Analysis of fractal manufacturing systems framework towards industry 4.0

Analysis of fractal manufacturing systems framework towards industry 4.0 M. Estela Peraltaa,*, Víctor M. Solterob a University of Seville, Department of Design Engineering, Higher Polytechnic School, University of Seville, 41011, Seville, Spain b University of Seville, Department of Design Engineering, Higher Polytechnic School, University of Seville, 41011, Seville, Spain Keywords: Fractal manufacturing Industry 4.0 Complexity Smart factory Cyber-physical system Project management A B S T R A C T Currently, ways to approach the design of Cyber Physical Systems in Industry 4.0 are under development. Emerging concepts of Smart Factories require the development of specialized knowledge; new working methods are also needed to manage the transition from conventional industry to industry 4.0. To achieve this objective, fractal theory could provide the appropriate knowledge and tools. Fractal systems applied to manufacturing have been widely used over the last decades to design complex adaptive systems: it allows the introduction of resilience requirements (capacity to react to changes in a turbulent environment) and to reduce the complexity of its structure, operation and management. In order to know the potential and the possibility of applying fractal theory to the design of systems in Industry 4.0, this article reviews the publications that develop fractal systems for manufacturing engineering. The review includes contributions published between 1985 (approximate date of the first works on the theory applied to manufacturing engineering) and 2019. The objective is to gather those strategies, methodologies and successful case studies that can be useful for the approaches of Industry 4.0 and to define a set of future lines of work for the adaptation of the fractal theory to the new challenges posed by Industry 4.0. 1. Introduction The latest advances in Smart Factory and Smart Industry have defined new challenges and opportunities for manufacturing, encompassed in the concept of Industry 4.0. The emerging technological bases propose new "zero defect" and connected (digitized and automated) industrial systems making use of the Internet of Things, ubiquitous computing, artificial intelligence, cloud manufacturing and maximizing Human-Machine collaboration (robotic, cobotic and collaborative robots). The aim is to create self-organized systems that efficiently achieve the objective for which they were designed [1,2]. The integration of these enablers creates new "smart" manufacturing ecosystems (as shown in Fig. 1) [3] forming collaborative clusters [4] that allow to maximize the performance of the production. The new intelligent manufacturing systems will be distributed (logically or geographically), digital and virtual (with the digitalization of factories) and extended and decentral, formed by autonomous, selfregulated, integrated and flexible units; they will be equipped with selfadaptive capacity to meet production needs; and they will also meet sustainable requirements, addressing new challenges on resource consumption, energy efficiency, climate change or social welfare [5]. Currently, the ways to approach the design and execute the implementation of the Industry 4.0 systems are under development. The emerging technological bases called enabling technologies [6,7] are restructuring production engineering approaches. The new lines of research propose the development of cyberphysical systems (CPS) at all levels of production organization: supply chain, industrial parks, business cluster, factories, job shops, processes and tasks. In these, clustering and cooperation is essential between organizations, since it will allow "connecting" operations to improve performance throughout the life cycle of products and services, but the concept of Smart Factory requires the development of specialized knowledge [8]: it will be necessary to find appropriate strategies to materialize the new industrial ecosystems and transform the current industry in 4.0 [9]. Analyzing the existing knowledge related to intelligent manufacturing systems, the concepts developed from fractal theory [10,11], their design principles and their implementation strategies, are an opportunity for the current objectives of Industry 4.0. Firstly, fractal theory proposes a similar concept to the intelligent factories defined in the Industry 4.0 roadmaps: a Fractal Manufacturing System (FrMS) is a complex system, with a structure of agents that cooperate and form decentralized and autonomous control units [12]; can adapt to continuous changes in the environment or maintain their operation efficiently in the face of external and internal turbulence; they are open systems (continuous learning and open innovation), with a selfsimilar network structure that has the capacity for self-organization, self-optimization and evolution; its operation is zero defect oriented and its growth and expansion is based on simple rules [13]. Secondly, fractal theory has been widely applied by the scientific community in different macroscopic systems related to physical, statistical, geometric, mathematical or biological phenomena. Specifically in manufacturing engineering, it has been widely used for the analysis of the complexity and behaviour of systems [12] (based on chaos theory and complex adaptive systems), in metrology and roughness analysis [13], description of time series from production process sensors [14], analysis of manufacturing defects (with 2D images) [15], surface roughness changes [16], corrugation assessment [17] or combined with Soft Computing in intelligent manufacturing [18]. Fig. 1. New self-similar industrial ecosystems in Industry 4.0. Throughout the last two decades (specifically since the contributions of Warnecke in 1993 [14] fractal theory has also been applied to organizational management in different sectors: manufacturing, financial, human resources, software development or organizational