research paper on inventory management system

Inventory management for retail companies: A literature review and current trends

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Research Article

Construction and optimization of inventory management system via cloud-edge collaborative computing in supply chain environment in the Internet of Things era

Roles Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Affiliation Xi’an Fanyi University, Xi’an City, China

• Published: November 3, 2021
• https://doi.org/10.1371/journal.pone.0259284
• Reader Comments

The PLOS ONE Editors retract this article [ 1 ] because it was identified as one of a series of submissions for which we have concerns about peer review integrity and similarities across articles. These concerns call into question the validity and provenance of the reported results. We regret that the issues were not identified prior to the article’s publication.

The author either did not respond directly or could not be reached.

6 Sep 2023: The PLOS ONE Editors (2023) Retraction: Construction and optimization of inventory management system via cloud-edge collaborative computing in supply chain environment in the Internet of Things era. PLOS ONE 18(9): e0291318. https://doi.org/10.1371/journal.pone.0291318 View retraction

The present work aims to strengthen the core competitiveness of industrial enterprises in the supply chain environment, and enhance the efficiency of inventory management and the utilization rate of inventory resources. First, an analysis is performed on the supply and demand relationship between suppliers and manufacturers in the supply chain environment and the production mode of intelligent plant based on cloud manufacturing. It is found that the efficient management of spare parts inventory can effectively reduce costs and improve service levels. On this basis, different prediction methods are proposed for different data types of spare parts demand, which are all verified. Finally, the inventory management system based on cloud-edge collaborative computing is constructed, and the genetic algorithm is selected as a comparison to validate the performance of the system reported here. The experimental results indicate that prediction method based on weighted summation of eigenvalues and fitting proposed here has the smallest error and the best fitting effect in the demand prediction of machine spare parts, and the minimum error after fitting is only 2.2%. Besides, the spare parts demand prediction method can well complete the prediction in the face of three different types of time series of spare parts demand data, and the relative error of prediction is maintained at about 10%. This prediction system can meet the basic requirements of spare parts demand prediction and achieve higher prediction accuracy than the periodic prediction method. Moreover, the inventory management system based on cloud-edge collaborative computing has shorter processing time, higher efficiency, better stability, and better overall performance than genetic algorithm. The research results provide reference and ideas for the application of edge computing in inventory management, which have certain reference significance and application value.

Citation: Ran H (2021) Construction and optimization of inventory management system via cloud-edge collaborative computing in supply chain environment in the Internet of Things era. PLoS ONE 16(11): e0259284. https://doi.org/10.1371/journal.pone.0259284

Editor: Haibin Lv, Ministry of Natural Resources North Sea Bureau, CHINA

Received: September 12, 2021; Accepted: October 17, 2021; Published: November 3, 2021

Copyright: © 2021 Hailan Ran. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the manuscript and its Supporting Information files.

Funding: This work was supported by Xi’an Fanyi University Research team (No. XF17KYTD202).

Competing interests: The authors have declared that no competing interests exist.

Introduction

With the rapid development of science and technology, the combination of manufacturing processes, industrial IoT (Internet of Things), advanced computing, and other technologies has become increasingly close. Meanwhile, the manufacturing mode has changed from a product-centric mode to a user-centric mode [ 1 , 2 ]. Due to the complexity of business processes in large manufacturing plants, it is necessary to coordinate the relationship between people, information system, and physical system, which causes the traditional imbalance between resource allocation and task planning [ 3 ]. Moreover, concepts such as the intelligent plant, intelligent transportation and smart city have emerged as AI (artificial intelligence) and computer technology develop fast. Lv et al. (2018) designed a new government service platform by using 3D (three-dimensional) geographic information system and cloud computing to effectively manage and use urban data. In addition, they achieved the 3D analysis and visualization of urban information through the smart city platform, which made the life of the masses more convenient [ 4 ]. This proves that the application of computer and AI technology has become a hot research topic.

The development of China’s industry in the next decade will shift from labor-intensive production to technology-intensive production, which will bring great progress in advanced technology. Correspondingly, domestic enterprises have begun to explore the transformation approach to adapt to market changes and meet government needs. The fast-growing IoT applications can produce enormous amounts of data at the network edge, effectively promoting the generation and development of edge computing. Edge computing is one of the crucial technologies to realize intelligent industry. In large manufacturing workshops, sensors, instruments, and intelligent devices can collect mass of machine data [ 5 ]. These kinds of data are the main sources of industrial big data. Moreover, it is difficult to effectively master and forecast market demands. To reduce the dependence on the accuracy of market demand forecasting and improve the efficiency of supply chain inventory management, it is necessary to improve inventory management efficiency to adapt to the changes in market demand. Besides, it is essential to use management methods to compensate for many negative impacts of market uncertainty [ 6 ]. In this case, the upstream and downstream enterprises of the supply chain must create a constant speed supply chain based on the network platform to reduce the inventory cost of the supply chain and meet the needs of customers in real time. Industrial big data is considered as a necessary means to further enlarge product profit margin. At present, industrial data platform is the paramount component of data storage, calculation and analysis for intelligent factories. With the increase in smart devices in smart factories, a large number of data such as RFID (radio frequency identification) is obtained, providing a rich data set for the manufacturing industry. As IoT applications develop rapidly, mass of data is generated at the edge of the network, effectively facilitating the emergence and development of edge computing. Consequently, in large manufacturing workshops, sensors, instruments, intelligent terminals, and other devices can collect a large amount of machine data, as the main source of industrial big data. Under the background of increasingly socialized mass production and global economic integration, all links of the supply chain, such as raw material supply, production, logistics, consumption, processing, distribution, and retail must cooperate closely. Nevertheless, the coordination and management in all links, including inventory management, are still relatively closed, significantly reducing the comprehensive benefits of the overall supply chain.

