A performance evaluation method for radio frequency identification–based tracking network of job-shop-type work-in-process material flows

Abstract

With the rapid development of the modern manufacture, a radio frequency identification–based tracking network has been gradually established to monitor and track the material flows in a job-shop floor. Based on an event-driven graphical schema, this article puts forward a new method for modeling and analyzing the job-shop-type work-in-process material flows tracking network. The schema elements are mapped into the network nodes, and the association relationships among the elements are mapped into the network edges. Furthermore, corresponding measures and metrics are presented to evaluate the work-in-process material flows tracking network performance. Finally, a simple example is given to verify the feasibility of the proposed method. It is expected that this study will provide a systemic evaluation method for guiding and optimizing the radio frequency identification–based tracking configuration solution for job-shop-type material flows.

Introduction

In order to realize flexible scheduling and visual management of a job-shop floor, it is important to collect and process the correct and real-time data from material flows. At present, the data acquisition methods, such as the manual recording, barcode and integrated circuit (IC) card, and so on, have been widely used in the production floor so as to track the work-in-process (WIP) material flows. Although the above methods have brought remarkable benefit for data collecting and automatic production, they also gradually reveal some shortcomings. ¹ For example, the manual recording is time-consuming, inefficient, and error-prone; the barcode and IC card are particularly vulnerable to be contaminated in a bad running environment. With the rapid developments of wireless sensors, communication, and information network technologies, especially radio frequency identification (RFID), these advanced wireless techniques have provided new solutions for data collecting and computing of the modern manufacturing floor. Through attaching an RFID tag to a product or tray, the relevant material flows data can be automatically collected, processed, stored, and transferred to information decision center in a simple but efficient way. Compared with the traditional data collecting methods, the RFID-based technique has many advantages, for example, accurate and fast data gathering without human intervention, repeated use and large storage capacity of electrical tags, and prominent adaptability in a harsh environment. Besides, the RFID-based tracking allows to capture detailed material flows, such as transport between the machines, which are generally less often tracked in the traditional methods. The related industrial practices have also showed a great potential in supporting the automation of manufacturing process, improving production efficiency and achieving value-added service after applying RFID technique to the manufacturing floor. ²

In a job-shop floor, a process flow is considered as a sequence of actions/operations that happens on/around a series of machine tools, turning a workpiece from a material to a finished part, while a WIP material flow is considered as the flow of a workpiece in its specific process flow, from one position to another. It is well known that the goal of tracking the WIP material flows is to identify the state changes of workpieces together with collecting the changing time and position information of their states. ³ Through establishing the RFID-based detecting spaces around machines/equipment and attaching electrical tags to workpieces, the above information can be collected. Furthermore, owing to different data requirements from upper information systems, such as enterprise resource planning (ERP), manufacturing execution system (MES), and so on, the tracking decomposition particle size for the machining or inventory processes will be not unique. Relying on the decomposition particle size, the RFID-based configuration solution for tracking WIP material flows will be different, which may lead to different detecting effects. A reasonable configuration solution may raise the visual management level and improve the production efficiency; instead, an unreasonable configuration solution may bring the resource waste or incomplete tracking data, which will have a passive influence on the whole production scheduling. Therefore, it is urgently needed to analyze and evaluate the RFID-based configuration solution for tracking WIP material flows.

As an effective tool to analyze the system performance, complex network theory (CNT) has provided a new idea for investigating the tracking performance of the RFID-based configuration solution from the perspective of a topology network. First, this article focuses on describing and establishing a WIP material flow tracking network (WIP-MFTN) model, whose configuration solution is given and determined. Then, corresponding measures and metrics are presented to evaluate the detecting performance of the established WIP-MFTN. It is expected that a systemic evaluation method will be developed to guide and optimize the RFID-based tracking configuration of WIP material flows.

In order to achieve this goal, the rest of the article is organized as follows. Section “Related work” reviewed the related work of applying the RFID technology and CNT in the manufacturing industry. In section “Event-driven graphical schema for job-shop-type material flows,” an event-driven graphical schema is used to describe the job-shop-type material flows. Based on this description, the mapping rules between the graphical schema and the WIP-MFTN topology model are given in section “Mapping procedure between the graphical schema and WIP-MFTN.” Section “Performance measures and metrics of the WIP-MFTN” formulates the corresponding parameters for evaluating the WIP-MFTN performance. A simple example is provided in section “A case study: a job-shop-type WIP material flow including four processes,” followed by sections “Discussion” and “Concluding remarks.”

Related work

As an emerging technology, in the past few years, RFID-based automatic identification has gained a rapid development and its tag price has reduced much more. ⁴ Against this backdrop, it has been widely applied to product assembly, part fabrication, and transportation for realizing the real-time tracking, reducing management cost, improving process efficiency, and raising the service level.^5,6 Much attention has been devoted to this topic not only in industrial practice but also in academic circles. Li et al. ⁷ highlighted the role of RFID in the emerging wireless internet manufacturing field. As an example, they investigated the case of Ford motor company that has successfully implemented RFID to improve the quality of products on the automated assembly production line. Liu et al. ⁸ designed a production management system (PMS) integrated with RFID-enabled real-time data capture system for Loncin motorcycle assembly line. Budak et al. ⁹ established a genetic manufacturing monitoring and analysis system through allowing a rapid development and deployment of an RFID-based manufacturing automation solution. Brusey and McFarlane ¹⁰ focused on the issue of correctly identifying, tracking, and dealing with objects in customized production with the use of RFID. Huang et al.^11–13 and Qu et al. ¹⁴ presented approaches for deploying RFID-based wireless manufacturing technology for tracking and managing WIP inventories, walking-worker assembly islands, and adaptive assembly planning in job shops. Bindel et al. ¹⁵ discussed the application of an embedded RFID device into printed circuit boards for life cycle monitoring of electronic products to support product service systems. By comparing the timing of the RFID reads for the same tag, Mo et al. ¹⁶ developed a directional discrimination system in which the direction of the RFID tag movement can be discriminated. Furthermore, they established a two-dimensional positioning system using an RFID array, and the preliminary experimentation showed that this system was capable of locating an object with an average accuracy of 67 mm, using an array with a 350-mm spacing between tags. ¹⁷

In general, the presented research mainly focused on applying RFID technology to monitor and identify the state changes of products through the collection of manufacturing data. Furthermore, it can be used to help make the real-time decisions and realize the closed-loop control of production process, thus making job-shop process controlling more feasible and effective. However, previous research has paid little attention to evaluating the configuration and operation of RFID-based manufacturing system. It is much essential to present a systemic evaluation method for guiding and optimizing the RFID-based tracking configuration solution.