engineering. The flexibility of its application has boosted the interest of its development, being possible to generate a fractal or "fractalize" any system at different levels (material resources, human resources, data and information, products or processes). Numerous examples of fractal systems can be found in the scientific and technical literature: works devoted to the fractal management of activity in the supply chain [15,16], business processes and workflows [17,18] or inventory flows [19]; design of business structures [20] for different sectors such as health systems [21], service-oriented systems [18,22,23], military defence systems [24], or education sector [25]; within organizations and socio-technical systems, fractal systems for the development of human resources capacities and skills focused on competence management [26], motivation management [27], knowledge management [28] or decision making [29]. Other more specific examples within the industrial field are studies on fractal systems for quality control [30], for information systems training and software engineering [31,32], business process reengineering [17] or urban traffic management [33,34]. It is possible to conclude that the fractal theory constitutes a consolidated research field; with adequate adaptation and updating, it could be the ideal framework for the design and development of the self-similar clusters of Industry 4.0. For this reason, this study carries out an exhaustive review of the scientific literature on fractal theory applied to intelligent manufacturing systems. The objective is to gather those strategies, methodologies and case studies applied in real contexts that can be useful for the objectives of Industry 4.0. With the obtained results, a set of future lines of work are defined for the update and adaptation of the fractal theory to the new challenges raised from Industry 4.0. For this, the article is structured as follows: in section 2, the revision methodology used is defined; section 3 exposes the revision of the fractal theory applied to FrMS; finally, in section 4 the results of the revision are analyzed and the different lines of future work necessary to update the fractal theory (applied to manufacturing systems) to the new environments of industry 4.0 are proposed, establishing the main conclusions in section 5. 2. Review methodology In the fractal manufacturing engineering knowledge area, a Status Quo review has been carried out. The review is a critical analysis of existing publications, identifying the current state of fractal theory, as well as patterns and trends in fractal manufacturing systems research for use in the new contexts of Industry 4.0. As shown in Fig. 2, the review is structured on the basis of the study of the main theoretical and conceptual contributions on fractal fabrication (section 3). Next, an exhaustive analysis of the existing frameworks for proposing the design of a FrMS (section 3.1) and of the four fractal design principles (section 3.2) will be carried out; work on the management and direction of fractal projects that make it possible to implement the solutions developed (section 3.3) will then be included, and the most significant pilot projects and real case studies will be evaluated (section 3.4). Finally, in section 4 the research effort is characterised and the adaptation of the fractal theory to the new contexts of Industry 4.0 is analysed, ending with the proposal of lines of work and updating of the same. The search process for Scientific Literature can be reproduced using the keywords listed in Table 1. They have been compiled from different Fig. 2. Structure of the review. studies [13,14,35–39] where the foundations of the fractal theory applied to manufacturing are collected. These words were organised into 3 key areas with the aim of carrying out a simpler and more structured search. These areas were then divided into different levels depending on the study objectives; these levels include the controlled vocabulary (thesaurus) used in the indexing process of the scientific articles. The most important engineering search engines and databases have been selected for this review: Web of Science, Scopus, Compendex, EIT Inspec & Inspec Backfile, Geobase and SciELO Citation Index. To select and classify all the publications, more than 300 scientific papers have been analysed, of which 168 have been selected using the following three criteria: a) Time criterion: papers published between 1985 (first contributions of fractal theory in manufacturing engineering) and 2019.Value-chain structure: A manufacturing system can be defined at different scales on which to organize the information network, facilities, infrastructure and resources (material, human and virtual) needed for the manufacture and distribution of products and services. In order to structure the review, the "value-chain structure" criterion organizes the publications in 3 levels (1) macrolevel or supply chain – FrSC [40], (2) mesolevel or business organization - FrO [41] and (3) microlevel or factory & manufacturing process – FrF [42]: o FrS (Fractal Suppy Chain) includes all the processes involved directly or indirectly to meet the supply requirements for the manufacture of products. It also includes the information structure, i.e. the communications and information exchange route between companies, distributors, suppliers and customers [40]. o FrO (Fractal Organization) is a socio-technical system formed by technology, human resources and business processes interrelated through work processes, technological functions and human Table 1 Key areas and thesauri to reproduce the review. KEY AREA 1. BASIC CONCEPTS KEY AREA 2. FRACTAL PRINCIPLES KEY AREA 3. FRACTAL ARCHITECTURE CONSTRUCTION Framework Self-similarity Goal-orientation Fractal elements Process and states Fractal theory Fractal Patterns Target Regulation Information System and Data Design Fractality Connectivity Con fl ict Detection Knowledge Modelling Chaos Theory