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Because of the advantages of the complex network in describing the interaction between nodes, the complex network theory is introduced into the production process of the modern workshop in this paper. According to the characteristics of the workshop, based on extracted key nodes, the complex network model of the workshop is constructed to realize the mathematical description of the production process of the workshop. Aiming at the multidisturbance factors in the production process of the workshop, the key disturbance factors are predicted based on the Markov method, and the propagation dynamics model close to the actual production of the workshop is established. Finally, the bottleneck prediction model of the workshop under the disturbance environment is established. The simulation results show that the proposed prediction model is in good agreement with the actual data, and the coincidence rate is as high as 93.7%.

Production workshop is the basic unit of manufacturing enterprises, which consists of equipment, personnel, departments, and various workpieces. In the production workshop, the workpiece is processed to the final product according to the established process route, and the process is accompanied by many uncertain factors. These disturbance factors lead to the generation, transfer, and disappearance of the bottleneck in the workshop, and the bottleneck unit restricts the effective output of the production system. Therefore, it is necessary to study the dynamic prediction of the bottleneck in the workshop under the disturbance environment for improving the management of the production system.

In the manufacturing process, how to establish a reasonable and accurate mathematical model to identify and predict bottlenecks can provide a theoretical basis for enterprises to make production plans and management. Wu et al. [

In recent years, more and more researchers have applied the complex network theory to the manufacturing industry in order to make new breakthroughs in complex product development, supply chain optimization, and enterprise production management and optimization. Ma et al. [

Nowadays, artificial intelligent algorithms had been applied in the construction for different applications. Kea et al. [

The definition and classification of bottlenecks are different according to different research objects, different methods, and different observation angles. Wang et al. [

The existing bottleneck research methods are limited to a specific parameter index, such as equipment, station, personnel, and materials, which lack systematic thinking. The bottleneck identification method in this paper is based on the complex network theory, the Markov model is simple, and it can be used to describe complex random phenomena. Markov process is used to analyze the disturbance factors, and the state transition probability and steady distribution of the Markov chain are obtained; it provides a way for the quantitative analysis of the disturbance factors in the production workshop. From the perspective of the complex network, all production factors are considered to identify and predict the bottleneck. And then, the accuracy and effectiveness of the proposed method are verified by the actual data of the workshop and simulation software.

In this paper, Markov model is used to evaluate and predict the intensity of disturbance factors. The method has a good effect on process state prediction, and it can be used for production site state prediction. However, it is not suitable for medium- and long-term system prediction. From the perspective of the production process, the disturbance factors of the workshop are analyzed, the disturbance factor intensity matrix is constructed, the relationship between the matrix and disturbance factor intensity is simulated, and the Markov chain prediction model is established to predict the change of disturbance factor intensity, so as to determine the key disturbance factors and their occurrence probability. The flowchart indicating the bottleneck prediction of the production workshop is shown in Figure

The flowchart indicating the bottleneck prediction of the production workshop.

In each link of the workshop, there will be a variety of disturbance factors, such as demand change, emergency order insertion, equipment failure, machining accuracy, and personnel absence. At the same time, there will be a lot of inaccurate information, such as material arrival time, manual clamping time, and auxiliary processing time. The existence of these disturbance factors will make the workshop conditions change dynamically and seriously affect the normal production activities.

The disturbance in the workshop mainly refers to the factors that affect the effective output of production units such as equipment, personnel, process, and department. Disturbance factors can be divided into the following four categories: internal production environment, external environment, monitoring technology, and human factors. Disturbance factors caused by the internal production environment: although the production in the manufacturing workshop has been oriented to standardization and precision, the microdifferences and randomness in time cannot be eliminated. These uncertainties are mostly related to the internal production environment, such as equipment random failure and equipment accuracy error. Disturbance factors caused by the external environment: they are materials not transported in place according to regulations, order changes, etc. The disturbance factors caused by the external environment will lead to the cancellation of existing production tasks or the change of production schedule, which is a kind of disturbance factors with great influence on the determination of results. The disturbance factors caused by monitoring technology include detection method, detection time, and detection environment. The influence of such disturbance factors is relatively weak. Disturbance factors caused by human factors mainly included workers absence, workers’ proficiency, and workers’ mood. These disturbance factors affect the quality and production schedule of the product directly.

