Multilayer Network-Based Production Flow Analysis
Read this article. The intent is to explore production technologies in relation to flow analysis. Pay attention to how production flow analysis is defined. Do you agree or disagree?
Multilayer-Network Representation of Production Systems
Essential information about the products to be assembled, parts to be manufactured, materials to be used, methods and techniques to convert the material to the required finished components, and manpower to operate the plant is usually available to a company, but rarely in an appropriate form for ease of digestion by the manager. In this section, we propose a network-based model to study the relationship between these elements.
As can be seen in Figure 1, the proposed network consists of a set of bipartite graphs representing connections between the sets of products , machines/workstations
, parts/components
, activities (operations)
, and their categorical properties (referred as activity types)
and skills of the operators needed to perform the given activity
.
Figure 1 Illustrative network representation of a production system. The definitions of the symbols are given in Table 1.
The relationships among these sets are defined by bipartite graphs represented by
biadjacency matrices, where
and
are used as a general representation of a sets of objects, as
.
The edges of these bipartite networks can represent material, energy or information flows, structural relationships, assignments, attributes, and preferences, and the edge weights can be proportional to the number of shared components/resources or time/cost needed to produce a given product (see Table 1).
Table 1 Definition of the biadjacency matrices of the bipartite networks used to illustrate how a production system can be represented by a multidimensional network.
Notation | Nodes | Description | Size |
A | Product (p)-activity (a) | Activity required to produce a product | Np × Na |
W | Activity (a)-workstation/machine (w) | Workstation assigned for the activity | Na × Nw |
A' | Activity (a)-activity (a') |
Precedence constraint between activities | Na × Na |
B | Product (p)-component/part (c) | Component/part required to produce a product | Np × Nc |
P | Product (p)-module (m) | Module/part family required to produce a product | Np × Np |
C | Activity (a)-component (c) | Component/part built in or processed in an activity | Na × Nc |
M | Activity (a)-module (m) | Activity required to produce a module | Na × Nm |
T | Activity (a)-activity type (t) | Category of the activity | Na × Nt |
S | Activity type (t)-skill (s) | Skill/education required for an activity category | Nt × Ns |
O | Skill (s)-operator ( |
Skills of the operators | Ns × No |
The proposed model can be considered as an interacting or interconnected network,
where the family of bipartite networks defines crossed layers. Since
different types of connections between the nodes can be defined, the
model can also be handled as a multidimensional network. Both of
these models are the special cases of multilayer networks, which
representation is beneficial, since the layers represent the direct
connections defined by the bipartite graphs, while the interlayer
connections help in term of the visualization of the complex system by
arranging the corresponding nodes at the same place within the layers
(as it is illustrated in Figure 2).
Figure 2 Visualization of the illustrative network as a multilayer/multiplex network highlights how the complex production system can be grouped into modules based on the “viewpoints” of the layers.
The previously presented example serves only as an illustration. For real-life applications, the model should be extended and standardized. Manufacturing systems and their information can be organized by following the 5Ms and 5Cs concepts. The 5Ms stand for materials (properties and functions), machines (precision and capabilities), methods (efficiency and productivity), measurements (sensing and improvement), and modeling (prediction, optimization, and prevention). The 5Cs stand for connection (sensors and networks), cloud (data on demand and at anytime), content (correlation and purpose), community (sharing and social), and customization (personalization and value). Based on the characteristic elements and connections of production systems, the type of nodes and edges of their network can be defined, and the relevant information is summarized in Tables 2–4. Although these concepts are already useful in structuring information, as a standardized solution, the applications of the ADACOR predicates that established relationships among the essential concepts of production management are recommended (see Table 5).
Table 2 The edge types of the proposed multilayer network.
Flow type | Attribute type | |
Definition | Material, energy, or information flow between the nodes | Representation of the property of the node |
Edge weight | Physical attributes of the flow, like quantity, or during discrete events, the frequency of the flow, like the number of hours between events | Similarity measure, meaning the quantity of equal attributes or the similarity of an attribute based on a scale |
Self-loop | Inner activities | Not interpreted, as self-similarities are trivial |
Parallel edges | Multiple flows can be represented by multilayer/multidimensional networks | Multiaspect similarities can be converted in to edge weights |
Serial connections | Paths of the flow of different entities | Interpreted in terms of the time-varying case; shows spreading of a property |
Modularity | Highly cooperative nodes | Highly similar nodes |
Table 3 Node types of the proposed network.
Event type | Resource type | Competency type | |
Fundamental properties | Occurrence probability, failure rate, cycle time, etc. | Physical properties, quality parameters (capacity, idle state, etc.) | Not generalizable, concept-dependent quantity and quality parameters |
Node degree | Event frequency | Resource usage metric | Spreading competency |
Modularity | Example: event sequence | Example: resources with the same usage parameters | Example: competencies possessed by the same resources/operators |
Table 4 Node edge matchings in the proposed network.
Flow type (edges) | Attribute type (edges) | |
Event type (nodes) | Process steps (nodes) and their input-output connections (edges) | Independent variables (nodes) and their settings (edges) |
Resource type (nodes) | Information exchange (edges) between information systems (nodes) | Colleges working (nodes) on the same workstations (edges) |
Competency type (nodes) | Commitment reporting between (edges) and jobs (nodes) | Same competency demanding (edges) jobs (nodes) |
Table 5 The ADACOR predicates can be directly applied to define layers of the network (please note that we use the term activity to refer to operations).
Thanks to the recent standardization and integration of enterprise resource planning (ERP), manufacturing execution systems (MES), shop floor control (SFC), and product lifecycle management (PLM), it is straightforward to identify the connections of the standardized variables of production management and transform them into a multidimensional network model. The model is capable of representing information at different levels, so it can support factory flow analysis and departmental flow analysis, or, according to the concept of Industry 4.0, it can also integrate interorganizational supply chains. The development of organizational models is also supported, for this purpose, solutions following the standard of UN/EDIFACT (the United Nations rules for Electronic Data Interchange for Administration, Commerce and Transport) could be used.
The extracted models lend themselves to be handled in the databases of graphs or RDF-based ontologies. In our work, the related technical details of building and storing graph-based decision systems are not the focus; rather, how information from this model can be extracted to support production flow analysis is of concern. In the next section, such techniques are presented.