Autonomy Con fl ict Resolution Resources Simulation Fractal System Fractal Theory Iterative Rules Fractal Dimension Variety Fractality Required Requirements: Cost, Quality … Business Skills Optimisation Assessment Complex Adaptive Systems Variety Required Trust Between Partners Collective Adaptive Systems Dynamism Coordination Target Individual Behaviour Fractal Levels Complex Adaptive And Emergent Systems CAES Vitality Autonomy Level Collective Behaviour Supply Chain Industry 4.0 Self-Evolution Target Balancing Process Control Software Hardware- Fractal Organization Complex Adaptive Manufacturing Innovation Changing Environment Layout Company Fractal Systems CAMS Flexibility Planning Process Fractal Virtual Organization Complex Adaptive Enterprise CAE Resilience Self-Organization Process Flow Fractal Fabrication Distributed Manufacturing Real Time Emergency Production Planning Fractal Factory Smart Manufacturing Systems Co- Evolution Self-Organization Task Scheduling Fractal Cell Complexity Entropy Self-Recon fi guration TIC Fractal Process Simplicity Continuous Adaptation Self-Adjustment Manufacturing Cells Fractal Product Chaotic System Autopoiesis Restructuring Manufacturing Processes Fractal Project Critics state Adaptability Regeneration Project Management Fractal Portfolio Dynamic System Recon fi guration Cultural And Business Values Fractal Program Fractal Architecture Homeostasis Business Process BFU (Basic Fractal Unit) Recovery Technology Fractal M.A.S. (Multi-Agent System) Human Resources Nested System Inventory Fractal Network Socio-Technical Systems Fractal Unit Sustainability communication to achieve a common goal in a given context (market, competition, customers, society, sector of activity) [41]. o FrF (Fractal Factory & Manufacturing Process) is a flexible manufacturing system composed of the characteristic elements of a factory (space, infrastructure, manufacturing cells, tools, machinery, processes, etc.) which exchange information, knowledge, material, human and virtual resources, etc. to produce material objects or offer related services [42]. 3. FrMS: fractal manufacturing systems Fractal theory applied to manufacturing engineering has evolved over the last decades from the first contributions developed by Warnecke in the book The fractal Company [14]. Since then, many researchers in different areas of knowledge such as organization engineering, manufacturing engineering, business processes or software engineering and information systems, have contributed by developing a multidisciplinary theoretical framework for its application in systems engineering (economic, human resources, business, information flows, telecommunications, organizational networks, among many others). All with the objective of designing a Fractal Manufacturing System (FrMS). Although in general the publications that analyze and develop the fractal theory in manufacturing (Table 2) attribute the first contribution to Warnecke [14], there are previous works; it is the case of Dyke's research [43] where the fractal theory is used for the configuration of a set of self-similar agents in distributed manufacturing control systems. Dyke takes the term fractal hierarchy from Hewitt and Jong [44,45], whose results are based on the studies of fractal theory and self-orga- nization developed in natural sciences by Mandelbrot [46] and Poincare's chaos theory [47]. From a mathematical point of view, Dyke uses a fractal metaphor for the construction of an intelligent agent architecture included in a prototype of a distributed manufacturing control system. The fractal analogy is used to manage the complexity of the system by reducing the total amount of code written (and its subsequent maintenance) and bringing flexibility to its operation. Subsequently, Tirpak published in 1992 A note on a Fractal Architecture for Modelling and Controlling Flexible Manufacturing System [42] where he re-designs flexible manufacturing systems with fractal theory. This research has been used later by other authors now considered as a reference in the knowledge area of production control and fractal fabrication, as is the case of Kwangyeol Ryu, Youngjun Son, Mooyoung Jung, Moonsoo Shin o Youngpil Cha. It should be noted that the main publication that establishes the conceptual basis from a business point of view is the book “The Fractal Company: A Revolution in Corporate Culture”, where Warnecke proposes the foundations and principles applied today [14]. Focused on industrial organization, business management and corporate culture, it defines a new perspective by developing the analogy between the natural system and the industrial system; the aim is to achieve a structure that continuously adapts to the work context (market, competition, customers or suppliers). Following this, Warnecke defines the management strategies with examples of fractal industries and positive experiences [48–50]. Since 1993, Warnecke's contributions have been used as a starting point for studies by other researchers that have broadened the knowledge base, and are currently being considered for application in Industry 4.0, for example, in the design of the E2E process (End-To-End Process) or networked and decentralized organized services. 