In a job-shop floor, a WIP material flow is considered as the flow of a workpiece in its specific process flow, from one position to another. In terms of the material flow equipped with the RFID devices, therefore, a variety of RFID-based tracking elements are formed in a complex system. While CNT^18,19 is an effective tool for analyzing the structural characteristics of complex system, it has been increasingly applied to manufacturing field. On one hand, the applications are mainly focused on the manufacturing job shops. For example, Liu and Jiang ²⁰ explored the inherent mechanism of machining error propagation through building a machining error propagation network. Zhang and Jiang ²¹ established a measuring and sensing network for analyzing product quality and equipment fault. Liu and Qi ²² applied CNT to mass customization and constructed a component relation network in which the modularization of a product family can be extracted. Through establishing a weighted network of complex product, Cheng and Chu ²³ provided an assessment approach for change impacts. Vrabič et al. ²⁴ presented a method of discovering autonomous structures in complex networks of work systems. On the other hand, much attention has been devoted to manufacturing networks. For example, Meepetchdee and Shah ²⁵ proposed a logistical network design framework through introducing important performance measures, robustness, and complexity into the logistical network design objective. Xuan et al. ²⁶ proposed a new framework to model and analyze the topological structure of supply networks, which suggested that real-world supply networks may benefit from its intrinsic mechanism on flexibility, efficiency, and robustness to target attacks. Zhang et al. ²⁷ established an enterprise collaboration network supported by service-oriented manufacturing and adopted an improved genetic algorithm to find the optimal manufacturing blocks. The above literature suggests that the CNT has a great potential for analyzing the system performance, and it has provided a new idea for investigating the tracking performance of RFID-based configuration solution.

In this article, we first established an event-driven graphical schema to describe the job-shop-type material flows. According to the schema elements and their coupling relationships, a topology model for tracking the material flows was built. On that basis, the key performance parameters were proposed to evaluate the RFID-based configuration solution.

Event-driven graphical schema for job-shop-type material flows

In order to describe and formulate a material flow in job shops visually, an “event-driven” graphical schema model is proposed in the authors’ early articles.^3,28 Table 1 shows the important concepts of the operations/actions, triggering times, positions, and workpiece states in this schema model. As illustrated in Figure 1, there are four steps to describe the WIP material flows using the event-driven graphical schema.

Table 1.

The important concepts in the event-driven graphical schema.

Concept	Symbol	Definition
Process	${\mathit{P}}_{\mathit{i}}^{\mathit{k}}$	A process is defined as a sequence of operations/actions that happens on/around a machine/equipment.
State	$S_{i,j}^k$	A state is defined as a kind of stable and unchanged situation, which lasts a period of time for a WIP.
Event	$E_{i,j}^k$	An event is defined as a kind of operations/actions, which happens at a special time point and causes a state change.
Actor	$R_{i,j}^k$	The actor of an event is defined as a person, who triggers the event.
Time	$t_{i,j}^k$	The triggering time of an event is defined as a special time point, which causes this event to run.
Position	$L_{i,j}^k$	The triggering position of an event is defined as a special position point, which causes this event to run.

WIP: work-in-process.

Figure 1.

An RFID-driven graphical method for describing the time-sensitive state and position changes of the WIP material flow in a job-shop floor.

• Step 1. Determining an RFID-based configuration solution based on process flow. In order to monitor the WIP material flow, RFID devices are deployed to/around the corresponding machine tools for collecting real-time data. According to the requirements from upper information systems, the decomposition particle size for a process ${\mathit{P}}_{\mathit{i}}^{\mathit{k}}$ may be not unique. Actually, it is a mapping between a single process flow ${\mathit{P}}_{\mathit{i}}^{\mathit{k}}$ and the RFID configuration solution space. As a result, a specific process flow equipped with RFID devices can be generated.

• Step 2. Using state blocks to formalize different processes. The key point of tracking WIP material flow is to identify the state and position changes of a WIP. There are four types of RFID-driven detecting solution identifying whether the tags of kth WIP have entered, stored in, or left detecting spaces. The detecting spaces controlled by antennae include fixed space, mobile space, fixed gateway, and mobile gateway. Accordingly, there are four types of valid tag states “tag-moving-in,”“tag-storing-in-space,”“tag-moving-out/tag-moving-to,” and “tag-going-through.” The tracking configuration for a WIP material flow is the combination of four types of state blocks.

• Step 3. Generating an event set automatically. Actually, an event is defined as one or more actions/operations that change the state continuously from one to another. The rule to generate an event set automatically is to build a process-related connection among state blocks that belong to different processes under the context of a WIP material flow. And then, an event can be modeled on the basis of a state pair s_i→s_i+1, which can be formulated as $E_{i,j}^k=f_e(S_{i,j}^k,S_{i,j+1}^k)$ . In this way, event sets that are corresponding with the machining and inventory processes can be formalized.

• Step 4. Using the event-driven graphical schema to describe a WIP material flow. As soon as formalizing all time-sensitive states, positions, and corresponding event sets in the WIP material flow of a workpiece, an extended event-driven graphical schema can be used to model such a material flow. This model can be formulated as $O_{i,j}^k:=〈E_{i,j}^k,t_{i,j}^k,R_{i,j}^k,L_{i,j}^k,E_{i,j+1}^k,t_{i,j+1}^k,R_{i,j+1}^k,S_{i,j}^k,L_{i,j+1}^k,T_{i,j}^k〉$ , where $T_{i,j}^k$ denotes the lasting time of state $S_{i,j}^k$ , given by $T_{i,j}^k=t_{i,j+1}^k-t_{i,j}^k$ . The above graphical schema is only a descriptive unit related to an event and its corresponding triggering time, happening position, and state pair. According to the event set related to a process, we can easily combine the graphical schema of each event into an event-driven graphical submodel ${\mathit{P}}_{\mathit{i}}^{\mathit{k}}:=\{O_{i,1}^k,O_{i,2}^k,\dots ,O_{i,j}^k,\dots ,O_{i,J}^k\}$ . Moreover, the event-driven graphical submodel of each process can be further combined into a complete graphical model for describing the WIP material flow of a workpiece ${\mathit{M}}_{\mathit{i}}^{\mathit{k}}:=\{P_1^k,P_2^k,\dots P_i^k,P_{i+1}^k,\dots P_n^k\}$ .