The industrial production data is investigated here based on the analysis of the related concepts and production modes of supply chain and cloud manufacturing. Then, the demand prediction method for different types of industrial spare parts and the inventory management system are proposed via cloud-edge collaborative computing. The purpose of this work is to optimize inventory management and utilization efficiency by predicting the demand for vulnerable spare parts, and improve the performance of inventory management system with the advantage of cloud-edge collaboration computing. Moreover, cloud computing and IoT technology are utilized to explore the implementation method of refining the traditional inventory management of the supply chain. The innovation of this study is that corresponding demand prediction methods are studied separately according to three demand modes of vulnerable spare parts, namely periodic demand, stationary demand, and trend demand. Specifically, the simple exponential smoothing method is used to predict demand of stationary spare parts. The quadratic exponential smoothing method is selected to predict the linear demand, and the feature synthesis method is proposed for forecasting the spare parts with periodic demand mode. On this basis, edge computing is employed to develop a cloud-edge collaborative computing architecture, to optimize the spare parts prediction algorithm and improve inventory management efficiency and pertinence.

Related theories and research methods

Overview and status of supply chain inventory management.

IoT technology is the combination of intelligent recognition technology, wireless sensor technology, ubiquitous computing technology, and network technology. The global IoT network is still in the stage of concept, demonstration, and test, many key technologies need to be further studied, and standardization norms need to be further developed. However, it has triggered the third wave of information industry development in the world after computers and the Internet, which is an impactful upgrade of the application of information technology to human production and life. Supply chain is a kind of complete and functional network chain consisting of suppliers, manufacturers, distributors, retailers and end users centering on the business center enterprise and formed through controlling feed-forward information flow and the feedback of material flow and information flow [ 7 ]. There are diversified research works about supply chain inventory management. Bornkamp (2019) emphasized the importance of supply chain in his research. The author believed that the renegotiation of the UK-EU relationship would most likely take several years, but European distributors had to assess their current inventory management to mitigate future disruptions. Moreover, with the political pattern continuing to change, the growing e-commerce market would bring trade growth, so managing availability and distribution of inventory was critical to reducing overall costs, improving cash flows and increasing flexibility in supply chain operations, in order to effectively serve the European market [ 8 ]. Aaha et al. [ 9 ] analyzed six professional education courses offered by THE Council of Supply Chain Management Professionals, including senior certified professional forecaster, certified production and inventory management professionals, certified supply management professionals, and supply chain professionals. They took personal interests and organizational interests as the two main standards, and took the professional education plan as an alternative [ 9 ]. Evidently, people have gradually realized the significance of supply chain, and delved into supply chain deeply and professionally. Fig 1 reveals the basic structure of the supply chain.

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https://doi.org/10.1371/journal.pone.0259284.g001

The supply chain not only aggerates the logistics information and funds of suppliers and users, but also forms its own value. In the distribution link of the supply chain, the appreciation in products has been achieved through packaging, processing, transportation, and delivery. Supply chain inventory management is the process of defining the overall goal of supply chain inventory management and reviewing the inventory strategy of enterprises on supply chain nodes. The supply chain inventory management aims to sustain the optimal overall supply chain inventory and reduce the total inventory to respond to changing market demands. The improvement of the cost of supply chain inventory and supply chain can enhance the rapid response of inventory to the market.

Introduction to concepts related to cloud-edge collaboration for logistics management

Cloud manufacturing includes cloud-edge collaboration technology, AI service technology, container-based platform service technology, digital twins service technology, data security, and other related technologies. It is a novel type of digital, intelligent, and smart networked manufacturing with Chinese characteristics. Fig 2 reveals the overall schematic of the system of cloud manufacturing technology.

https://doi.org/10.1371/journal.pone.0259284.g002

The foundation of intelligent cloud manufacturing is a ubiquitous and human-centered network, which integrates digital technology such as information manufacturing technology and intelligent technology comprehensively [ 10 ]. The cloud manufacturing system enables users to obtain manufacturing resources and capabilities according to their own needs anytime and anywhere through the cloud-based manufacturing service platform, and intelligently perform various activities throughout the life cycle.

In the industrial field, the IoT proactively identifies and remotely controls all physical devices in the cloud manufacturing scenario of existing network infrastructure, and obtains content in the physical world (real space) in the information world (cyberspace). The data reflects the whole life cycle of the corresponding physical equipment, and realizes the digital twins [ 11 , 12 ].

Internet technology facilitates the active and independent analysis of industrial product manufacturing process, generates intelligent perception and active prediction of the outside world, and forms a closed-loop process of automatic repair and complete feedback. With the emergence of intelligent control, industrial IoT can optimize all aspects of industrial systems, including intelligent manufacturing and business systems, real-time monitoring, supply chain collaboration, value-added services, and other business needs. The wide application of industrial IoT technology makes the production process more active and intelligent, which can accurately predict and effectively solve the potential obstacles, to effectively increase corporate profits [ 13 , 14 ].