The intensity of the disturbance factor is a quantitative description of the disturbance factor. The expression of disturbance factor intensity is different in different fields. The intensity of the disturbance factor reflects an inherent dynamic characteristic of the disturbance factor, which is used to describe the direct influence of the disturbance factor on the workshop network. The influence of different disturbance factors on the workshop is different; Chin et al. [

The bottleneck influencing factor matrix.

Disturbance factors | Disturbance intensity level | |||||
---|---|---|---|---|---|---|

Level 1 | Level 2 | Level 3 | Level 4 | Level 5 | ||

0-0.1 | 0.1–0.3 | 0.3–0.5 | 0.5–0.8 | 0.8–1.0 | ||

External disturbance factors | Order change | |||||

Material supply | ||||||

Production plan | ||||||

Policy changes | ||||||

Internal disturbance factors | Equipment failure | |||||

Route change | ||||||

Machining accuracy | ||||||

Dispatcher change | ||||||

Human factors | Personnel absence | |||||

Proficiency | ||||||

Monitoring factors | Monitoring method | |||||

Monitoring technology | ||||||

Monitoring environment |

There are various uncertain disturbance factors in the process of production and processing. The occurrence of disturbance factors may lead to the generation, transfer, increase, or decrease of bottlenecks in the production workshop. In this paper, the intensity of the disturbance factor is defined to express the comprehensive action degree of various disturbance factors in the process of production and processing. The intensity of the disturbance factor is expressed as follows:

Because the intensity of disturbance factors in the production workshop is a comprehensive quantitative index of various disturbance factors and the intensity of disturbance factors is a fuzzy quantity, the intensity of disturbance factors in the production workshop can be measured by the fuzzy evaluation method at all levels, analytic hierarchy process, expert scoring, and other comprehensive methods. The specific steps are as follows:

Step 1: the set of disturbance factors in the workshop is established.

Step 2: the workshop influence evaluation set is established. By using the expert scoring method, the manufacturing workshop bottleneck research experts score the intensity of disturbance factors in the production workshop and grade different disturbance factors. Each disturbance factor is divided into five levels according to the influence level, and the level from low to high represents the influence degree. It is assumed that the evaluation set is

Step 3: the evaluation of the disturbance factor to disturbance factor intensity is obtained by expert scoring, fuzzy function

The obtained values are imported into the upper layer by the analytic hierarchy process and then evaluated. Finally, the overall disturbance factor intensity is calculated as

The bottleneck of the production workshop is produced in the production activities, and it is the result of the comprehensive effect of various disturbance factors in the production activities. The intensity of disturbance factors caused by human disturbance factors is divided into states. Markov model is used to predict the divided states. Finally, the probability of each state is obtained to predict the key disturbance factors.

In this paper, Markov chain is used to model the disturbance intensity caused by disturbance factors in the workshop.

State of disturbance factors.

Frequency of disturbance factors | State |
---|---|

The initial probability of the state set is determined by fitting the curve with the historical data of disturbance factors in the workshop. The probability of the initial state is expressed by vector

In the Markov process,

According to the Markov theory, the probability of the state of disturbance intensity in the workshop can be calculated as follows:

In a workshop,

The workpiece sequence is represented by

Machining time series of the workpiece is represented by

Each resource node (such as workshop department, equipment personnel, and tools) involved in the production process of a production workshop is regarded as a network node. The possible process routes and logistics paths between nodes are regarded as the connecting edges in the network. The direction of the connecting edges between nodes is determined by the priority relationship of processes; as the weight on the connected edge of the network, the device load is used to measure the closeness of the relationship between nodes. Therefore, each production process constitutes a complex multitask weighted directed network model. An example of a workshop network model is shown in Figure

An example of a workshop production network model.

Figure

Considering the interaction between nodes and the dynamic characteristics of nodes in the whole network, a coupled map lattice node state prediction model with the network scale of

In this paper, from the perspective of the complex system, considering the network characteristics such as node degree value and clustering coefficient, the bottleneck judgment standard is given. Finally, according to the judgment standard, the bottleneck classification is implemented, such as primary and secondary bottlenecks and nonbottlenecks [

Therefore, the bottleneck identification formula in the network is defined as follows:

In order to analyze the fluctuation and influence of disturbance factors on the production process of the workshop, the load change rate

In the experiment, the actual production workshop data of an automobile manufacturing enterprise [

Disturbance factors and their weights in the workshop.