Mapping procedure between the graphical schema and WIP-MFTN

Through deploying RFID readers and antennas at different tracking nodes, the dynamic and real-time state information of WIP attached with electrical tags can be collected. Using the event-driven graphical schema, the time-sensitive states and position changes of WIP material flow can be formulated as ${\mathit{M}}_{\mathit{i}}^{\mathit{k}}:=\{P_1^k,P_2^k,\dots P_i^k,P_{i+1}^k,\dots P_n^k\}$ in which the process set P^k , the event set E^k , the triggering time set t^k , the actor set R^k , the position set L^k , and the state set S^k are covered.

Furthermore, the above graphical schema model of describing the WIP material flows can be evolved from the perspective of a topology network. The tracking elements generated by schema model are mapped into the network nodes and the association relationships among tracking elements are mapped into the network edges. Therefore, a WIP-MFTN is developed. It can be described as G = (V, E), where V = (v₁, v₂, v₃, …, v_N) denotes a node set and v_i ( i = 1, 2, …, N) denotes the node extracted from the graphical schema and E = (e₁, e₂, e₃, …, e_M) denotes an edge set and e_i ( i = 1, 2, …, M) denotes the edge among different graphical schema. The mapping rules between the graphical schema and the WIP-MFTN are outlined as follows.

Mapping rules between graphical schema elements and WIP-MFTN nodes

In order to describe and formalize the WIP material flows, there are six element sets considered in the extended event-driven graphical schema. They are formulated as follows:

• Machining or inventory process $P_i^k\in {\mathit{P}}^{\mathit{k}}$ , ${\mathit{P}}^{\mathit{k}}:=\{P_1^k,P_2^k,\dots ,P_i^k,\dots ,P_n^k\}$

• Workpiece state $S_{i,j}^k\in {\mathit{S}}_{\mathit{i}}^{\mathit{k}}$ , ${\mathit{S}}_{\mathit{i}}^{\mathit{k}}:=\{S_{i,1}^k,S_{i,2}^k,\dots ,S_{i,j}^k,\dots ,S_{i,m}^k\}$ , ${\mathit{S}}_{\mathit{i}}^{\mathit{k}}\subseteq {\mathit{S}}^{\mathit{k}}$ , ${\mathit{S}}^{\mathit{k}}:=\{S_1^k,S_2^k,\dots ,S_i^k,\dots ,S_n^k\}$

• Event $E_{i,j}^k\in {\mathit{E}}_{\mathit{i}}^{\mathit{k}}$ , ${\mathit{E}}_{\mathit{i}}^{\mathit{k}}:=\{E_{i,1}^k,E_{i,2}^k,\dots ,E_{i,j}^k,\dots ,E_{i,m}^k\}$ , ${\mathit{E}}_{\mathit{i}}^{\mathit{k}}\subseteq {\mathit{E}}^{\mathit{k}}$ , ${\mathit{E}}^{\mathit{k}}:=\{E_1^k,E_2^k,\dots ,E_i^k,\dots ,E_n^k\}$

• Actor $R_{i,j}^k\in {\mathit{R}}_{\mathit{i}}^{\mathit{k}}$ , ${\mathit{R}}_{\mathit{i}}^{\mathit{k}}:=\{R_{i,1}^k,R_{i,2}^k,\dots ,R_{i,j}^k,\dots ,R_{i,m}^k\}$ , ${\mathit{R}}_{\mathit{i}}^{\mathit{k}}\subseteq {\mathit{R}}^{\mathit{k}}$ , ${\mathit{R}}^{\mathit{k}}:=\{R_1^k,R_2^k,\dots ,R_i^k,\dots ,R_n^k\}$

• Triggering time $t_{i,j}^k\in {\mathit{t}}_{\mathit{i}}^{\mathit{k}}$ , ${\mathit{t}}_{\mathit{i}}^{\mathit{k}}:=\{t_{i,1}^k,t_{i,2}^k,\dots ,t_{i,j}^k,\dots ,t_{i,m}^k\}$ , ${\mathit{t}}_{\mathit{i}}^{\mathit{k}}\subseteq {\mathit{t}}^{\mathit{k}}$ , ${\mathit{t}}^{\mathit{k}}:=\{t_1^k,t_2^k,\dots ,t_i^k,\dots ,t_n^k\}$

• Triggering position $L_{i,j}^k\in {\mathit{L}}_{\mathit{i}}^{\mathit{k}}$ , ${\mathit{L}}_{\mathit{i}}^{\mathit{k}}:=\{L_{i,1}^k,L_{i,2}^k,\dots ,L_{i,j}^k,\dots ,L_{i,m}^k\}$ , ${\mathit{L}}_{\mathit{i}}^{\mathit{k}}\subseteq {\mathit{L}}^{\mathit{k}}$ , ${\mathit{L}}^{\mathit{k}}:=\{L_1^k,L_2^k,\dots ,L_i^k,\dots ,L_n^k\}$

Actually, one actor is usually responsible for one machining or inventory process in a job-shop floor, which means that the process ${\mathit{P}}_{\mathit{i}}^{\mathit{k}}$ is in accordance with the actor ${\mathit{R}}_{\mathit{i}}^{\mathit{k}}$ . Therefore, they are merged into the same schema element in the mapping procedure. As a result, five elements extracted from the extended event-driven graphical schema are mapped into the nodes V^k in the WIP-MFTN, which are formulated as ${\mathit{V}}^{\mathit{k}}=P^k\cup S^k\cup E^k\cup t^k\cup L^k=\{v|v\in P^k\vee v\in S^k\vee v\in E^k\vee v\in t^k\vee v\in L^k\}$

Mapping rules between graphical schema elements relationships and WIP-MFTN edges

There are two kinds of mapping relationships among the schema elements. One is the logic-sequenced mapping as shown in Figure 2 in which the detailed relationships among different schema elements are described.