The continuous development of the mobile Internet has brought new convenience for people’s life and production, as well as more needs and challenges, such as higher requirement of timeliness, security, and reliability. Hence, edge computing is needed to improve cloud computing ability. Fig 3 illustrates the typical architecture of edge computing for intelligent plants.

https://doi.org/10.1371/journal.pone.0259284.g003

Many problems such as single-point faults may occur in industrial applications. In addition to the unified control of the cloud, the edge nodes have the computing ability to independently make decisions and solve problems, which can improve factory productivity, while avoiding equipment failure. In IoT scenarios, edge computing focuses on solving problems of lightweight data size closer to the user’s by transferring computing operation [ 15 ]. Therefore, it cannot completely replace cloud computing, but assists cloud computing to improve work efficiency. With the deepening of industry research and academic research, cloud collaboration is widely used in numerous fields such as medical treatment, industry, and finance. Cloud-edge collaborative architecture can balance the load and reduce the hardware requirements of edge devices, making the peripheral equipment more convenient while maintaining the capacity [ 16 , 17 ]. Fig 4 provides a manufacturing factory example based on cloud-edge collaborative computing architecture.

https://doi.org/10.1371/journal.pone.0259284.g004

Demand prediction of vulnerable spare parts in IoT supply chain environment

In the cloud manufacturing scenario, the amount of data sent by the terminal equipment deployed in each plant is different for various plant equipment and actual business needs. Therefore, it is necessary to design a scheme for the edge server equipped in different plants to effectively reduce the procurement funds of enterprises and avoid the waste of limited resources. Based on this consideration, a demand prediction method is proposed for vulnerable spare parts, and it is combined with the cloud-edge cooperative inventory management system to improve the efficiency and quality of inventory management.

Timely maintenance and supply of spare parts are two important components of the after-sales service system provided by large equipment manufacturers in the service network [ 18 ]. Among them, the efficiency of spare parts inventory management determines whether spare parts can reach the demand in time, which directly affects the market competitiveness of service systems and manufacturers. In the IoT era, many consumption data and consumption behaviors based on IoT provide sufficient data basis for market demand prediction. Shen et al. (2020) extracted knowledge from user generated content and depicted the differences between IT service companies’ use of social media and users’ expectations based on daily interaction between suppliers with customers [ 19 ]. The data analysis method is also adopted here to forecast the spare parts demand.

The purpose of inventory management is to deal with various changes and uncertainties in spare part supply to ensure the normal operation of spare part supply. According to the function and direction of spare parts, they can be divided into two categories: maintenance spare parts and service spare parts.

The function of maintenance spare parts is to ensure the normal operation of production equipment, while the function of service spare parts is to ensure the after-sales service of products. Different types of spare parts have diverse inventory management purposes and management methods [ 20 ]. In summary, in the case of low total cost of spare parts inventory, it is very practical to study how to optimize the inventory management system according to the actual situation of enterprises to achieve a significant improvement in service level. The spare parts inventory management strategy includes spare parts classification, spare parts demand analysis, spare parts shortage management, spare parts inventory mode, and inventory strategy.

The common vulnerable parts of pump trucks in industrial production are taken as the research object here to predict their needs, including conveying cylinder, concrete piston, and cutting ring, usually with relatively large demands. Through the analysis of the sales volume of concrete piston in different regions, the demand is classified into the following three categories: periodic demand time series, demand time series with rising trend, and stable demand time series [ 21 ].

The prediction based on periodic demand time series is first discussed. Spare parts with periodic changes in demand patterns include random components and periodic components in the past demand time series [ 22 , 23 ]. The proposed prediction method calculates the cycle length according to the time series of spare parts demand in the past, calculates the demand data of original spare parts according to the cycle length, and divides each segment and performs polynomial fitting. The polynomial function of each cycle is integrated to obtain a new polynomial function to extract periodic ports and remove random factors, which is used as a prediction model to predict the demand of the next period.

In Eq (1) , T is the target time series, S denotes the time series needed for similarity measurement, and n represents the length of two time series. Besides, t i or s i refers to a factor at a time in a time series.

In Eq (2) , P TS refers to the correlation coefficient of time series. Meanwhile, d ( T , S ) stands for the Euclidean distance of two time series data, and f ( T , S ) is the similarity measure function.

In Eq (4) , the value of a is 1, and the value of b is n/2. α signifies the threshold.

There are several methods to predict the continuous demand of spare parts for the non-periodic demand time series, such as the exponential smoothing method and the weighted moving average method. The exponential smoothing method is an improvement of moving average method characterized by simple form, easy implementation, and high precision, which can accurately reflect the changes in demand data and is widely used in practice. Therefore, the exponential smoothing method is selected as the spare parts demand prediction method based on aperiodic demand time series here.

Among Eqs ( 7 ) and ( 8 ), a denotes the smooth constant, and S t + 1 stands for the smooth value of (t+1) period.

For the prediction of intermittent time series, the intermittent demand time of spare parts has two characteristics. (1) There is less demand. In other words, there is no demand during this period. (2) There is great volatility in demand value. These two characteristics cause a large prediction error of intermittent time series [ 27 ]. Furthermore, the time aggregation prediction method is used to predict the demand of intermittent time series.