3.1. Frameworks for FrMS Since the first publications by Warnecke, Dyke and Tirpak, fractal theory has been applied to manufacturing engineering to provide solutions to complex systems in their different conceptions [61,62]: Complex adaptive system – CAS [63], Collective Adaptive Systems [64], Complex adaptive emergence systems – CAES or Adaptive Complex Enterprise ACE [36]. Existing frameworks are qualitative contributions; that is to say, they are methods that allow the conceptual design of a fractal architecture to be put forward. Generally, any of the elements within the architecture of a FrMS are subject to fractalization: information and data management, information technology systems, tacit and explicit knowledge, company competencies (training, skills, psychosocial, etc.), collective and individual behaviour of members of the organisation, trust between partners,organisational culture, business strategies, human resource organisation, inventory management, socio-technical systems, plant layout design, communication technology, manufacturing processes, production planning, scheduling, distribution and design of manufacturing cells, product and service requirements (cost, quality, time, etc.) or material and immaterial flows (work, process and tasks, resources), control systems (hardware and software) and project management. First, the frameworks developed for application in Fractal Supply Chain (FrSC) design apply fractal theory in order to streamline the exchange of goods and services between suppliers, distributors and producers, minimize inventory costs and responsibly meet customer demand. It should be noted that, with the development of the global economy, the supply chain can be understood as a complex system, and in this context, fractal theory is used to minimize complexity through: inventory control [15,65], the exchange of information [15,65–67], control of relations between stakeholders (manufacturer, distributors, retailers or final sellers) [68], manage operations (production, demand, storage, transport) [69], integrate vertical (supply-demand, business and manufacturing) and horizontal supply chain management (product, production and sales) [16], and control the uncertain relationships between the main elements of the chains: suppliers, distributors, manufacturers and customers [70]. Second, the frameworks developed to design Fractal Organization (FrO) apply fractal theory to create organizations that are self-adaptive to new market demands and reduce the complexity of changes in their management and production system. To this end, time optimization (Prisecaru et al., 2012), quality management [71], management and minimization of cost [72], management of communication, information and data [73–76], control de la ventaja competitiva [26], collective and social behaviours (macro-ergonomics) (Florio et al., 2013), design process management and engineering [77] o security and control of change tolerance [12,31,32] Finally, existing Fractal Factory & Manufacturing Process (FrF) design frameworks allow a manufacturing system to be broken down into units of similar structure and control in order to maximize local functionality and minimize operational complexity; A Multi-Agent System (MAS) [78,79] is used for this purpose, which will perform all operations autonomously. Generally, the following basic agents are selected: observer, analyzer, organizer, resolver, and reporter [68], which manage and control incoming and outgoing flows (materials and information), production units and transport, analyse task results and redesign their performance to optimise results. The first published work fractalizing a manufacturing system was developed by Tirpak et al. [42]; the fractal architecture proposed by the author, has been subsequently used as a starting point by other researchers applying fractal theory to self-reconfiguring manufacturing systems [13,80], minimize investment costs and maximize workflow performance with layout design, cellular manufacturing system [81] and job shops [82,83], minimize time and costs [84–86] to perform the Interenterprise Quality Tracking and Control [87], design of Extended Digital Manufacturing Systems (EDMS) for the creation of production and business system [88,89], design control and automation systems [90] or control the costs and management of human resources [27]. Table 2 Main publications on the theoretical foundations. Reference Objective Scope [14,48,49] Basic fundamentals Concepts, terms and principles [38,51,52] Analysis and detailed description Applied Knowledge Base Glossary of extended terms Detail of fundamental principles Methods, procedures and application examples [10,53,54] Advantages and disadvantages Comparison of design features Comparison of operating mechanisms. [55] Fractal system modeling Fractal system managementMetamodels for the design, con fi guration and modeling of FrMS companies Metamodels for theirs management systems [56] Implementation strategies Analysis of the implementation in manufacturing and production planning Analysis of the implementation supply chain [37,57–60] New approaches New markets New contexts of manufacturing and industry 4.0. 3.2. FrMS design principles Warnecke defined the properties and requirements to be introduced in the FrMS, from which the four fundamental design principles shown in Fig. 3 were derived [14]: self-similarity, self-oganization, goal-or- ientation and dynamism. The frameworks and design strategies for FrMS in section 3.1 are conceptual proposals. The need for a detailed design process, made different authors focus their studies on the proposal of functioning mechanisms for fractal theory, developing methods, techniques and tools that facilitate the process of detailed design and evaluation of a FrMS. The existing publications are explained and collected in the following sections.Principe of self-similarity Self-similarity integrates the concepts of similarity, analogy and cascade structure; it is the property of a system that makes the whole (macroscopic level) equal to the parts (microscopic level). Applying this principle, the architecture of a FrMS is created by dividing its global objective into different self-similar units (characterized by the same configuration and structure), which work autonomously (with their own function or service) and which interact with the rest of the units through cooperative relationships. To achieve scalar invariance a repetition pattern called the Basic Fractal Unit (BFU) is created which, in a repetitive manner (to a greater or lesser extent), forms the architecture of the FrMS. This "cascade structure" includes the physical and behavioral configuration of the system. [91]. Fig. 4 represents an example of BFU [13]. Self-similarity in a FrMS can be applied to different elements of the system architecture, which define the "fractal dimension" [92] or characteristic pattern represented by the BFU: structure of the organization (fractal of departments) [16], information flow (fractal data) [12,31,32], system results (fractal of product families and process platform) [82,83], production flows, operations and functions (fractal of resources, products and services) [77,88,89,93], knowledge (competence fractal) [26,64], or any other requirement or feature of the FrMS that evolves over time. The BFU is the only pre-defined configuration [94]; it will be used as a pattern to create basic operational units with identity and self-suffi- ciency configured according to their objective and needs; that is, they will be self-sufficient and will be equipped with their own resources, they will develop by themselves the capacities and abilities required to approach in a collaborative way the activities that they have associated, adapting this BFU to their needs. That is, the FrMS will be a set of BFUs adapted according to the scale level and for the different dimensions that characterize the system; the adaptation of the BFU will depend on the functions to be developed by the fractal units (FU) and the type of relations that they have in their context [42]. In this way, fractal units (FU) are independent from each other; that is, they evolve in time autonomously to carry out their objective. This implies that they must have all the information and resources necessary for their autonomous action. As there is no external intervention for their management, structuring and improvement, they will be selfsufficient units in terms of functioning and internal and external interaction. The autonomy of the fractal units makes them develop their objective without interference with the rest of the units, speeding up Fig. 3. Principles of fractal organization. Fig. 4. Self-similar basic fractal unit (BFU). the action, evaluation and management of the behaviour of the global system. In this way, fractal units will create a collaborative network to maintain the state of global equilibrium, where cooperation will be necessary to achieve the objective of the higher level, but without interference between sub-objectives. The system architecture will meet the following states of self-simi- larity [95]: 1 Structural self-similarity for organizations, departments and working groups: similar training structures in teams and departments [96]. 2 Self-similarity in planning: similarity in planning and management protocols, i.e., in defining objectives, decision-making, problem solving, operations planning, task sequencing and resource setting [97]. 3 Self-similarity of operation and work performance: same structure in the performance and operation of the different departments or teams based on modularity, information, time and approaches to action protocols (for example, with Deming cycles) [98]. Self-similarity reduces complexity (static and dynamic) [99] selfsimilarity reduces complexity (static and dynamic) throughout the FrMS life cycle and improves efficiency in process outcomes; self-si- milar structures make operations more flexible and can be expanded when demand increases and eliminated or reassigned when workloads decrease. In addition, the knowledge and experience of each of the units may be duplicated in other units when it is required. In this way, thanks to the principle of self-similarity, the following characteristics are achieved for a FrMS: (1) flexibility and adaptability or maintaining stability and order in response to internal or external changes using available resources [99]; (2) modularity that facilitates continuous improvement in real time thanks to a configuration based on commonality [100]; (3) scalability, with the possibility of increasing or decreasing production capacity to adapt to changes in demand [69]. Table 3 lists the publications that develop the principle of self-si- milarity for FrMS; the works propose the necessary mechanisms for the design of fractal structures and their operation, developing modeling, simulation, optimization and similarity assessment techniques applicable to different levels of supply chain, organization and process. 3.2.1. Principle of self-organization Self-organization occurs in a variety of physical, biological, chemical, or social phenomena. From a general point of view, it is the spontaneous process that occurs in open non-linear systems, in which coordination arises from local interactions between initially disordered components. It is a mechanism that governs the dynamic variation of the system and allows it to explore regions in its state space to reach the state of equilibrium; it is imply that the system has a high homeostatic capacity and is able to maintain its dynamics close to a certain state or states (attractors) [39]. The fractal theory applied in manufacturing, adopts the approach of the Systems Theory, where the self-organization allows the fractal system to determine and modify its structure, functions and characteristics for its survival in the context, providing it with autonomy and Independence. Therefore, the principle of self-organization serves to create the architecture of the system from the BFU, adapting the fractal units to their objective and their environment. This principle provides flexibility (easy reconfiguration and quick adaptation) and limits the degrees of freedom of the structure, behaviour and configuration of the operation (reaching a balance between autonomy and cooperation, and reducing entropy) [17,104]. Fernandez et al. [39] studies the mechanisms needed to provide the capacity for self-organization to a System: (1) emergence (properties of a phenomenon which are present at one scale and are not at another scale, temporal or spatial); (2) self-organization (the system increases its own organization); (3) complexity (balance between change (chaos) and stability (order); (4) homeostasis (system stability or internal maintenance of a near-constant environment); y (5) autopoiesis (regulate the production and regeneration ofthe system’s components, having the potential to develop, preserve, and produce their ownorganization [105]). These measures of complexity contribute to the control and balance of the system, that is, the reduction of entropy when: (1) there is external turbulence which may disrupt the proper functioning of the FrMS and therefore its efficiency and effectiveness, and this will require global or partial changes to restore the balance; and (2) continuous improvement of the FrMS is required. Table 4 lists different publications that establish the objectives and application of the self-organiza- tion mechanisms for a FrMS. The principle of self-organization is applied to all elements of the FrMS architecture (structure, objectives, functions and processes) [14,93]: (1) at the structural level for adaptation of the BFU and creation of the fractal system structure; (2) at the operational level, to specialize fractal operation and collaboration procedures; and (3) at the tactical and strategic level, to formulate operational objectives and strategies and select methods for problem solving and decision making. Table 5 lists the publications that develop the principle of selforganization in FrMS; the works propose techniques for the design, Table 3 Design and evaluation of the principle of self-similarity in FrMS. Reference and scope Measure or index developed Self-similarity parameters evaluated FrSC: Supply Chain Coordination [40] Weighting index that quanti fi es self-similarity (1) Information exchange (2) Operations coordination (3) Integration: organizational structure and organizational culture FrSC: supply chain knowledge [91,101] Tacit knowledge order (1) Skills (2) Cognitive Development (3) spiritual schema FrSC: Cluster supply chain – CSC [70] fractal dimensions size of Cluster Supply Chain CSC (1) Formal or informal contracts of trust and commitment (2) Value chain agents: Suppliers, manufacturers, distributors, retailers and customers FrO: socio-technical systems [95] Modeling and simulation of self-similarity in OSTO architecture (Open, Socio-Technical-Economic System). FrO: alliance - industrial cluster [102] Fractal dimension in a networked cooperative business alliance (with similar products and technologies) Work processes, combination of technologies and human communication (1) Structure of the organization (2) Innovation process (1) Production, technology and market (2) Functional structure and work fl ows FrF: Manufacturing results and resource allocation [97] FrF: Quality control for network manufacturing systems [103] Networked organizations and distributed manufacturing systems. ERP system development Dynamic Restructuring Process -DRP: Real-time monitoring system Activity space (tasks and resources) (1) Objectives (time, quality, speed and cost) (2) Performance and performance (3) Results: values (strategy and culture) and resources (social, fi nancial, informational and process) (1) Agent tasks (2) Activity demand modeling, simulation, optimization and evaluation of self-organizing mechanisms applicable to supply chains, organizations and processes. 3.2.2. Principle of goal-orientation The principle of goal-orientation allows to reach the main objective of the system in an optimal way and with zero defects; for this, this principle allows to define the objectives, to control the interferences and to evaluate the performance by means of some measurement variable, to readjust in real time the deviation between the obtained results and the desired ones. In fractal theory applied to manufacturing, the objective is the result of an operation; it will be composed by the set of sub-objectives (operations) of the fractal units (UF) that will work without contradictions or external interferences [14]; the scope of these sub-objectives will allow the main function of the FrMS to be carried out. In this way, the principle of orientation to the objective allows to create the optimal function and operation state of the FrMS, reducing the complexity of operation since its activity will be focused exclusively on the objective it has assigned. The principle of target orientation requires the definition of: (1) an objective formulated as a quantifiable and measurable intent, (2) a set of attributes, performance criteria and performance evaluation parameters to enable real-time monitoring of the FrMS [98,121] and (3) target management, interference and conflict resolution processes to resolve potential inconsistencies between fractal units. The requirement (3) is necessary because, as the units are autonomous in the definition of their own objectives, they can create interference with other units, causing problems in the overall operation of the FrMS. Fig. 5 shows the execution of this principle by different agents with the tasks of defining, assigning, analyzing and correcting objectives [98]. To carry out the process represented in Fig. 5, a set of mechanisms (Table 6) are used to create real-time feedback between operation and environment, as well as cooperation to control joint action within and outside each fractal unit, contradictions and conflicts [122]. In addition, it will be necessary to have a database (FrMS memory and knowledge unit) where the functions and the set of variables, criteria and specific restrictions related to the system properties are collected; this database will be used by a "cognitive agent" [123] which can match a manager, an observer, a user, a designer, the client, or be part of the intelligent infrastructure of the Multi-Agent System (MAS) used by PLM platforms (producto life cycle management), MES (Manufacturing Execution System) or ERP (enterprise resource planning), among others. Table 7 lists the most relevant publications for the three levels of FrMS analysed. Due to their complexity, studies applied to supply chains and organizations are