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At present, radio frequency identification (RFID) technology has been widely applied in manufacturing industry. How to use collected RFID data to effectively evaluate process logistics state is an urgent problem. Firstly, process logistics state model based on extended disjunctive graph was established. Secondly, configuration scheme of RFID readers/tags and production elements was proposed according to the time and space characteristics of process logistics. Then, process logistics state matrices including jobs, warehouses, buffers, machine tools, and vehicles were constructed. The real-time process logistics states can be deduced by operation of above data matrices. Finally, a case study was proposed to verify the feasibility of the proposed methods.

With the fierce market competition and customer demands’ diversification, modern manufacturing enterprises have to change from a single variety of mass production mode to multivarieties and small-batch personalized customization mode [

In recent years, Internet of Things (IoT) technology and the concept of big data have brought about greater demand and higher requirements for information sensing technology. As a noncontact data acquisition and communication technology, radio frequency identification (RFID) has attracted wide attention from academia and industry. RFID technology has many advantages, such as long-distance identification, large storage capacity, fast reading speed, and high reliability. At present, a lot of advanced manufacturing enterprises have equipped their workshops with RFID devices to collect production logistics data, so as to reflect the real-time operation of the workshop, and provide data support for the upper evaluation and decision-making system.

From the perspective of data matrices, a state evaluation method was proposed for process logistics. There are two highlights in this article. Firstly, process logistics states model based on extended disjunctive graph was proposed. Secondly, data matrices of process logistics states were constructed, and the coupling relationship between process logistics and production elements was discussed.

The rest of this article is organized as follows. Section

At present, RFID technology has been widely used in warehouse management, supply chain, production logistics, and other fields [

Disjunctive graph proposed by Ron and Sussman in 1964 [^{P}=_{ij} denotes the process nodes of the_{th} process of job_{i} (_{i},_{i} is the process number of job_{i}).^{P} =_{ij}, _{i}. According to the process route planning of the job_{i}, the previous process_{ij} is directed to the subsequent process _{ij},_{uv}) denotes the disjunctive arcs between two processes of different jobs machined on the same processing unit. According to the production scheduling of different jobs, the previous process_{ij} is directed to the subsequent process_{uv}, namely,

A disjunctive graph including 3 jobs and 3 processing units.

As shown in Figure _{11},_{23}, and _{21},_{12}, and _{31},_{22}, and

An extended process logistics state.

In Figure _{th} process of_{th} job machined in_{th} processing unit_{k} (_{U});_{U} is the number of processing units; _{th} job enters in-buffer of processing unit_{k}; _{th} job is machined on processing unit_{k}; _{th} job enters out-buffer of processing unit_{k}. Then, it was transported to next processing unit or finished parts warehouse. Consequently, there are three states in processing unit for workpieces “In-buffer, Machined and Out-buffer”. In combination with disjunctive graph and extended process logistics state, the process logistics model can be formulated as

In order to effectively identify the different states of process logistics, it is essential to collect the underlying process logistics data in real time and effectively. After decades of development, RFID technology has been widely used in logistics tracking. RFID devices consist of readers and electronic tags. There is no mechanical contact between the electronic tags and the readers. When the tags are within the range of the readers’ electromagnetic induction signal, they can sense and read the corresponding tags information. RFID readers usually contain fixed, mobile, and vehicle-mounted [

From the above process logistics model, it can be known that state information of process logistics includes time and space attributes. First of all, fixed RFID readers are installed in the entrance guard system of the raw material warehouse and finished parts warehouse, respectively. Then, in-buffer area, machine tool and out-buffer area in processing units need to deploy fixed readers based on different requirements of tracking granularity. At the same time, vehicle-mounted RFID readers are deployed on the vehicle used for transporting jobs. Then, the configuration scheme of the RFID readers in the workshop can be formulated as_{MS} and_{FS} denote the RFID readers installed on the entrance guard system of the raw material warehouse MS and the finished parts warehouse FS, respectively. _{k} of the processing unit_{k}, the machine tool_{k}, and the transportation vehicle_{k}.

While one-to-one strategy is used to binding RFID tags and jobs or trays for holding jobs, the configuration scheme of the tags and the job can be formulated as_{i} denotes the_{th} job or tray for holding_{th} jobs;_{i} denotes the RFID tags attached to_{th} job.

When the tags on jobs are detected by the readers of entrance guard system or processing units, the state of the jobs at the current time is recorded in the form of RFID raw data. The raw data includes the reader’s ID, detected tag’s ID, and detected time. The data structure can be formulated as

Based on the one-to-one binding strategy for RFID readers/tags and production elements, data structure

It must be noted that the physical positions of each reader in (

The process logistics state matrices are composed of four two-dimensional matrices reflecting the position of the job in the workshop and the corresponding triggering time. It can be used to collect the relevant data provided by the logistics state_{W}(

_{i} is taken out of warehouse or its finished part is putting in warehouse, its attached RFID tag_{i} can be detected by the fixed reader

_{i} reaches the processing unit_{k}, its attached RFID tag_{i} can be detected by the fixed reader _{st} job reaches the buffer of_{st} processing unit.