Inventory management system based on cloud-edge collaboration

Core competitiveness is crucial to large equipment manufacturers, because efficient management of spare parts inventory can effectively reduce costs and improve service levels. The engineering machinery and equipment usually have a complex structure and various components and parts. However, the existing spare parts inventory management is still cumbersome and unsystematic, which determines inventory according to personal experience and plans demands according to inventory proportion, bringing great pressure to the production department and other related departments. The solution of traditional cloud computing architecture is to download the sensor data of various factory equipment, and use the data analysis technique of big data. Meanwhile, it transits the downloaded data to remote cloud servers through the data acquisition module, to improve work efficiency and competitiveness [ 28 , 29 ]. Here, the cloud-edge collaborative computing in industrial IoT is proposed to solve the rapid response problem of real-time control and data fast processing in large-scale manufacturing plants. Fig 5 provides the architecture of cloud-edge collaborative computing.

https://doi.org/10.1371/journal.pone.0259284.g005

The deployment of industrial IoT in intelligent manufacturing environment mainly contains the equipment perception layer, data resource layer, service application layer, and operation and maintenance management layer, which work together to maintain all data links [ 30 , 31 ]. From the specific business point of view, the cloud components are mainly responsible for the formation of the model of the collected data, and the peripheral components are basically responsible for obtaining the model from the data dictionary, providing timely services for factory equipment in real time. Reducing the training time of models and networks can shorten the response time of the closed-loop system and improve the overall production quality of the plant equipment. OpenStpack and Starling X enable companies to build their own cloud- edge collaborative computing services using the most advanced open-source cloud computing platform and the latest distributed cloud computing platform, respectively.

The solution of traditional cloud computing architecture is to upload all kinds of sensor data from factory equipment, such as vibration, pressure, and temperature, to the cloud remote server through data acquisition module. Besides, it utilizes the popular big data analysis technology to establish the mathematical model of index data and factory equipment performance, to enhance the production quality, work efficiency, and market competitiveness of factory equipment. Taking the coal industry as an example, the mine is generally located in a remote location where it is difficult to implement network communication. Due to the characteristics of large scale, numerous varieties, low value density, and fast update and processing requirements of coal mine data, the traditional cloud computing architecture is inadequate, because it is easy to produce problems of single point faults and slow closed-loop response. Based on the above analysis, the cloud-edge collaborative computing architecture is selected for the industrial IoT to cope with the problems of fast real-time control response and fast data calculation in large manufacturing workshops. Fig 6 illustrates the workflow of cloud-edge collaborative computing architecture, where various data acquisition devices and user requests are collectively referred to as collectors. The smart endpoint simply pre-processes information from the collectors and sends it to the computing node in the edge server cluster [ 32 ]. Then, the I/O intensive virtual machine on the computing node receives the information and stores it in the database on the storage node.

https://doi.org/10.1371/journal.pone.0259284.g006

The following is the specific processing of the edge server:

• the intelligent terminal sends the collected data to the edge data storage module;
• data processing module retrieves the corresponding data from the edge data storage module according to the user’s request;
• data processing module carries out lightweight big data analysis according to the model parameters provided by the data dictionary module. Besides, the edge data dictionary module is analyzed and synchronized;
• the decision module outputs the processing results of the data processing module to the intelligent equipment and checks them accordingly.

The procedure of the remote centralized server is as follows:

• the edge server and remote centralized data storage module synchronize incremental data;
• data processing module retrieves data from the remote centralized data storage module according to user needs;
• the data processing module conducts large-scale big data analysis according to the model parameters provided by the data dictionary module.

The analysis and synchronization of the remote data dictionary module are presented as follows:

• edge server synchronizes incremental data with the remote centralized data storage module;
• the data processing module retrieves data from remote centralized data storage module according to user needs;
• the data processing module conducts large-scale big data analysis according to the model parameters provided by the data dictionary module. Meanwhile, analysis and synchronization are performed on the remote data dictionary module;
• the remote data dictionary module synchronizes data processing with edge data dictionary module according to specific requirements.

Edge servers and remote centralized servers regularly analyze and use stored data, and the data dictionary is updated to ensure the correctness of the decision message.

Simulation and experimental design

Three time series prediction methods are provided for the demand prediction of vulnerable parts based on spare parts. The demand data of high-strength circular chains in the mining industry is used here for verification. The circular chain is also a spare part of construction machinery, and the experimental data comes from the network. In the simulation experiment, the genetic algorithm is introduced as a comparative algorithm to verify the performance of the inventory management system based on cloud-edge collaborative computing architecture. Table 1 indicates the task parameters under different configurations in this experiment.

https://doi.org/10.1371/journal.pone.0259284.t001

Analysis of demand prediction results and the performance verification of inventory management system

Comparison results of the prediction method based on demand of vulnerable spare parts..

After the prediction model is established, the predicted value of spare parts demand is calculated to be compared with the true value. The polynomial is established and fitted according to the period length. Fig 7 illustrates the relationship between fitting times and prediction errors.

https://doi.org/10.1371/journal.pone.0259284.g007

Fig 7 shows that the prediction error decreases first and then increases with the increase of fitting times. When the fitting time of the polynomial reaches 10, the prediction error begins to stabilize. After 13 times of fitting of the polynomial, the prediction error reaches a minimum of 11.7%, and then begins to increase. Based on this result, in the following simulation experiment, 13 times of fitting are used to obtain the fitting polynomial of each section when the polynomial regression model is used to fit the demand data of spare parts.