Symbol | ||||||

Disturbance factors | External disturbance | Order change | Material supply | Demand change | Policy change | Environment change |

Weight | 0.5637 | 0.1947 | 0.4628 | 0.1889 | 0.0725 | 0,.0733 |

Symbol | ||||||

Disturbance factors | Internal disturbance | Equipment failure | Process change | Machining accuracy | Workshop scheduling | |

Weight | 0.2631 | 0.2751 | 0.0643 | 0.5502 | 0.1236 | |

Symbol | ||||||

Disturbance factors | Human factor | Personnel absence | Skill level | Quality defects | ||

Weight | 0.1202 | 0.0927 | 0.5201 | 0.3896 | ||

Symbol | ||||||

Disturbance factors | Monitoring | Monitoring method | Monitoring technology | Monitoring environment | ||

Weight | 0.0565 | 0.6386 | 0.1037 | 0.2579 |

After classifying and subdividing the disturbance factors and calculating the weight, the occurrence frequency is fitted according to the historical data of the disturbance factors in the production workshop. The state probability transition matrix is determined according to Table

The production process parameters of the workshop are shown in Table

The production process parameters of the workshop.

0.2652 | 1 | ||

0.3275 | 0 | ||

0.1861 | 1 | ||

0.3785 | 1 | ||

0.3952 | 0 | ||

0.3562 | 1 | ||

0.3283 | 0 | ||

0.3183 | 1 | ||

0.5902 | 3 | ||

0.3392 | 0 | ||

0.3287 | 1 | ||

0.3916 | 1 | ||

0.3285 | 1 | ||

0.3852 | 0 | ||

0.3907 | 1 | ||

0.5589 | 2 | ||

03205 | 0 | ||

0.5960 | 3 | ||

0.2298 | 2 | ||

0.3805 | 5 | ||

0.3607 | 3 | ||

0.2385 | 1 | ||

0.3762 | 2 |

According to Table

According to the expert scoring method, the initial state probabilities of ten disturbance factors to the disturbance factor intensity are determined as follows:

In this way, the prediction probability of each node state

It can be seen that, in the production process, in each state of 23 production process indicators, the key disturbance factors are equipment failure, material supply, order change, and so on, and the influence of the occurrence probability of these disturbance factors accounted for 86.2%.

Aiming at an auto parts production workshop, the data of the production process are collected in hours by sensors on the production line. According to the working characteristics, resource flow, process constraints, information flow, and personnel allocation of the production workshop, the data are collected, and the key nodes are extracted, and the complex network model is constructed to realize the network mathematical description of the production process of the production workshop. The specific production data of 10 sets of equipment and 6 workpieces’ sequence are shown in Table

Original data of workpiece production.

Workpiece | Process route/arrival rate per unit time/processing rate per unit time | |||||
---|---|---|---|---|---|---|

_{1} | — | |||||

_{2} | — | |||||

_{3} | — | — | — | |||

_{4} | — | — | — | |||

_{5} | — | — | — | |||

_{6} | — |

The layout of the workshop is shown in Figure

The layout of the workshop.

After the initial state of each node is set, the subsequent state of each node is calculated according to the prediction model. The node state values without disturbance are shown in Table

Node state values without disturbance.

Time (d) | Node state values | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 0.875 | 0.400 | 0.875 | 0.625 | 0.538 | 0.763 | 0.429 | 0.542 | 0.365 | 0.625 |

2 | 0.677 | 0.706 | 0.687 | 0.809 | 0.925 | 0,.736 | 0.659 | 0.980 | 0.937 | 0.836 |

3 | 0.675 | 0.833 | 0.738 | 0.639 | 0.206 | 0.755 | 0.482 | 0.196 | 0.286 | 0.569 |

4 | 0.565 | 0.686 | 0.737 | 0.579 | 0.198 | 0.859 | 0.783 | 0.837 | 0.691 | 0.896 |

