Complexity in manufacturing systems: a literature review

The business environment is increasingly complex and competitive so organizations must respond to different market conditions by reconfiguring their processes, products and services. The objective of this article is based on a literature review under a scientometric and bibliometric approach, referring to the complexity in manufacturing systems, allowing to find answers to relevant questions with respect to the subject matter and to show literally the scientific fields of application, factors of complexity and methods of solution. Methodologically, a first stage is developed on the problems and formulation of the research questions, the second stage establishes the information search strategy and finally a statistical analysis is carried out. The findings show a positive trend and interest on the part of the scientific community in the number of publications related to the subject in the different databases, highlighting the exercise of the theory of complexity in different disciplines but on a smaller scale in scientific fields such as manufacturing and supply chain management.


Introduction
There are factors linked to the complexity of manufacturing systems that influence the development of processes and impact on the performance indicators of a company, due to the fact that numerous resources interact and that a high variety of elements intervene. According to [1] the level of complexity depends on the characteristics of how the system is structured, being made up of the quantity and variety that participate and relate to each other. Studies on complexity are often becoming more frequent and fundamental for modern organizations [2][3][4][5][6] because those who administer them try to manage, reduce or eliminate it in their processes, thereby reducing costs, increasing revenues and improving competitiveness in internal and external markets. In a manufacturing system, complexity is always present, from the time raw materials enter until the finished product leaves. As companies have to expand their capacity due to the volatility of demand, operations likewise have to become increasingly complex. Today, there are several definitions of complexity as an immense international interest and knowledge for the scientific base. There are two different forms of complexity: (1) static or structural complexity that is designed into the system architecture, (2) operational or dynamic complexity that can also change drastically in short periods of time according to its environment [7]. This article presents a literature review on complexity in manufacturing systems. Methodologically based with a first stage on the problems and formulation of the research questions, the second stage establishes the strategy for searching for information and finally a statistical analysis is made. The work is divided into three sections, first the method is developed, then the results are presented and finally the conclusions.

Method
In order to carry out the study, the construction of the proposed methodology comprises three phases (See Table 1).

Problem solving and guiding questions
Given the need for companies, especially small and medium-size industries, to offer optimal levels of service, it is necessary to implement efficient manufacturing systems in order to minimize production costs, deliver the largest number of orders to customers, and increase revenues [8]. The research conducted by [9] establishes that complexity negatively impacts the company's indicators and generates losses related to profits, revenues, sales volume and customer losses. Similarly, [10] establish that the impact is reflected on productivity and process quality. On the other hand, [11] in their research show that costs related to inventories are linked to manufacturing complexity. Likewise, the uncertainty of the market which increases the complexity in the productive systems [12]. Given the above, some guiding questions have been defined according to the research taken as reference, derived from experimental studies on "Complexity in manufacturing systems", so as to minimize the possible biases of the observer in a systematic literature review.
• What is complexity as a system? •

Information search strategy
In order to search for information, the use of scientific databases was used, using the tools they provide for the extraction and analysis of information.
For the search of the information, the use of scientific data bases was resorted to, by means of the tools that these provide for the extraction and analysis of the information. The search strategy was built in four stages, (1) General database search, in this stage all research related to complexity in manufacturing and supply chain systems are searched in the mentioned databases, this bibliographic review was carried out by searching information in Emerald, IEEE Xplore, Science Direct, Springer and Taylor and Francis from the route of < Title > "Complexity and Manufacturing System" and < Title > "Complexity and Supply Chain". (2) Search with filter according to the keywords, in this stage a more detailed search is made taking into account the complexity, manufacturing and supply chain, in the same way in the databases previously mentioned, through the route < Title-Abstract-Keywords > "Complexity and Manufacturing System" and < Title-Abstract-Keywords > "Complexity and Supply Chain". This process allowed to refine the research of the thematic axis, which provided to limit the field of study passing from a general total of 308,407 research works to 1451 in filtered form.
(3) Extraction of the results obtained, in this stage the data are imported and organized in a spreadsheet or through the VosViewer software and (4) Statistical analysis of the results, where characteristics such as year of publication, types of publications, journals, authors and most relevant words are examined (See Fig. 1).

Statistical analysis of information
For the analysis of the information, a time horizon corresponding to the last four (4) decades was taken. It is worth mentioning that the cenciometric and bibliometric analysis started in January and ended in September 2018. For this, graphic tools such as line diagram, bar graph and network diagram were applied. Table 2 shows the amount of research 1 3 published from the 1980s to the present. The last few years are representative for the analysis of this last decade.