Figure 2.

The logic-sequenced mapping relationship among schema elements.

• The actor ${\mathit{P}}_{\mathit{i}}^{\mathit{k}}$ (i.e. also ${\mathit{R}}_{\mathit{i}}^{\mathit{k}}$ ) is responsible for executing the ith event subset ${\mathit{E}}_{\mathit{i}}^{\mathit{k}}$

• The execution of the event $E_{i,j}^k$ will bring the change of the workpiece state from $S_{i,j}^k$ to $S_{i,j+1}^k$

• The execution of the event $E_{i,j}^k$ will generate two physical attributes (triggering time $t_{i,j}^k$ and position $L_{i,j}^k$ ) as well

The other one is time-sequenced mapping, as shown in Figure 3. In a job-shop floor, the machining or inventory process ${\mathit{P}}_{\mathit{i}}^{\mathit{k}}$ , workpiece state $S_{i,j}^k$ , event $E_{i,j}^k$ , triggering time $t_{i,j}^k$ , and position $L_{i,j}^k$ are changed with the time sequence, respectively.

Figure 3.

The time-sequenced mapping relationship among schema elements.

According to the mapping relationships of the schema elements, the mapping rules between graphical schema elements relationships and WIP-MFTN edges are described in Table 2. The total mapping relationships among schema elements for WIP material flows can be formulated as ${\mathit{U}}^{\mathit{k}}=\{U_{p\to p}^k,U_{e\to e}^k,U_{s\to s}^k,U_{t\to t}^k,U_{l\to l}^k,U_{p\to e}^k,U_{e\to s}^k,U_{s\to e}^k,U_{e\to t}^k,U_{e\to t}^k\}$

Table 2.

Mapping rules between the graphical schema elements relationships and the WIP-MFTN edges.

Logic-sequenced mapping		Time-sequenced mapping
Edges	Elements relationships	Edges	Elements relationships
$U_{p\to e}^k$	$<P_i^k,E_{i,j}^k>$	$U_{p\to p}^k$	$<P_i^k,P_{i+1}^k>$
$U_{s\to e}^k$	$<S_{i,j-1}^k,E_{i,j}^k>$	$U_{s\to s}^k$	$<S_{i,j}^k,S_{i,j+1}^k>$
$U_{e\to s}^k$	$<E_{i,j}^k,S_{i,j}^k>$	$U_{t\to t}^k$	$<t_{i,j}^k,t_{i,j+1}^k>$
$U_{e\to t}^k$	$<E_{i,j}^k,t_{i,j}^k>$	$U_{e\to e}^k$	$<E_{i,j}^k,E_{i,j+1}^k>$
$U_{e\to t}^k$	$<E_{i,j}^k,L_{i,j}^k>$	$U_{l\to l}^k$	$<L_{i,j}^k,L_{i,j+1}^k>$

i, j∈N∪ 0 < i < n∪ 0 < j, j+ 1 < m, where n denotes the number of processes included in a WIP material flow M^k and m denotes the number of event subset ${\mathit{E}}_{\mathit{i}}^{\mathit{k}}$ that happen at the process ${\mathit{P}}_{\mathit{i}}^{\mathit{k}}$ .

Topology modeling of the WIP-MFTN

According to the above mapping rules, a WIP-MFTN model can be established. Owing to the strict logic-sequenced and time-sequenced relationships among different nodes, the established WIP-MFTN G = (V, E) is a regular and directed topology network. In this network, V = (v₁, v₂, v₃, …, v_N) denotes a node set and v_i ∈ V ( i = 1, 2, …, N) and E = (e₁, e₂, e₃, …, e_M) denotes an edge set and e_i ∈ U^k ( i = 1, 2, …, M) denotes the coupling relationships among different nodes. Its adjacency matrix can be formulated as A(G) = (a_ij) $a_{\mathrm{ij}}=\{\begin{array}{cc}\hfill 1\hfill & \hfill 〈v_i,v_j〉\in U^k\hfill \\ \multicolumn{1}{c}{0}& \hfill 〈v_i,v_j〉\notin U^k\hfill \end{array}$ .

Figure 4 shows the topology model of the established WIP-MFTN.

Figure 4.

Topology model for the WIP-MFTN based on the event-driven graphical schema.

Encoding rule for the WIP-MFTN nodes

During the procedure of modeling the above WIP-MFTN, how to effectively manage and identify those schema elements is an important issue. In terms of the characteristics of different schema elements, a simple encoding rule is proposed here.

1. The kth workpiece for different batches production in a given time interval is denoted by WP_ID, and ID∈ [0, 99] consists of two numbers.

2. The machining or inventory process ${\mathit{P}}_{\mathit{i}}^{\mathit{k}}$ for kth workpiece is denoted by OP_ID, including WP_ID+ machining or inventory process ID, and ID∈ [0, 99] consists of two numbers. For example, OP0305 represents the 5th process of 3rd workpiece.

3. The state $S_{i,j}^k$ in the process ${\mathit{P}}_{\mathit{i}}^{\mathit{k}}$ for kth workpiece is denoted by WS_ID, including WP_ID+MP_ID+ workpiece state ID, and ID∈ [0, 99] consists of two numbers. For example, WS080304 represents the 4th state of 8th workpiece in the 3rd process.

4. The events $E_{i,j}^k$ in the process ${\mathit{P}}_{\mathit{i}}^{\mathit{k}}$ for kth workpiece are denoted by OE_ID, including WP_ID+MP_ID+operation event ID, and ID∈ [0, 99] consists of two numbers. For example, OE070109 represents the 9th operation event of 7th workpiece in the 1st process.

5. The triggering time $t_{i,j}^k$ for operation event $E_{i,j}^k$ is denoted by TT_ID, including WP_ID+MP_ID+ triggering time ID, and ID∈ [0, 99] consists of two numbers. For example, TT040307 represents the 7th triggering time of 4th workpiece in the 3rd process.