The eigenvalues and the weighted fitting process of each cycle are shown in Fig 8 .

Eigenvalues and the weighted fitting processes ((a): eigenvalues of each cycle; (b): weighted fitting processes of each cycle).

https://doi.org/10.1371/journal.pone.0259284.g008

Fig 8 displays the intermediate process of eigenvalue fitting. As can be seen from Fig 8B , the prediction error of monthly demand after weighted fitting is smaller. The mean value of the sum of eigenvalues and the weighted sum of eigenvalues shown in Fig 8A is used to synthesize new feature sets. In other words, the determination of values of a n , b n , and c n is similar to the determination of polynomial degree. Through experimental analysis, the prediction accuracy is the highest when w = 0.1, w = 0.1, and w = 0.8.

Fig 9A illustrates the mean value of the sum of eigenvalues and the weighted sum of eigenvalues shown in Fig 8A . Fig 9 provides the prediction results of spare parts demand based on the weighted synthesized eigenvalues.

Prediction results of spare parts demand based on weighted eigenvalues ((a): weighted eigenvalues; (b): prediction results based on weighted eigenvalues; (c): error comparison of two processing methods).

https://doi.org/10.1371/journal.pone.0259284.g009

According to Fig 9b , from a macro perspective, the prediction result based on the weighted sum is closer to the real value than the prediction based on the mean value of sum of the eigenvalues. From the perspective of error value, the highest prediction error based on the weighted eigenvalues is 34.9%, and the lowest is 2.2%. Through the comparison of error in Fig 9C , the average relative error based on the weighted fitting is lower than that based on the mean value of the sum of eigenvalues, the former is 11.7%, and the latter is 18.4%. Therefore, the prediction accuracy of the prediction model established by the weighted fitting method is higher. To sum up, the prediction method based on weighted fitting of eigenvalues has the smallest error and the best fitting effect in the demand prediction of machine spare parts.

Verification results of the perdition method based on vulnerable spare parts demand. The simulation experiment adopts the moving average period coefficient prediction of the prediction method based on weighted eigenvalues as a comparison with the true value. The specific results are presented in Fig 10 .

Weighted eigenvalues and prediction results ((a): weighted eigenvalues; (b): fitting processing of weighted eigenvalues; (c): comparison between prediction results and true results).

https://doi.org/10.1371/journal.pone.0259284.g010

In Fig 10A , a n refers to the first set of eigenvalues, b n denotes the second set of eigenvalues, c n represents the eigenvalues after fitting, the value range of cycle length is 1 ~ 13, and the threshold is 10% of the mean value. Polynomial fitting is carried out for the first two data segments to obtain the periodic term of the data segment, which is used to predict the true value of the third cycle segment. When n = 10, the prediction error is the smallest, so the degree of the fitting polynomial is n = 10. The fitting polynomial function of each segment is obtained. From Fig 10 , the average relative error between the actual value of spare parts demand and the predicted value is 9.4%. When the moving period coefficient method is used to predict the demand for spare parts, the average relative error between the predicted value and the actual value is 13.0%.

The proposed prediction method is also used to predict the demand of the circular chain, and the results are compared with those of the moving average period coefficient method, to further verify the advantages of this method. The comparison results are shown in Fig 11 .

https://doi.org/10.1371/journal.pone.0259284.g011

From Fig 11 , the average absolute error of the actual value and predicted value of spare parts demand based on the moving average period coefficient method is 286.8, and the average relative error is 12.8%. The average absolute error of the polynomial fitting model is 250.7, and the average relative error is 11.7%. Therefore, the proposed prediction mode has a better prediction effect.

The prediction results of exponential smoothing method and quadratic exponential smoothing method are shown in Fig 12 .

The prediction results of exponential smoothing method and quadratic exponential smoothing method ((a): the prediction results of exponential smoothing method; (b): the prediction results of quadratic exponential smoothing method).

https://doi.org/10.1371/journal.pone.0259284.g012

The simple smoothing index prediction method is used to investigate the spare parts demand data with the nonlinear trend. According to Fig 12A , the predicted value of spare parts demand by smoothing index prediction method is close to the actual value, and the average relative error is 18.0%. The quadratic smoothing index prediction method is aimed at the spare parts demand data with linear trend. From the results in Fig 12B , the predicted value of demand of the quadratic exponential smoothing method is close to the actual value, and the average relative error is 11.3%. In conclusion, the exponential smoothing method and quadratic exponential smoothing method both have high prediction accuracy in spare parts demand.

To sum up, the cycle length detection method based on similarity is adopted to calculate the cycle length. Then, the data is divided into several segments according to its cycle length, and polynomials are used to fit the data in the cycle segment. Moreover, the polynomials are synthesized to obtain a new polynomial function, which is used as the prediction model to predict the demand in the next cycle. The experimental results demonstrate that this prediction method can achieve high prediction accuracy.

Performance verification results of inventory management system based on cloud-edge collaborative computing. The algorithm of the inventory management system optimizes the resource allocation for virtual machines from the impact of virtual machines on the performance of physical machines and the impact of different configurations of virtual machines on task execution time. Table 2 and Fig 13 signify the resource allocation scheme for the best virtual machine performance obtained by the two algorithms and the comparison of the results after 100 executions of six tasks at the same time, respectively.