Results
This section presents the results obtained according to the questions asked. In this way, the section is separated by ten

What is complexity as a system?
Making a review of the literature on complexity since its first appearance in 1963, Table 3 presents a list of the main elements of definition of complexity, considering criteria such as (1) importance, (2) dependence and (3) impact. These criteria were selected to expand the knowledge and corroborate the level of relevance of the topic addressed.

Scientific fields of interest of complexity
Complexity has had different directions or paths due to the different disciplines that exist within a business environment, among these are (1) Management Sciences, (2) Operations Management, (3) Manufacturing, (4) Organizational Sciences and (5) Supply Chain Management. Table 4 presents a review of documents found in the different fields of interest of complexity, is notorious a large number of research in disciplines such as Management Sciences, Organizational Sciences and Operations Management and on a smaller scale scientific fields such as Manufacturing and Supply Chain Management. It is evident that studies of complexity in Latin American countries such as Colombia, Argentina, Chile, Ecuador and others, associated with business environments present a high degree of scarcity, therefore, is a weak aspect in the manufacturing systems  [37] Article The complexity of a system depends on the components that will interact in the development of manufacturing 2014 Schuh [38] Book The complexity depends on its temporal variability, due to specific industry and business effects 2013 Chryssolouris et al. [39] Article The complexity is increasing because they have to face a series of strategies nested with the environment 2013 Byrne and Callaghan [40] Article The greater the number of agents that participate and interact, the greater the complexity in a supply chain 2013 Schuh [41] Book It depends on the variety of a product or factors within the production 2012 Singh et al. [42] Article Increasing complexity in systems affects operational development time and effort 2011 Garbie and Shikdar [7] Article It is useful for improvement analysis and business restructuring 2000 Stacey et al. [43], Gare [44] Book It depends on the heterogeneity, diversity and plurality of the different elements that make up the system 1991 Simon [45] Article It depends on the high variety of elements that when relating to each other, are not so simply done 1988 Ulrich and Probst [46] Book It is understood as a quality of the system where the degree is subject to the quantity of elements that exist in the system 1985 Klir (1985). [47] Article The complexity of the system should be proportional to the amount of information required to describe the system 1978 Yates [48] Article It depends on the size of the system, the randomness, the asymmetry and the non-holonic constraints 1977 De Rosnay [49] Book The complex system that is more heterogeneous 1963 Ashby [50] Book Only complexity absorbs complexity. This law suggests that the greater the complexity, the greater the control of the system and supply chains you want to manage, reduce or eliminate factors that affect complexity.

Complexity in manufacturing systems
Manufacturing is the process of adding value to a material to build a product [13]. The art of manufacturing involves a process, or a repetitive sequence of operations, used to construct the product. Manufacturing requires resources to produce the product, including an infrastructure of persons in an organization that provides the necessary support for manufacturing. [14] in its research establishes to carry out a manufacturing engineering process it is necessary to take into account some activities such as: (1) Choice of process, The study of complexity is born from trying to explain and predict the behavior of a system through formal models. Models describe a set of input variables that are transformed into a variable or set of output variables, through a set of internal processes in order to predict the behavior of a system. For [15] a system is a conglomeration of elements such as plant, process, product and parts that interact and relate to each other, in this sense, systems can be considered as a representation of a reality. Similarly a complex system is a mixture of aspects related to material, machinery, people, process, facilities and flows related to information, materials and documents. All manufacturing systems are composed of input entities such as raw materials, information and energy, and output entities associated with finished products, waste and information [16].
Manufacturing systems are characterized by instability, due to the resources involved and the uncertainty of external variables. According to [17], this is due to four important aspects such as: (1) Interdependence, within a manufacturing system work stations depend on each other, regardless of whether the type of process is Flow shop, Job shop or by Project, (2) The relationship between the events that occur and the state changes that are generated, (3) Uncertainty, this due to dynamic, uncontrollable and unpredictable external variables and (4) irreversibility which is linked to the degree of uncertainty and the costs that are generated. In short, in a manufacturing system there are production factors that intervene, associated (1) with materials when they do not meet time, quantity and quality specifications, (2) with labor when there are changes in work pace, absenteeism and accidents, (3) with machines when they fail, absence of spare parts and tools. Where variables of quantity and variety of processes, products and services make systems unstable and complex. As a consequence, there are mismatches in the plans and reprogramming, which increase the costs reflected in the consumption of hours of preparation of the machines, repair times, overtime, among others. Understanding the existence of these characteristics allows us to consider that manufacturing companies are complex systems in complex environments and that administration or management becomes complex. In addition, manufacturing systems must monitor the environment in which they predominate, given that any social, political, legal, cultural, demographic, economic, technological, environmental change, with suppliers, intermediaries, customers and consumers, will bring with it environments of uncertainty and complexity within the system. The effects of globalization and the accelerated growth of economies lead to bankruptcies, so companies must prepare themselves to survive. In conclusion the business environment is increasingly complex and competitive where organizations must respond to different market conditions by reconfiguring their processes, products and services. In the studies and analysis of complexity in the literature review, uncertainty clearly appears in the concept of complexity, where [18] establish that uncertainty is everything that is not precisely known about its behavior, and define it as the deviation of the system from what was planned. According to [19], planning in manufacturing systems helps companies better determine the use of their resources to achieve their goals. According to [20], complexity mathematically can be measured when the real is related less than the predicted. Therefore, from the framework of complexity, a window of research would be to help manufacturing planners to manage the appropriate levels of complexity that a system can handle, because it is an aspect that will always exist in all types of scenario.