6. The triggering position $L_{i,j}^k$ for event $E_{i,j}^k$ is denoted by OP_ID, including WP_ID+MP_ID+ triggering position ID, and ID∈ [0, 99] consists of two numbers. For example, OP020807 represents the 7th triggering position of 2nd workpiece in the 8th process.

Performance measures and metrics of the WIP-MFTN

This section mainly focuses on exploring the properties of the established WIP-MFTN by means of providing the corresponding definitions on performance measures and metrics. In the first subsection, much attention has been devoted to the investigation on the structural measurements, such as degree, clustering coefficient, shortest path, and so on. In the second subsection, much attention has been devoted to the investigation on the physical measurements, such as tracking particle size, configuration cost, vulnerability, and so on.

Structural measurements

Definition 1

The degree of node i in the WIP-MFTN is written as k_i, which describes the local tracking importance of the node i. Because WIP-MFTN is a directed graph, the degree of node i has two components: the in-degree $k_i^{\mathrm{in}}$ and the out-degree $k_i^{\mathrm{out}}$ . The in-degree $k_i^{\mathrm{in}}$ describes the influence of other nodes on node i, and the out-degree $k_i^{\mathrm{out}}$ describes the influence of node i on the other nodes

$$\mathrm{ki}=k_i^{\mathrm{in}}+k_i^{\mathrm{out}}$$

(1)

where $k_i^{\mathrm{in}}=\sum _{j=1}^N{a}_{\mathrm{ji}}$ denotes the sum of the directed edges from other nodes to node i; $k_i^{\mathrm{out}}=\sum _{j=1}^N{a}_{\mathrm{ij}}$ denotes the sum of the directed edges from node i to other nodes; and a_ij and a_ji are determined by the influence weight of node i on j, which are extracted from the adjacency matrix A(G).

Definition 2

The clustering coefficient of node i in the WIP-MFTN is written as c_i, which describes the global tracking importance of the node i. Its value is obtained by calculating the ratio between e_i and $k_i(k_i-1)/2$ . The bigger the value of c_i is, the closer the connections among different graphical schema nodes are. By definition, $0\le c_i\le 1$ . Only if the neighborhood of node i is fully connected, the clustering coefficient c_i is equal to 1. On the contrary, if the value is close to zero, it suggests that there are hardly any connections in the neighbors

$$c_i=\frac{2e_i}{k_i(k_i-1)}=\frac{\sum _{j,m\in N}{a}_{\mathrm{ij}}{a}_{\mathrm{jm}}{a}_{\mathrm{mi}}}{k_i(k_i-1)}$$

(2)

where k_i denotes the number of the neighbors of node i; $e_i=\left(\sum _{j,m\in N}{a}_{\mathrm{ij}}{a}_{\mathrm{jm}}{a}_{\mathrm{mi}}\right)/2$ denotes the actual number of edges in the subgraph oriented for node i; and a_ij, a_jm, and a_mi are extracted from the adjacency matrix A(G).

Definition 3

The average clustering coefficient of the WIP-MFTN is written as C, which describes the global tracking importance for all nodes in the WIP-MFTN. The bigger the value of C, the closer the connections among different graphical schema nodes are

$$C=\frac{1}{N}\sum _{i=1}^N{c}_i$$

(3)

where N denotes the node number in the WIP-MFTN.

Definition 4

The shortest path of the WIP-MFTN is written as H, which describes the tracking efficiency of the WIP-MFTN. A higher efficiency can result in more frequent interactions among different graphical schema nodes. Therefore, it plays an important role in exploring the tracking characterizations of the WIP-MFTN

$$H=\frac{100}{N(N-1)}\sum _{i,j\in N,j\ne i}\frac{1}{d_{\mathrm{ij}}}$$

(4)

where d_ij denotes the shortest path between nodes i and j. It should be noted that d_ij can be $\infty$ if there is no directed edge connecting nodes i and j.

Definition 5

The state motif in the WIP-MFTN is written as r_i, which describes a four-node (E_i, S_i, t_i, L_i) directed subgraph within the network as shown in Figure 5. It must be pointed out that the state S_i−1 is not included in this motif r_i for it is treated as the input of this event E_i and the output of the previous event E_i−1. Actually, the motif r_i is the basic unit of the WIP-MFTN, which reveals the subgraph generation principle of the WIP-MFTN owing to the happening of the event E_i.

Figure 5.

State motif consisting of four-node directed connected subgraphs.

The above definitions are mainly used to investigate the structural properties of the WIP-MFTN. On the basis of the above definitions, the metrics for analyzing the physical properties of the WIP-MFTN are provided below.

Physical measurements

Definition 6

The tracking particle size for machining or inventory process p_i is written as α_i. From the literature,^3,28 we can get that the RFID-based detecting spaces are used to monitor the workpiece states. Therefore, the number of workpiece states during a process is corresponding with the number of RFID-based detecting spaces, and this parameter can be used to describe the tracking intensity of the process

$${\alpha }_i=\sum _{j\in J}{{\mu }_i}_j$$

(5)

where µ_ij denotes the jth detecting space during the process p_i. J denotes the number of the detecting spaces in the process p_i.

Definition 7

The configuration cost for the RFID-based detecting space µ_ij in the process p_i is written as g_ij, which describes the expenses of fulfilling the tracking tasks. It must be pointed out that this cost comprises the expenses from purchasing, installing, testing, and maintaining the hardware and software of RFID readers/antennas

$${\text{g}}_{\mathrm{ij}}=\sum {\eta }_l$$

(6)

where η_l denotes the decomposed and smaller expenses during the normal service life for the RFID-based detecting space µ_ij, such as installing.

Definition 8

The extending degree of the WIP-MFTN is written as ν_λ, which describes the network structural changes when adding λ motifs into the WIP material flow. It is defined as the ratio between new added degree and the previous one

$${\nu }_{\lambda }=\frac{\sum _{\lambda }k(P,E,S,T,L)}{\sum _{n}k\left(P\right)},\lambda \ge 1$$

(7)

where $\sum _{n}k\left(P\right)$ denotes the original degree of the initial WIP-MFTN in which there are no detecting space configured and $\sum _{\lambda }k(P,E,S,T,L)$ denotes the new added degree of the WIP-MFTN in which there are λ motifs used to describe the WIP material flow.