Performance comparison between two algorithms ((a)-(f) represent the experimental results from Task 1 to Task 6).

https://doi.org/10.1371/journal.pone.0259284.g013

https://doi.org/10.1371/journal.pone.0259284.t002

Fig 13 illustrates the performance comparison between the proposed algorithm and the genetic algorithm. Specifically, the average completion time of the six tasks executed by the genetic algorithm is 15.64 seconds, 14.92 seconds, 21.55 seconds, 21.34 seconds, 24.03 seconds, and 23.95 seconds, respectively. The average completion time of the six tasks by the proposed algorithm is 15.10 seconds, 15.00 seconds, 20.35 seconds, 20.60 seconds, 23.66 seconds, and 23.59 seconds. From the completion time point of view, the proposed virtual machine performance algorithm has shorter processing time and higher efficiency than genetic algorithm. In terms of stability, the genetic algorithm fluctuates greatly, so the proposed algorithm has higher stability.

In conclusion, in the prediction of spare parts demand with strong periodicity, the prediction method based on weighted fitting of eigenvalues has the smallest error and the optimal fitting effect in the prediction of machine spare parts demand, and the lowest error after fitting is only 2.2%. For spare parts with non-periodic linear demand and spare parts with nonlinear demand, exponential smoothing method and quadratic exponential smoothing method are used for prediction respectively, and the prediction results are close to the actual value. The spare parts demand prediction method proposed here can well complete the prediction for three different types of time series of demand data of spare parts, and the relative error of prediction is maintained at about 10%. The prediction effect can meet the basic requirements of spare parts demand prediction, and the prediction accuracy is higher than that of periodic prediction method. Compared with genetic algorithm, the cloud-edge collaborative computing algorithm for inventory management system takes less processing time and has higher efficiency. In terms of stability, genetic algorithm fluctuates greatly, but the algorithm reported here is much more stable.

Conclusions

Efficient spare parts inventory management can reduce inventory costs, improve service level, and bring huge benefits to large equipment manufacturing enterprises. There are a variety of spare parts for large-scale equipment as well as many uncertain factors in the supply process. Therefore, it is essential to continuously update relevant technologies for higher efficiency of spare parts inventory management, to save inventory costs. Based on the supply chain background, the critical role of inventory management plan and spare parts demand relationship in improving the core competitiveness of enterprises. Secondly, according to different types of spare parts demand prediction data, different spare parts and demand prediction methods for vulnerable parts are proposed. In addition, the efficiency of inventory management is improved by predicting the demand for industrial vulnerable parts. For the three spare demand models of vulnerable parts, including periodic model, stationary model, and trend model, the corresponding demand forecasting methods are studied respectively. The simple exponential smoothing method is used to predict the spare parts with stable demands, while the quadratic exponential smoothing method is used to predict the demand for spare parts with linear trend. Meanwhile, the prediction method based on weighted fitting of eigenvalues is adopted to predict the periodical demand of machine spare parts. Finally, an inventory management system based on cloud-edge collaborative computing is proposed to reasonably allocate inventory resources and improve the utilization of inventory resources. The prediction method based on weighted fitting of eigenvalues proposed here has the smallest error and the best fitting effect in the demand prediction of machine spare parts, and the lowest error after fitting is only 2.2%. Exponential smoothing method and quadratic exponential smoothing method are used for spare parts with non-periodic linear demands and spare parts with nonlinear demands, respectively, and the prediction results are close to the actual values. In terms of completion time, the virtual machine performance algorithm reported here realizes shorter processing time and higher efficiency than genetic algorithm. In terms of stability, this research algorithm is much more stable than the genetic algorithm. Despite particular outcomes achieved in this work, due to the limitations of research level and some objective factors, there are still some deficiencies. On the one hand, there remains space for improvement in the relative error of the prediction method for vulnerable spare parts proposed here. It is expected to further improve the accuracy and efficiency of prediction by introducing the deep learning algorithm in future. On the other hand, there lacks the combination of the prediction method based on vulnerable spare parts and the inventory management system based on cloud-edge collaborative computing reported here. The follow-up work will make efforts to integrate spare parts demand forecasting and inventory resource management into one intelligent system.

Supporting information

https://doi.org/10.1371/journal.pone.0259284.s001

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• Zixi Hu 1 ,
• Shuang Liu 1 ,
• Fan Yang 2 ,
• Xiaodong Geng 1 ,
• Xiaodi Huo 3 &
• Jia Liu 4  

Aiming at the problems of slow convergence speed and low precision probability of multi-objective optimization of energy storage materials, a multi-objective optimization model of energy storage materials based on NSGA-II algorithm was proposed. The association rule set of storage materials in the joint supply chain operation performance management system is extracted, and the rough vector feature distribution set multi-objective optimization method is used to decompose and optimize the characteristics of storage materials in the joint supply chain operation performance management system. Using NSGA-II optimization analysis method, this paper summarizes the power storage materials under the joint supply chain operation performance management system, and summarizes three kinds of inventory control: periodic inventory, inventory coding, and computerized inventory. Combined with the positive regression learning method of organizational operational performance, the multi-objective optimization decision of electric storage materials under the joint supply chain operational performance management system is realized. The simulation results show that under the joint supply chain operation performance management system, the proposed method reaches the optimal convergence after 65 iterations, the convergence speed is fast, and the accuracy probability reaches 1.000 after 80 iterations, which solves the problems of slow convergence speed and low accuracy probability, and has a good scheduling ability of energy storage materials.