scarce. On the other hand, in the development of factories and manufacturing processes, the contributions of Kwangyeol Ryu, Mooyoung Jung, Moonsoo Shin and Youngpil Cha [98,121,122]. The authors developed a Multi-Agent System called "Goal-Formation Process - GFP" for the coordination of the objectives between the participating units and the modification (if necessary), to ensure a coherent and joint action. The publications that allow the implementation of this principle are summarized in Table 7. Finally, it should be noted that this principle is closely related to self-optimization and co-evolution, contributing to the continuous improvement of the system's performance since it guides the activities and optimizes the performance of each fractal unit; it also requires information obtained from the principle of dynamism in charge of the real-time evaluation of the system's results. Table 4 Self-organizing mechanisms in FRMS. Mechanism and reference Type mechanism Application Synergy [106,107] Cooperation management System formation: coordination in structure control (form and order) Emergency [108] Cooperation management System formation: creation of coherent patterns and disorder control (entropy) Requisite Variety [109 – 112] Complexity management and entropy reduction Autopoiesis [17,39,65,104,105,112] Self-production and selfmaintenance Real-time adaptation of the state of the system: evolution of the state of equilibrium, autonomous control of scalability, reuse and modularization of the system. Balance between autonomy and cooperation. Self-optimization [65,95] Autonomy Management Assurance and sustainability of the system objective: Reconfiguration Table 5 Principle of self-organization in FrMS. Scope Measure or index developed Self-organization parameters evaluated FrSC: Dynamic evolution of the supply chain [113] FrSC: Self-Organized Supply Chain Networks (SCN [96] FrSC: Supply chain cluster with high risk transactions [114,115] Mathematical model for supply chain that predicts the evolutionary direction and the necessary recon fi guration characteristics Nonlinear mathematical model for modeling selforganized supply chains Resilience: Multi-Agent System model for the evaluation of self-organization and supply chain resilience (1) Operation and establishment of strategic goals (2) Resource, technology and market (1) Retailer, distributor, producer; (2) Time, demand, stock security, logistics and production (1) Changes and defects; (2) Resilience, performance and resilient e ff ect management ability FrO: Fractal organizations [17] Self-regulation, self-coordination and selfadministration FrO: Decision Support System - DSS [116] Model for the decision-making procedure; development of the nonlinear dynamic state equation Time, quality, information integration, cost, human resources management, reverse engineering, education and training (1) Goals, decisions, system status (number of processes), resources consumed and value of the problem; (2) goals, risks and time FrO: Quality control in distributed fractal manufacturing companies [117] Time, risk, cost and quality (1) Quality in planning, assignment, management and evaluation; (2) information: environment changes, restrictions (time, cost, quality, risk); (3) structure and recon fi guration of tasks and quality control functions FrF: Smart manufacturing systems [118] Autonomy, fl exibility and reactivity to context changes Self-con fi guration and static and dynamic con fi gurable systems, autonomy, learning and adaptability FrF: Production planning [119] Continuous factory adaptation to minimize costs Agents: production, order and resources FrF: Product design and development [120] Design con fi guration Unit (CU) Product: structural characteristics, materials, design parameters, and restrictions and limitations 3.2.3. Principle of dynamism FrMs are self-regulating dynamic structures that can adapt to changes in the context (internal and external environment). To develop this property, Warnecke [14,48] selects the term vitality from biology and studies the FrMS - ecosystem analogy. It defines vitality as the ability to "maintain and sustain efficient behaviour", i.e. to react to environmental influences in response to internal factors (e.g. costs, research and development, management efficiency, location, human resources, product portfolio, quality of results, etc.) or external factors (e.g. market and sales sector, competition, supply chain, legislation and regulations, etc.) [127]. In this way, the principle of dynamism (Fig. 6) allows fractal units to carry out a continuous process of analysis and evaluation to manage changes in the search for balance. To do this, the FrMS requires the following mechanisms: 1 Self-assessment: includes internal (within the fractal unit) and external (between fractal units) information gathering operations. This mechanism allows to know in real time the performance of the system; and it can activate the necessary actions to restore the balance [128]. 2 Co-evolution: based on the analysis of the interrelationships within and between fractal units [14,128], this mechanism adapts the fractal unit (activities, functions and decision-making) to the requirements of the environment and other fractal units of the FrMS. 3 Operation: short-term management actions to maintain system quality and improve efficiency [104]. 