Definition 9

The physical vulnerability for the RFID-based detecting space µ_ij is written as δ_ij, which describes the error rate that the valid electronic tags going through or storing in the detecting space have not been well identified. In the area of industrial applications, the error rate of RFID devices has much to do with the environmental conditions. At present, most ubiquitous system engineers mainly rely on their experience, knowledge, and know-how in a trial-and-error manner when developing RFID systems. Here, this parameter is mainly obtained by the testing experiments in the site environment.

Definition 10

>The structural vulnerability for tracking workpiece state s_i in the WIP-MFTN is written as u_i, which describes the failure behaviors of the WIP-MFTN when the workpiece state in the WIP-MFTN has not been well identified. Since the failure in identifying the workpiece state s_i can lead to that the state motif r_i has not been executed, the structural vulnerability u_i can be defined as the degradation rate of network efficiency for removing the ith state motif from the WIP-MFTN. The larger the value of u_i is, the more important the state motif r_i is

$$u_i=\frac{|H-H_i|}{H}$$

(8)

where H denotes the efficiency of the WIP-MFTN and H_i denotes the efficiency after removing the state motif r_i from the WIP-MFTN.

Definition 11

The comprehensive vulnerability for tracking workpiece state s_i is defined as the U_i, which describes the spreading effect in the WIP-MFTN when the valid electronic tags have not been well detected. It is a comprehensive evaluation parameter integrating the physical vulnerability and structural vulnerability

$$U_i=1-(1-{\delta }_i)\times (1-u_i)$$

(9)

A case study: a job-shop-type WIP material flow including four processes

The WIP-MFTN including four processes

This section provides a case to verify the feasibility of the proposed methods. Figure 6 illustrates a simple WIP material flow in a job-shop floor including four processes, which is a real scenario generated from “State Key Laboratory for Manufacturing Systems Engineering” of Xi’an Jiaotong University. In this case, $P_1^1$ denotes the inventory process of raw material; $P_2^1$ denotes the rough machining process; $P_3^1$ denotes the finished machining process, which takes an active role in the WIP production control; $P_4^1$ denotes the inventory process of finished products; and the green dotted lines marked in Figure 6 denote the transportation route of the WIP. Based on the RFID-based configuration solution, there are six detecting spaces selected to track the state of 1st workpiece attached with electronic tag in this case. As shown in Figure 6, the orange dotted boxes denote the corresponding detecting spaces generated by different RFID antennas. For each detecting space, the detailed RFID-based configuration list is shown in Table 3.

Table 3.

The RFID-based configuration solution for tracking the WIP material flow.

ID	Detecting space		RFID
	Type	Location	Reader	Antenna	Supplier
1	Fixed	Storage cells	ALR9900	ALR-9610-BC ×2	Alien
2	Fixed	Storage buffer		ALR-9610-BC ×2	Alien
3	Fixed	CNC lathe	ALR9650	Integrated with readers	Alien
4	Fixed	Buffer of CNC center	ALR9900	ALR-9610-BC ×2	Alien
5	Fixed	CNC center		ALR-9610-BC ×2	Alien
6	Mobile	Vehicle	PRO7527	Integrated with readers	Teklogix

CNC: computer numerical control; RFID: radio frequency identification.

Figure 6.

A real case for a WIP material flow including four processes.

According to the above RFID-based configuration solution, the time and position changes of the WIP states can be identified. Using the event-driven graphical schema, the WIP material flow can be formulated. Figure 7(1) shows the above WIP material flow including four processes, in which corresponding RFID devices are deployed; Figure 7(2) shows its graphical description in terms of using state blocks; Figure 7(3) presents four groups of event sets concerning those four processes; and Figure 7(4) deals with modeling the above four processes by means of using the extended event-driven graphical schema.

Figure 7.

The WIP material flow described by an event-driven graphical schema.

According to the above graphical schema for describing the material flow, 93 schema elements are extracted to establish a WIP-MFTN. Specifically, there are 4 process nodes (MP01/MP02/MP03/MP04), 22 event nodes, 22 triggering time nodes, 22 position nodes, and 23 state nodes. It is noted that initial state (WS0100) is involved in this topology network since it is used as the input state of the WIP. The partial adjacency matrix of the established WIP-MFTN is shown in Table 4. The adjacency values among nodes are determined by the mapping rules among schema elements. In addition, the adjacency values between the same nodes are set to zero.

Table 4.

Partial adjacency matrix of the established WIP-MFTN.

	MP01	WS0100	OE0101	WS0101	TT0101	OP0101	OE0102	WS0102	TT0102	OP0102	OE0103	WS0103	TT0103	OP0103	OE0104	WS0104	TT0104	OP0104
MP01	0	0	1	0	0	0	1	0	0	0	1	0	0	0	1	0	0	0
WS010	0	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
OE0101	0	0	0	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0
WS010	0	0	0	0	0	0	1	1	0	0	0	0	0	0	0	0	0	0
TT0101	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
OP0101	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0
OE0102	0	0	0	0	0	0	0	1	1	1	1	0	0	0	0	0	0	0
WS010	0	0	0	0	0	0	0	0	0	0	1	1	0	0	0	0	0	0
TT0102	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
OP0102	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
OE0103	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	0	0	0
WS010	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	0	0
TT0103	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0
OP0103	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
OE0104	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1
WS010	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
TT0104	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
OP0104	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Based on the adjacency matrix A(G), the topology model of the WIP-MFTN is shown in Figure 8. The MP-XX nodes represent machining processes; the OE-XXXX nodes represent operation events; the WS-XXXX nodes represent the WIP states; the TT-XXXX nodes represent the triggering times; and the OP-XXXX nodes represent the operation positions. It is noted that the established WIP-MFTN is a regular and directed network.

Figure 8.

Topology model for the established WIP-MFTN.

The performance evaluation of the established WIP-MFTN

On the basis of the established WIP-MFTN, the corresponding performance evaluation metrics were calculated and their analysis results were outlined as follows.

The small-world property

As shown in Table 5, the average shortest path (H) for this WIP-MFTN is 2.416 and the clustering coefficient (C) for this WIP-MFTN is 0.098. But by contrast, for the random network with the same size (nodes = 93/edges = 198), the average shortest path is 5.998 and the clustering coefficient is 0.023. The calculated result shows that this established WIP-MFTN has both a small shortest path (like random graphs) and a high clustering coefficient (like regular graphs). Therefore, this WIP-MFTN has the small-world property.