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1 Introduction

Distribution management is an important part of logistics management. At present, the logistics management planning of enterprises recognized at home and abroad generally includes four levels. From top to bottom is the strategic layer, structural layer, operational layer, and support layer [ 1 ]. Foreign countries have been at the forefront in planning and research on warehouse management in terms of warehousing, especially the United States and Japan, which are good at breaking the traditional warehousing form and using more advanced technology to plan and manage warehouses. Material storage and distribution is an important link in the field of electric power logistics and circulation. China pays more and more attention to the material storage management in the electric power industry, and the construction of power storage systems is relatively perfect in many companies [ 3 , 4 ]. Heilongjiang No. 3 Thermal Power Engineering Company has planned and designed the material warehouse, North China Electric Power Company has done research on the warehouse management in North China power grid system, and Yunnan Thermal Power Construction Company has done research on the logistics and warehouse management of power grid operators. From a nationwide perspective, the planning of electric power material warehouse has not been in a state of blooming, and there are still many problems: the utilization rate of computers and automation is low; the warehouse information system is not perfect; the storage equipment and facilities are not arranged according to the actual situation, resulting in problems such as idle equipment, accumulation of goods, and low efficiency [ 5 ].

Material distribution is the key link of material transportation in terms of distribution, which is not only related to the fact that distribution needs to be realized by information network technology. The whole process of distribution should be guaranteed by modern technology and equipment. Most scholars establish optimization models and it use algorithms to solve them for the research of material distribution, especially the popularization of intelligent algorithms, which makes the optimization research increasingly mature. The application of intelligent methods such as genetic algorithm, particle swarm algorithm, simulated annealing, ant colony algorithm, fish swarm algorithm, and neural network makes the solution more convenient. But each method has its own advantages and disadvantages. The requirements of material distribution [ 6 ] are closely related to the construction of local government projects and the operation of completed electrical equipment for electric power enterprises. Compared with other industries’ material distribution management, the characteristics of power material distribution are changeable and uncertain [ 7 ]. At the same time, the reliability and timeliness of the distribution process are higher to meet customers’ demand for electricity in time. At present, the main idea of research on electric power dispatching and distribution at home and abroad is to drive system integration through advanced intelligent algorithms and complete intelligent operation through software development. However, due to the uneven adoption of modern technology and equipment by enterprises, the distribution is still different in scale, level, efficiency, speed, and quality, and the distribution process is difficult to follow the main principles of reliability, timeliness, high quality, convenience, and economy. Carrying out information management of materials is in response to the development of the times, an effective way to improve the standardized management level of project materials. According to the standard requirements set up by enterprises, the information management of materials can flow according to procedures in the processes of material warehousing, turnover, and distribution. The establishment of this information system will provide a standardized, efficient, and scientific platform for enterprises to manage materials, and can be used for effective supervision and management. It not only standardizes the flow of materials circulation, but also realizes the sharing of data resources and the reasonable storage of inventory materials to the maximum extent. Reduce the occupation of reserve funds. Improve work efficiency and management level.

It is necessary to optimize the scheduling control of electric storage materials according to the growth mode of economic benefits with the increase of electric storage materials, and it improves the dispatching ability of electric power storage materials, establish an electric power storage materials management model under the joint supply chain operation performance management system, and adopt the data characteristic analysis method to carry out multi-objective optimization of electric power storage materials under the joint supply chain operation performance management system. A multi-stage dynamic scheduling algorithm is proposed in Ref. [ 8 ]. The static material distribution scheduling problem is decomposed into three optimization sub-problems in the first stage, and the optimal initial scheduling scheme is obtained using dynamic programming algorithm. In the second phase, a two-stage rescheduling algorithm incorporating removing rules and adding rules was designed according to the status update mechanism of material demand and multi-load AGVs. However, this method has the problem of small application range and low accuracy probability. Ref. [ 9 ] conducted an in-depth study on the overall efficiency improvement of cross-district material handling systems, and analyzed the integrated scheduling problem combining vehicle scheduling and parking targets on intervehicle-to-vehicle expressways. To meet the needs of adaptive adjustment, efficient scheduling, and multi-objective optimization, an improved parallel multi-objective genetic algorithm is designed by making full use of parallel strategy, multi-objective evolutionary process, and local search strategy. However, this method has the problem of slow convergence.