Classification of complexity in manufacturing systems
Within a manufacturing system, complexity is defined with respect to variables such as origin, quantity, variety, time, and system relationships. According to the literature review, there are several types of complexity associated with these variables or the combination between them.
(1) Related to origin, for [21] the reasons causing complexity may originate from inside or outside the company, presenting three main categories: internal, external and total. Internal complexity is associated with flows within the manufacturer, and can be caused by factors external to the organization called external complexity, which is associated with flows in the supply chain. And the total complexity covers all internal and external complexity. According to time and its behavior, (2) Depending on time and behavior, for [17] complexity in manufacturing systems can be static or dynamic. Static complexity refers to a characteristic that can be associated with the systems, and also with the production processes, it is linked to the structure or design of the plant. Unlike dynamic complexity which is related to the changes of relevant variables in the process over a time horizon.
According to [9] internal complexity relates to variables between flows within manufacturing, and external complexity depends on variables between upstream agents with respect to the supplier and downstream associated with the customer. According to [22], static complexity is that in which variables do not change over time; otherwise, dynamic complexity is that in which variables evolve with respect to time. More specifically [17,18,[23][24][25] determine and establish that static complexity is that which studies the structural part of the system and dynamic complexity studies the uncertainty in the behavior of those operations.
In synthesis, according to the literature review within the scientific field of manufacturing complexity types, the internal, static and dynamic prevail. Where it is considered internally in the company its structure on the processes and/or products and at the same time the behavior of the existing variables in a horizon of time, that lead to the generation of uncertainty. Table 5 presents a review of complexity studies conducted in the different types of complexity.

Sources of complexity in manufacturing systems
In manufacturing systems it is important to mitigate complexity, for this reason the relevant factors that affect performance indicators must be identified. According to [26,27] there are determining factors in the complexity of manufacturing such as: (1) the structure of the product, which relates to the components, subassemblies, (2) the structure of the plant, refers to the number of physical resources needed, (3) the production planning that is associated with the quantity of products to be produced, when it is to be produced and the sequencing of production orders; (4) the flow of information between agents, departments and workstations, (5) the uncertainty resulting from variability in resources and (6) regulations and standards. Table 6 presents a set of factors according to type of complexity and according to origin, which have been identified and/or treated by various authors as sources of complexity. Reviewing the literature on static complexity, it has been studied that it has a negative effect on productivity and quality [10], given that a large number of products and/or the variety of their components generates difficulties in the design and operation of assembly lines [28]. Likewise, static complexity related to the product has a negative impact on production costs [29], so the greater the dynamic complexity, the greater the costs [30]. Experts say there are three main strategies to combat the negative effects of complexity: avoid it, reduce it, or control it [31]. Studies by Bick and Drexl-Wittbecker (2008) [31] state that 25% of the total costs of manufacturing companies are due to the complexity within the process and the different characteristics associated with the product. In short, industrial companies must make decisions to avoid, reduce or control complexity. According to [32], the use of computer and technological resources is prominently recognized in the management of complexity. In [33], a set of solution strategies linked to assistive technologies is presented to reduce or eliminate complexity in manufacturing scenarios (see Table 7).
The literature highlights different types of methods that could be applied to mitigate the effects produced by complexity and at the same time put into practice the different solution strategies. Table 8 lists some tools in the field of Table 6 Review of complexity sources in manufacturing systems

