offers a vocabulary with which to discuss the challenges of servitization at the abstract level.Such discussions may help practitioners overcome their businesses' dominant logics, which could be inhibiting their innovation of new solutions to servitization-related problems.

Conclusion
This study has enhanced the conceptual foundations of servitization research by establishing a theoretical connection with complexity management.Our proposed framework has provided a properly grounded foundation for analyzing complexity-management mechanisms, and their interplay, in servitization.We have identified and classified the complexity-management mechanisms that servitization has adopted to reduce or absorb complexity.Moreover, we have analyzed interpretations of these mechanisms on digital platforms, recognizing digital platforms as flexible organizational arrangements that can drive complexity-management synergies.

Figure 1 .
Figure1.This study's domain theory and method theory Figure 2. Our conceptual framework using complexity's dimensions and domains Figure 4. Our conceptual framework applied to platforms Figure 5.The interplay between complexity-reduction and -absorption mechanisms on our example platforms