_{i} is fixed on the processing unit_{k}, its start machining operation can be detected by sensors installed in processing unit. The trigger time can be recorded in the_{st} job on the

_{i} is taken out of the processing unit_{k} and transported to next processing unit or to the finished part warehouse, the attached RFID tag_{i} can be detected by the vehicle-mounted reader_{Ck}. The trigger time can be recorded into the_{st} processing unit.

When starting to machine new job, the four process logistics state matrices must be cleared first. Then, position and trigger time of the corresponding job can be recorded in real time into the corresponding logistics state matrices when the attached RFID tags are detected by the readers installed in entrance guard system, processing unit and vehicles.

On the one hand, the trigger time of each job in a certain state can be directly extracted from the state matrices. On the other hand, production information such as out/in warehouse information, job-processing state, processing progress, operation time, machine tool loading, job flow density, etc. can be mined by analyzing the element values of the four process logistics state matrices and their relationships.

To normalize the term description, define the relevant symbols:

_{th} column of matrix A construct a one-dimensional column vector;

_{th} row of matrix A construct a one-dimensional row vector;

_{th} column in matrix A and all nonnegative element values of_{th} row, respectively;

The number of nonzero elements in the first column and the second column of the W_S(

When there is no zero element in the first column, that is, N_BL (T) =

When there is no zero element in the whole matrix, the maximum element value minus the minimum element value denotes the total time spent on finishing the jobs, which is formulated as T_TO:

Extract the element values of_{th} row in W_B(

This matrix records the state information in the processing unit of raw material of the job_{i} from transporting out of raw material warehouse (the element of _{th} row in W_S(_{th} row in W_S(

_{i} is currently at the moment. The line number 1 is for waiting for processing, the line number 2 is for processing, and the line number 3 is for the current process to be transported to another processing unit or to the finished part warehouse.

_{i} at the current moment, and is described as N_FPi(_{i} minus the number of columns in the nonzero column denotes the number of remaining unprocessed process number at the current time, described as N_UPi(

_{st} job in_{st} processing unit.

_{st} job in_{st} processing unit.

_{th} row of matrix W_B(_{g} to transport to next processing unit_{h} can be calculated by (

_{i}, that is, the transportation time WCT(

_{th} (_{U}) column of W_M_T(_{k} in processing unit_{k} up to the current time, described as L_Mk(

_{th} processing unit is_{k}, the machining cost per processing unit can be described by the vector CS_U, namely,_{1} denotes the machining cost of_{st} job_{1}.

Construct a zero matrix D_U(_{th} row and_{st} column element DU(_{k} and_{l} at the current time. Therefore, the value of “DU (_{k} and_{l}. The greater the density is, the closer the connection between the processing unit_{k} and_{l} is. The magnitude of job flow density between any two processing units can be calculated by (_{th} rows and_{st} column or the element value DU'(l,_{th} rows and_{th} columns denotes the job flow density between processing units_{k} and_{1}.

Taking the production of an automobile workshop as an example, the above state evaluation method for process logistics was verified.

According to the results of production planning and scheduling, there are 10 types of parts waiting for processing. And process number of each job is N_{1}=7, N_{2}=8, N_{3}=8, N_{4}=6, N_{5}=7, N_{6}=7, N_{7}=6, N_{8}=8, N_{9}=7, and N_{10}=7, and there are 8 processing units in the workshop, that is _{1}, Rk_{2}, and Rk_{3}, respectively, denote the reader ID of buffer, machine tool, and vehicle on the_{th} processing unit (_{i} denotes the tag ID attached to_{th} job or the tray loading_{th} job. According to one-to-one binding strategy between RFID readers/tags and production elements, the configuration scheme is shown in Figure

RFID configuration scheme.

According to the process route planning and production scheduling of the workshop, the job-warehouse matrix W_S(

At

According to the mapping relationship between the trigger time of the RFID readers and the process logistics states, the above four state matrices are assigned in real time. Up to

In the matrix W1_U(25), max(W1_U(25))=W1_U(25)(1, 6)=25, that is, the maximum value is in 1 row and 6 columns. It can be seen that_{th} processing unit. According to (

Job processing state and processing progress.

Jobs | J_{1} | J_{2} | J_{3} | J_{4} | J_{5} |

| |||||

Processing units | U_{6} | U_{5} | U_{7} | U_{3} | U_{8} |

| |||||

State | Waiting for processing | Processed | Transported | Transported | Waiting for processing |

| |||||

Progress | +5 | +7 | +5 | +4 | +4 |

-2 | -1 | -3 | -2 | -3 | |

| |||||

Jobs | J_{6} | J_{7} | J_{8} | J_{9} | J_{10} |

| |||||

Processing units | U_{4} | U_{2} | U_{7} | U_{7} | U_{5} |

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State | Waiting for processing | Transported | Processed | Waiting for processing | Waiting for processing |

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Progress | +4 | +2 | +4 | +4 | +3 |

-3 | -4 | -4 | -3 | -4 |

Note: “+” denotes the number of processes finished, and “-” denotes the number of remaining unprocessed processes.