Number of publications
For the analysis of the number of publications, the decade from the 1980s to the present day (1983-2018) was taken as a parameter. A search for the term: "Complexity, in the manufacturing system and in the supply chain" shows that the first investigations began to appear in 1983 and that they have been increasing over the years. Figure 2 shows a positive trend in the number of publications related to the subject in the different scientific databases such as Springer, Emerald, Taylor and Francis, highlighting a notorious behavior in Science Direct and IEEE Xplore. It should be noted that the scale on the horizontal axis has variable time steps.

Types of publications
When verifying the different databases and filtering the search by key words, of a total of 1451 documents, 766 documents represented in 52.8% correspond to research articles, 442 documents equivalent to 30.4% refer to publications through conferences, 134 documents represented in 9.2% correspond to publications through research books, the rest equivalent to 7.6% correspond to publications developed by chapters of books, symposia and other types of publications. In the case of analysis, it is possible to identify that the subject matter presents a high level of information in the types of publication such as research articles. (See Fig. 3).

Relevant journals
From the information obtained, it is highlighted that there are 18 relevant journals which have published more than 10 researches on the subject "complexity in the manufacturing system and the supply chain". As shown in Table 9.

Authors with the most publications and citations
For the authors' analysis, the Scopus database was used as a reference, and it was found that a large number of  Fig. 3 Types of publications authors have published on the research topic "complexity in supply chains and manufacturing systems". This information was used as input to use the VosViewer software tool, which identified the visualization and construction of bibliometric networks. Figure 4 represents the most relevant authors with respect to the number of publications developed in recent years. These are represented by larger circles and a larger font. It is evident that authors such as Ma, J; Tiwari, M.K; Modrak, V; Chan, F.T.S.; Wang, Y y Wang, H, are considered as main authors, so they allow the connection or are bridges of communication between eleven (11) groups of information networks. In Fig. 5 it can be seen that the author Ma, Junhai together with the author Tiwari, Manoj Kumar are the ones who have made the greatest number of publications on the approach to the subject and additional to that have been consistent over time.
However, there are also authors who are in adjacent clusters, who likewise have great value for the quality of their contributions and research, as is the case of Calinescu, A; Efstathiou, J; Srinivasan, R; Hernandez, J.E and Kumar, S. Since these authors particularly research and carry out joint work, in order to encourage aspects of collaboration and cooperation. A fractional count analysis was conducted, which attributes authorship credit proportionally to the total number of authors participating in a document. As the interest is to show the relationships and partnerships that exist between the authors. Figure 6 shows the most representative ones.
It is also important to highlight, within the research network, the citations made to each of the authors, which frames the quality of the contributions and the generation of new knowledge provided to the sciences. Figure 7 shows the

Words most related
Using the VosViewer software, a study was carried out of the most frequently used words in the summary of the documents studied. This tool made it possible to visualize a large number of words related to the subject of complexity in supply chains and manufacturing systems. In Fig. 8, most of the occurrences are related to supply chain, modeling, complexity; Approach; Analysis; Supply chain management; Supply chain network; Research and development. It is worth mentioning that within a supply chain different processes are involved, among which the manufacturing or fabrication of goods stands out.

Conclusion
From the literary environment, it should be noted that manufacturing systems inhabit elements associated with variability and uncertainty, making them difficult and complex systems. Therefore managing complexity within these is a necessary action. It is important to consider and carry out optimal management of complexity, so that the company reflects positive impacts on performance indicators and customer satisfaction. This research included a literature review on definitions of complexity, scientific fields of application, complexity factors according to type and origin, and strategies, methods and solution tools. In general terms, it could be seen that the field of research has been broad, taking into account the different disciplines in which they have been researched. However analyzed the theory of complexity in different disciplines but on a smaller scale in scientific fields such as manufacturing and supply chain management, where the types of complexity in a prevailing manufacturing system are internal, static and dynamic.
The literature highlights different types of methods and tools related to operations management, which could be applied to counteract the effects of complexity and in turn implement different solution strategies. It supports and assists in decision making for manufacturing planners, as it allows them to manage the desired levels of complexity in the system.