Mathematical Model Construction of the Production Workshop Based on the Complex Network and Markov Theory

Gang Guo,Fengjing Shao,Libor Pekař

doi:10.1155/2021/1912442

Abstract

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%.

Highlights

Production workshop is the basic unit of manufacturing enterprises, which consists of equipment, personnel, departments, and various workpieces
The workpiece is processed to the final product according to the established process route, and the process is accompanied by many uncertain factors. ese 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
Disturbance factors caused by the external environment: they are materials not transported in place according to regulations, order changes, etc. e 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. e disturbance factors caused by monitoring technology include detection method, detection time, and detection environment. e influence of such disturbance factors is relatively weak

Summary

Introduction

Production workshop is the basic unit of manufacturing enterprises, which consists of equipment, personnel, departments, and various workpieces. Rui and Cheng [17] studied the workshop of the assembly line production mode, constructed a mathematical model based on the balance rate of the production line, and identified the bottleneck in real time. 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. E 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 caused by the internal production environment: the production in the manufacturing workshop has been oriented to standardization and precision, the microdifferences and randomness in time cannot be eliminated. ese uncertainties are mostly related to the internal production

Bottleneck determination mechanism

Disturbance intensity level

Simulation Results and Discussion

Symbol Disturbance factors Weight

Bottleneck node

Conclusions