The negative element in matrix W_B_T (25) denotes that the job has not been machined in the corresponding processing unit; the zero element in matrix W_M_T (25) denotes that the job has not been processed at the corresponding processing unit, and the negative element denotes that the job has not been machined in the corresponding processing unit at this time; the transportation time of job can be calculated by (

Transportation time of jobs.

J_{1} | J_{2} | J_{3} | J_{4} | J_{5} | J_{6} | J_{7} | J_{8} | J_{9} | J_{10} |
---|---|---|---|---|---|---|---|---|---|

MS → U_{7} | MS → U_{2} | MS → U_{1} | MS → U_{8} | MS → U_{6} | MS → U_{5} | MS → U_{4} | MS → U_{3} | MS → U_{1} | MS → U_{3} |

1 | 1 | 1 | 1 | 2 | 1 | 2 | 2 | 1 | 2 |

| |||||||||

U_{7}→ U_{3} | U_{2}→ U_{4} | U_{1}→ U_{4} | U_{8}→ U_{7} | U_{6}→ U_{7} | U_{5}→ U_{7} | U_{4}→ U_{2} | U_{3}→ U_{4} | U_{1}→ U_{2} | U_{3}→ U_{6} |

1 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 2 | 1 |

| |||||||||

U_{3}→ U_{5} | U_{4}→ U_{6} | U_{4}→ U_{5} | U_{7}→ U_{1} | U_{7}→ U_{5} | U_{7}→ U_{2} | — | U_{4}→ U_{5} | U_{2}→ U_{8} | U_{6}→ U_{8} |

1 | 1 | 1 | 3 | 2 | 2 | 2 | 2 | 2 | |

| |||||||||

U_{5}→ U_{2} | U_{6}→ U_{1} | U_{5}→ U_{2} | U_{1}→ U_{3} | U_{5}→ U_{2} | U_{2}→ U_{6} | — | U_{5}→ U_{1} | U_{8}→ U_{5} | U_{8}→ U_{5} |

1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | |

| |||||||||

U_{2}→ U_{1} | U_{1}→ U_{7} | U_{2}→ U_{7} | — | U_{2}→ U_{8} | U_{6}→ U_{4} | — | U_{1}→ U_{7} | U_{5}→ U_{7} | — |

2 | 1 | 2 | 1 | 1 | 1 | 1 | |||

| |||||||||

U_{1}→ U_{6} | U_{7}→ U_{8} | — | — | — | — | — | — | — | — |

1 | 1 | ||||||||

| |||||||||

— | U_{8}→ U_{3} | — | — | — | — | — | — | — | — |

1 |

Accumulative load table for machine tool.

Machine tools | M_{1} | M_{2} | M_{3} | M_{4} | M_{5} | M_{6} | M_{7} | M_{8} |

| ||||||||

Accumulative load | 11 | 12 | 12 | 7 | 13 | 9 | 9 | 7 |

_{1}=9, CSU_{2}=6, CSU_{3}=12, CSU_{4}=7, CSU_{5}=9, CSU_{6}=10, CSU_{7}=8, and CSU_{8}=12. And the machining cost of the various jobs up to the present moment is calculated by (

Machining cost of the jobs.

Jobs | J_{1} | J_{2} | J_{3} | J_{4} | J_{5} | J_{6} | J_{7} | J_{8} | J_{9} | J_{10} |

| ||||||||||

Machining cost | 97 | 64 | 62 | 101 | 67 | 69 | 40 | 67 | 72 | 88 |

In matrix D_U'(25), the maximum value is “3”, while D_U' (25) (1, 7) =D_U'(25) (7, 1) =3, D_U' (25) (5, 7) =D_U'(25) (25) =3. That is, the flow density between the processing unit U_{1} and U_{7} is 3; the flow density between the processing unit U_{5} and U_{7} is 3. It can be seen that up to the present moment, there is a close connection between the processing unit U_{1} and U_{7}, and between U_{5} and U_{7}.

In view of the advantages of RFID technology in automatic information collection, one-to-one strategy was adopted to bind the RFID readers with the production elements of the workshop and bind the tags with the jobs. Four logistics state matrices including jobs, warehouses, buffers, machine tools, and vehicles were constructed. According to the mapping relationship between trigger time and trigger positions of RFID readers, the logistics state matrices were assigned in real time. Through the analysis of element value of data matrices, the basic process logistics state, such as number of raw materials and the number of finished parts, can be calculated. Through the analysis of operation between different data matrices, real-time process logistics state, such as cumulative processing load of machine tools, machining costs, job flow density between processing units, etc., can be deduced. The above results of process logistics state can provide support for optimizing and improving the resource allocation and operation efficiency of workshop.

The data used to support the findings of this study are included within the article.

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

The research work presented in this article is supported by the National Natural Science Foundation of China (nos. 51605041 and 51705030), Natural Science Basic Research Plan in Shaanxi Province of China (no. 2018JQ5059), and the Fundamental Research Funds for the Central Universities, China (no. 300102258112).