5 | 0.763 | 0.902 | 0.849 | 0.782 | 0.390 | 0.491 | 0.509 | 0.359 | 0.425 | 0.739 |

6 | 0.803 | 0.285 | 0.729 | 0.832 | 0.849 | 0.729 | 0.492 | 0.401 | 0.839 | 0.685 |

7 | 0.586 | 0.339 | 0.605 | 0.572 | 0.449 | 0.839 | 0.837 | 0.938 | 0.729 | 0.817 |

8 | 0.806 | 0.839 | 0.358 | 0.609 | 0.362 | 0.937 | 0.885 | 0.829 | 0.582 | 0.606 |

Table

When the disturbance factor is added, the node state values of the workshop after 3 hours of disturbance are shown in Table

Node state values after 3 hours of disturbance.

Time (d) | Node state values | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 0.875 | 0.400 | 0.875 | 0.625 | 0.538 | 0.763 | 0.429 | 0.542 | 0.365 | 0.625 |

2 | 0.677 | 0.706 | 0.687 | 0.809 | 0.925 | 0,.736 | 0.659 | 0.980 | 0.937 | 0.836 |

3 | 0.875 | 0.952 | 0.896 | 1.000 | 0.984 | 1.255 | 0.482 | 1.000 | 0.325 | 1.000 |

4 | 0.865 | 0.977 | 0.904 | 0.892 | 0.795 | 1.389 | 0.886 | 0.949 | 0.892 | 0.916 |

5 | 0.763 | 0.902 | 0.849 | 0.782 | 1.286 | 0.695 | 0.616 | 0.479 | 0.495 | 0.739 |

6 | 0.933 | 0.858 | 0.786 | 0.897 | 1.497 | 0.881 | 0.797 | 0.771 | 0.739 | 0.657 |

7 | 0.266 | 0.217 | 0.605 | 0.572 | 1.930 | 0.780 | 0.633 | 0.814 | 0.796 | 0.817 |

8 | 0.766 | 0.583 | 0.658 | 0.509 | 3.362 | 0.837 | 0.775 | 0.626 | 0.594 | 0.316 |

According to the criterion of bottleneck judgment [

Statistics of workshop network parameters.

Node | Node degree | Clustering coefficient | State fluctuation rate | Node average state value | Bottleneck node |
---|---|---|---|---|---|

3 | 0.667 | 0.196 | 0.722 | — | |

4 | 0.333 | 0.175 | 0.672 | — | |

4 | 0.167 | 0.189 | 0.736 | — | |

5 | 0.500 | 0.072 | 0.741 | — | |

3 | 0.333 | 1.020 | 1.106 | Secondary bottleneck | |

6 | 0.667 | 1.108 | 1.528 | Primary bottleneck | |

2 | 0.167 | 0.207 | 0.532 | — | |

3 | 0.200 | 0.433 | 0.602 | — | |

4 | 0.500 | 0.051 | 0.622 | — | |

3 | 0.333 | 0.176 | 0.752 | — |

As shown in Tables

In order to verify the rationality and correctness of the model, the production process of the workshop is simulated and analyzed. Through the simulation analysis, when there is no disturbance factor, the production activities of the workshop are normal, and there is no bottleneck. With the input of the disturbance factor, the process matrix changes, resulting in the changes of the network topology, clustering coefficient, node degree value, node state, and process matrix. Accuracy index is used to verify the accuracy of the prediction model, and it is defined as follows:

The fluctuation caused by disturbance is positively correlated with the degree value, but not with betweenness and clustering coefficient. After the disturbance, the proposed prediction method in this paper is in good agreement with the actual data, and the coincidence rate is as high as 93.7%. The coincidence rate with other prediction methods [

In this paper, a complex network is introduced into the production process of the production workshop. According to the characteristics of the production workshop, such as the working characteristics, resource flow, process constraints, information flow, and personnel allocation, the data are collected, and the key nodes are extracted, and then the complex network model is constructed to realize the network mathematical description of the production process of the production workshop. The disturbance factors are described mathematically, and the mechanism of the disturbance factors in the complex network system is constructed, so as to identify the bottleneck position of the production workshop under the disturbance factors.

The basic data used in this article are downloaded from the online public dataset weighted tardiness (

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by a grant from the National Natural Science Foundation of China (no. 91130035).