Table 5.

The comparison between the WIP-MFTN and the random network with the same size.

Property	Nodes	Edges	Degree	C	H
Real WIP-MFTN	93	198	2.13	0.098	2.416
Random network	93	198	2.13	0.023	5.998

WIP-MFTN: work-in-process material flows tracking network.

This small-world property of the WIP-MFTN plays an important role in evaluating the tracking performance of material flows. On the one hand, the high clustering coefficient denotes the close connections among different graphical schema nodes. On the other hand, the small shortest path denotes the efficient connections among different graphical schema nodes. Therefore, the small-world property reveals the tracking efficiency of material flows. According to the above analysis, the established WIP-MFTN has an efficient tracking performance of material flows.

Scale-free degree distribution

The degree distribution of a scale-free network follows a power law for large k, $p{\left(k\right)}_{}A{k}^{-r}$ . As shown in Figure 9, the in-degree, out-degree, and total degree curves for the WIP-MFTN have not displayed a power law distribution. Therefore, the established WIP-MFTN has not a scale-free property. Another finding is that these distribution curves are not consistent with each other. To be specific, the nodes whose in-degree is 2 play an active role in the in-degree distribution curve; the nodes whose out-degree is 1 play an active role in the out-degree distribution curve; and the nodes whose total degree is 3 play an active role in the total degree distribution curve. The reason is that the triggering time nodes and position nodes have the similar structural characteristics, and they account for around 47% of the node number within the WIP-MFTN. Their in-degree, out-degree, and total degree are 2, 1, and 3, respectively. The above finding demonstrates that the established WIP-MFTN has a stable topology, which can lead to a strong tracking performance of material flows.

Figure 9.

In/out/total degree distribution curves for the WIP-MFTN.

In general, the above structural properties have a lot to do with the mapping rules between the event-driven graphical schema and the WIP-MFTN. However, these analyzing results about structural properties will provide a basis for investigating its physical properties.

Configuration complexity

In this case, there are two machining processes and two inventory processes considered. Owing to their different roles in the whole job-shop-type production and user’s monitoring requirements, the tracking particle size for each process is different from others. At the inventory process of raw material and finished products, two detecting spaces are deployed around the storage cell and buffer, respectively. At the rough machining process, one detecting space is deployed around a computer numerical control (CNC) lathe. At the finished machining, two detecting spaces are deployed around the buffer and machining area of a CNC center. According to the above particle size for tracking WIP material flow, the RFID devices made by Alien and Teklogix are deployed to fulfill the configuration tasks. And their costs for purchasing, installing, testing, and keeping the corresponding readers/antennas are listed in Table 6. In terms of the list, the total RFID-based configuration cost for establishing this WIP-MFTN is $11,940.

Table 6.

The cost list for implementing RFID-based configuration solution.

Supplier	Reader			Antenna
	Type	Price ($)	Number	Type	Price ($)	Number
Alien	ALR9900	2600	2	ALR-9610-BC	240	8
Alien	ALR9650	1500	1	Integrated with readers
Teklogix	PRO7527	3320	1	Integrated with readers

The price mentioned here includes the expenses for purchase, installation, testing and keeping the corresponding RFID hardware and software.

Therefore, the determination of tracking particle size for one process is largely influenced by the production and user’s monitoring requirements. Usually, the simplest configuration case is to detect the “move-in/move-out” states of workpieces during a process, while the most complicated configuration case is to detect all the states of the workpieces during a process. Obviously, the smaller particle size can lead to the more RFID-based configuration cost. In this case, the RFID-based configuration solution is the trade-off between tracking requirements and cost.

Network-extended property

In the practical production, it is essential to dynamically add or delete the detecting spaces in terms of the real-time monitoring requirements. Based on the calculating result of the structural metrics, this subsection pays more attention on the network-extended property of the WIP-MFTN for adding new detecting spaces. As is well known, the detecting spaces are used to monitor the workpiece states, and the state changes of workpieces happen by the actions/operations from operators. In order to facilitate our study, here, the motif is the basic unit for analyzing the extended property of the WIP-MFTN.

On the one hand, we have examined the extending degree for adding λ motifs into the WIP-MFTN. The detailed extending degree v_λ for this WIP-MFTN is formulated as the ratio of the new network degree to the original network degree. It is noted that the initial WIP-MFTN includes five element nodes, which are MP01, MP02, MP03, MP04, and WS0100 and its original degree is 3

where l(x_i, x_j) denotes the coupling relationship between element x_i and element x_j. The calculating formula shows that the network structure of WIP-MFTN has significantly increased when adding λ motifs into the original network.

$$\begin{array}{l}{\upsilon }_{\lambda }=\frac{{\displaystyle \sum _{\lambda }k(P,E,S,T,L)}}{{\displaystyle \sum _{n}k(P)}}\\ =\frac{l(p_1,e_1)+l(s_0,e_1)+l(s_0,s_1)+\lambda \times (l(e_i,s_i)+l(e_i,t_i)+l(e_i,l_i))+(\lambda -1)\times (l(p_i,e_j)+l(e_i,e_j)+l(s_i,e_j)+l(s_i,s_j)+l(t_i,t_j)+l(l_i,l_j))}{n-1}\\ =\frac{3+3\lambda +(\lambda -1)\times 6}{4-1}\\ =3\lambda -1(\lambda \ge 1)\end{array}$$

On the other hand, we examined the growth model, which is defined as the changes of the node number, total degree, average degree, and shortest path when adding a new motif into the WIP-MFTN continuously. As shown in Figure 10, it can be concluded that the node and degree of the WIP-MFTN are in an approximately liner increase with the adding of new motifs. Figure 11 reveals that the average degree of the WIP-MFTN tends to be stable with the addition of new motifs. On the contrary, the shortest path of the WIP-MFTN has a continual growth.

Figure 10.

The node and degree changes of the WIP-MFTN with the new motifs added continuously.

Figure 11.

The average degree and shortest path changes of WIP-MFTN with the new motifs added continuously.