4 Exploration: medium- and long-term management actions for the search of new opportunities for future improvement with open and closed innovation [104]. To make these capabilities possible, the FrMS must have an information management and control network that captures and exchanges data in real time. The structure of the system of agents (Multi- Agent System) will be created according to the different levels required, which can be: management, data processing, schedules and working hours, informal, physical (infrastructure and resources), psycho-sociological (socio-technical system), technological and financial, among others. The principle of dynamism (Table 8) applied to supply chains facilitates the management of entropy (or degree of disorder and non- Fig. 8. Distribution of research e ff ort by dimensions. There are some studies that take into account the design in social sustainability and the control of socio-technical systems to increase motivation, capacity and skills of human resources, knowledge management and improvement of social relations, but always from a point of view of economic improvement and the survival and temporal evolution of the organization. Similarly, the publications do not incorporate ecological design and configuration criteria so that fractal systems are oriented to the creation of value and reduction of environmental impacts. There is only one publication that mentions the need for green supply chains, but it does not specify their design and development. Finally, to indicate that fractality is not unconnected with sustainability. From different fields of study of sustainable development (including manufacturing engineering), the scientific and technical community has opted for a self-similar model called Triple Bottom Line [167], where the three economic, social and environmental dimensions are fractured. Therefore, fractal theory applied to manufacturing should include the updating of its principles for the management of the sustainable performance of the manufacturing system. 5. Conclusions The fractal theory allows to design enterprise and manufacturing systems that have to operate in turbulent business environments, providing agility and viability, through a balance between complexity and simplicity in organizational management and operations. As identified in this paper, Different authors have applied fractal theory for the configuration and management of complex adaptive manufacturing systems. This work has allowed to know the current state of knowledge related to the development of fractal manufacturing systems, both in the research and professional fields. Methodologies, techniques and tools available in the scientific literature have been identified and the current situation of the existing knowledge base has been reflected, specifying which are the current needs to adapt and extend it to the new challenges identified by Industry 4.0 for the Smart Factories. The results of the review have shown that it is necessary to expand and adapt the scope of fractal theory to the new challenges of the Fourth Industrial Revolution, introducing into the design and development of manufacturing systems, (1) virtualization using cyberphysical systems (CPS) and (2) sustainability requirements. As for the first adaptation, the enabling technologies of Industry 4.0 will make it possible to incorporate the "intelligence" capacity into FrMS more easily by building cyberphysical systems [6,168,169]; these are responsible for coordinating human-machine integration (humancentered manufacturing). This could be done by creating a specialized technological basis for use in fractal theory by improving the humanmachine connection based on four dimensions: I Product design and process automatization (physical domain): with facilitators focused on "production hardware" such as robotics, selfreconfiguring machines, autonomous vehicles, modular production, additive manufacturing, self-diagnostic machines, among others. II Control and monitoring with digital interfaces (physical domain): with facilitators to improve the "human-machine-factory interface": intelligent products, wareables, intelligent environmental recognition, cobotics, preventive maintenance, virtual work, virtual reality, among others. III Work organization, interoperability and interconnectivity (virtual domain): with facilitators of "data exchange, management and processing software": big data, data mining and cloud computing (CBDM - Cloud-Based Design and Manufacturing), data management platform (PLM, ERP, MES, HCM, etc.) among others. IV Precise and flexible manufacturing operation (virtual domain): with "computer hardware" facilitators for intelligent management of orders, demand, quality prediction, digital prototyping, generation of process documentation and intelligent manuals, among others. As for the second adaptation "sustainability", the main current drawback of the fractal theory applied to manufacturing is that it does not incorporate any environmental criteria. The extension of the scope of the current "fractal-manufacturing" analogy to "fractal fabrication as second nature" [170] should be considered, where a FrMS was identified as an artificial ecosystem similar to a natural ecosystem. In natural ecosystems it is possible to identify the four principles of self-similarity, self-organization, goal orientation and dynamism as mechanisms for the balance between all living organisms and the physical environment (atmosphere, hydrosphere and lithosphere) where they are related. The extension of the analogy requires the incorporation into fractal theory of the concept of the TRIPLE BOTTOM LINE for the creation of sustainable value [167] in the economic, social and environmental dimensions. This would allow modifying the process of design and execution of the FrMS with a double focus: (1) eco-efficient (for the minimization of negative impacts) and eco-effective (for the creation of value and regeneration of the damage caused so far) [171]. Finally, it would be convenient to develop a methodology that incorporates the four design principles (self-similarity, self-organization, goal orientation and dynamism) in a single procedure for the design, modeling, simulation and optimization of sustainable cyberphysical systems (S- CPS), which facilitates the analysis of the performance and the economic, ecological and social viability of the FrMS in real time for its intelligent control. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] Radanliev P, De Roure D, Nurse JRC, Nicolescu R, Huth M, Cannady S, et al. 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