To sum up, the above analysis results reveal the generating principle of a WIP-MFTN and further confirm that the established WIP-MFTN is a regular network.

System vulnerability

According to the above analysis about the extending degree and growth model of the WIP-MFTN, we can conclude that the established WIP-MFTN has a unique network structure. This subsection mainly focuses on discussing the WIP-MFTN vulnerability. Here, the physical vulnerability is considered as the undetected probability when the workpieces attached with valid tags passing through or storing in the valid detecting spaces. Through adopting the statistical analysis technique, the error rates of RFID-based detecting spaces in this case are tested. The testing result is shown in Table 7.

Table 7.

The testing result for RFID readers and antennas detecting valid tags.

ID	Location	Readers	Antennas	Tag type	Error rate (%)
1	Storage cells	ALR9900	ALR-9610-BC ×2	ALN-9654 “G”	3
2	Storage buffer		ALR-9610-BC ×2	ALN-9654 “G”	7
3	CNC lathe	ALR9650	Integrated with reader	ALN-9654 “G”	9
4	Buffer of CNC center	ALR9900	ALR-9610-BC ×2	ALN-9654 “G”	5
5	CNC center		ALR-9610-BC ×2	ALN-9654 “G”	6
6	Vehicle	PRO7527	Integrated with reader	ALN-9654 “G”	10

CNC: computer numerical control.

The structural vulnerability for tracking the WIP material flow is considered as the degradation rate of network efficiency for removing the motif from the WIP-MFTN. Its comprehensive vulnerability is considered as the combined evaluation parameter through integrating the physical vulnerability and structural vulnerability. The above vulnerability parameters for different motifs in the WIP-MFTN are illustrated in Figure 12 in which the structural and comprehensive vulnerabilities have shown bow-shaped curves.

Figure 12.

The vulnerability diagram for different motifs in the WIP-MFTN.

From the vulnerability diagram, it is concluded that the network structural properties play active roles in analyzing the comprehensive vulnerability of the WIP-MFTN. As for the structural and comprehensive vulnerabilities, much attention should be paid to the motifs near the middle position. It is noted that these results are well in accordance with the fact. The goal of establishing the WIP-MFTN is to obtain a complete data flow for tracking the material flow in which the workpieces state information is collected by different detecting spaces. Once the RFID devices deployed near the middle position in the material flow do not work, their tracking data will be missed and the corresponding data flow will be interrupted. Therefore, much more attention should be paid to these detecting spaces. Another finding is that the physical vulnerability for detecting spaces has a relatively small impact on the comprehensive vulnerability because RFID technology has developed very rapidly in the past few years and RFID product reliability has been greatly improved. To sum up, all these analysis results will provide a base for raising the WIP-MFTN robustness effectively.

Discussion

The aim of this research is to propose a novel method that can be used to evaluate the RFID-based tracking performance for job-shop-type material flows. The example given in the case study suggests the feasibility and effectiveness of the proposed method. The configuration complexity shows that the RFID-based configuration solution for a WIP material flow is a trade-off between the configuration cost and tracking particle size. On one hand, the smaller tracking particle size will raise higher configuration cost and obtain more accurate tracking data. On the other hand, more RFID detecting spaces will lead to a more complex and unstable structure of the WIP-MFTN. All these issues are described and investigated quantitatively in this article.

At present, there are almost no systemic and reasonable methods in theory for analyzing the RFID-based configuration solution. It is expected that the proposed method will provide practitioners with a holistic perspective of implementing RFID systems. Through the mapping between the event-driven graphical schema and the topology model for WIP material flows, the authors used the CNT to analyze the RFID-based monitoring performance. The advantage of this method is that it is easy to implement and obtain the configuration performance from both macro and micro aspects. From the macro perspective, the statistical properties of the WIP-MFTN (such as the degree distribution, network efficiency, clustering coefficient, and state motif) can be obtained, while from the micro perspective, the physical properties of WIP-MFTN (such as the configuration cost, tracking particle size, growth rate, and vulnerability) can be obtained. The above results will provide a guide for optimizing the RFID-based tracking solution.

However, much attention of this article is paid on the modeling and analysis of a single WIP tracking network. It is expected that much more convincing results can be explored by means of comparing and analyzing the WIP-MFTNs with different tracking particle size for the same WIP material flows. Obviously, this is our research direction in future work.

Concluding remarks

As a powerful communication means, RFID technology has become an important driver in the production and logistics activities of today’s information-based manufacturing industry. Taking RFID-based configuration solution for monitoring job-shop-type material flow as the research object, this article established a WIP-MFTN through the mapping between event-driven graphical schema and topology model. Furthermore, the structural and physical properties of the WIP-MFTN were investigated. The performance was evaluated and the reasonable suggestions for improving the RFID-based configuration solution were given. Based on the above investigation and case study presented in this article, the following conclusions can be made.

• The RFID-based tracking procedure of the WIP material flows in a job-shop floor can be described and formulated by the event-driven graphical schema-based operation model. The operations/actions, triggering times, positions, and states of WIP material flows are included in this schema.

• The mapping rules between the event-driven graphical schema and the network topology model were investigated. The schema elements were mapped into the network nodes, and the relationships among schema elements were mapped into the network edges. On this basis, an RFID-based tracking network of job-shop-type WIP material flows was established.

• A case study for a job-shop-type WIP material flow including four processes shows that the established WIP-MFTN has a small shortest path and a high clustering coefficient. The different schema nodes have the efficient links in this WIP-MFTN.

• The research shows that the RFID-based configuration solution is the trade-off between tracking particle size and cost. The more RFID detecting spaces will lead to the more complex and unstable structure of the WIP-MFTN. The analysis for its network-extended property and vulnerability can prove this point.

In the development of this article, two research directions should be paid much more attention. One is to compare and analyze the WIP-MFTNs with different tracking particle size for the same WIP material flow. Further research is to investigate all the material flows in the entire job-shop floor as this work mainly focused on the performance evaluation for a single material flow. In the modern job-shop-type floor, the manufacturing tasks are usually multi-varieties and small batch. And this mixed production mode has resulted in more complex material flows. Therefore, how to investigate the tracking performance from the perspective of the whole job-shop-type material flows is the next research direction.