The NSGA-II algorithm is a well-known multi-objective optimization algorithm used to solve optimization problems with multiple independent and competing objective functions [ 10 , 11 , 12 ]. By performing non-dominated sorting on individuals, it is possible to effectively preserve diversity within the population while preserving a good solution set. And through the calculation of crowding degree, the diversity between individuals is maintained. When selecting the next generation of individuals, the fitness and crowding degree of each individual are comprehensively considered, which is conducive to avoiding the population from falling into local optimal solutions and has strong universality and applicability. In this regard, this article studies the multi-objective optimization model of energy storage materials based on the NSGA-II algorithm. A comprehensive analysis and research were conducted on the multi-objective optimization problem of energy storage materials under the joint supply chain operation performance management system. First, by establishing a distributed energy storage material structure matching model and applying statistical analysis methods to construct the distribution matrix of energy storage material association rules, the definition and optimization of the spatial clustering model for energy storage materials were achieved. On this basis, with the help of fuzzy optimization methods, the output information of energy storage materials was automatically planned, improving the multi-objective optimization ability of the system. By mining the distribution time series and fuzzy features of energy storage materials, a fuzzy feature distribution set and optimization results for energy storage material mining were obtained. Finally, the NSGA-II algorithm was used for multi-objective optimization of inductive loop inventory, inventory coding, and computerized inventory, effectively improving the efficiency and effectiveness of inventory control strategies. By applying the NSGA-II algorithm, the system can more efficiently find the optimal solution and achieve the goal of optimizing inventory management.

2 Problems and Big Data Analysis of Power Storage Materials

2.1 the concept of power storage and material distribution and power materials.

Logistics mainly refers to a way of commodity circulation, which belongs to one of the new circulation ways in the process of modern commercial development. Modern logistics and distribution system refers to the unified information scheduling and management of the whole logistics and distribution system after receiving customers’ logistics and distribution requirements, and combining with the specific requirements of customers’ orders, doing a good job of tally and goods selection in the logistics base, and finally delivering the configured goods to the consignee [ 13 ]. Logistics is a non-single business form in logistics activities, and it needs to be closely integrated with many modules such as business flow, logistics, and capital flow, realizing the common utilization of logistics resources, facilities and equipment, logistics management, and so on. Overall, logistics and distribution management consists of six main parts, which are also comprehensively expounded here. First, stock up. This link is the basic link of logistics and distribution. The main logistics and distribution entities gather the related needs of users and form a certain scale of stocking. In this process, enterprises also need to control the stocking cost and improve the comprehensive benefits of logistics and distribution management system. Second, storage [ 14 ]. This stage refers to the storage process of each logistics product and the process of waiting for the product to enter circulation. Third, sorting and distribution. This step involves sorting and delivering goods based on specific order contents. Enable the goods to truly enter circulation activities. Fourth, try on the clothes. The planning of vehicles for different commodities is carried out after the selection of commodities is completed. This process requires the main body of logistics and distribution management to do a good job in macro-planning and fine analysis of logistics and distribution vehicles and the goods transported on each vehicle in combination with the actual situation. Fifth, logistics and transportation. Complete the distribution of each logistics commodity according to the order address, so that it can reach the consignee’s hands. In this process, it is necessary to plan the logistics route and combine the actual situation to form the best distribution route. Sixth, logistics delivery. The logistics goods are really delivered to the users [ 2 ] after this link.

Material is the abbreviation of material information. Material refers to the various means of production consumed in the process of commodity production in the production of enterprises. Material is very important for enterprise development and belongs to the core resource. Material refers to all kinds of material materials consumed in the process of power production and supply in the power industry [ 15 ].

Material management refers to P8, which is the plan and organization of purchasing and using related materials during the production process. In the old concept of material management, more attention is often paid to the possession and distribution of resources; new material management pays more attention to the use of system management to allocate material resources accordingly. Material management can be divided into broad sense and narrow sense conceptually. First of all, in a broad sense, it refers to the management of raw materials to the management of materials until the final scrap of materials. The narrow sense of material management refers to the management from the warehousing of materials to the warehousing of materials. It mainly includes the determination of material plan and procurement, etc. [ 16 , 17 , 18 , 19 , 20 ].

Electric power materials can be divided into generators according to their functions, power transmission and transformation equipment, electrical equipment, power electronic equipment, electromagnetic measuring instruments and meters, etc. Reasonable classification and analysis of electric power materials can better provide a good basis for planning and building warehousing and distribution systems, introducing intelligent loading and unloading equipment, and calculating reasonable storage capacity. The electric power materials of Company A studied in this paper can be subdivided into main network materials, distribution network materials, marketing materials, emergency materials, etc., according to the actual work needs. Among them, the main network materials mainly refer to the materials used in substations of 110 kV and above, mainly including transformers, outlet bushings, and other equipment. These materials have high requirements for models and specifications, and cannot be stored in large quantities; distribution materials mainly refer to the materials used in distribution networks of 10 kV and below, including distribution transformers, disconnectors, and other equipment. It is used for daily emergency repair of power failure. It needs a certain reserve; marketing materials mainly refer to equipment such as electric meters on the user side, which need a certain reserve when newly installed residential quarters or large-area electric meters are rebuilt; emergency materials mainly refer to relay protection plug-ins and cables with different voltage levels, etc., which have strong versatility and need a large amount of reserves [ 21 ].

2.2 Target Distribution of Electric Power Storage Materials

The statistical analysis of electric power storage materials under the joint supply chain operation performance management system is carried out by combining the fuzzy feature clustering analysis method to realize the multi-objective optimization of electric power storage materials under the joint supply chain operation performance management system, the information processing of electric power storage materials under the joint supply chain operation performance management system is realized, the optimized database retrieval model is established, and the access and multi-objective optimization ability of electric power storage materials under the joint supply chain operation performance management system is improved. It is necessary to construct a data collection model for energy storage materials under the joint supply chain operation performance management system, establish a distributed structure matching model for energy storage materials under the joint supply chain operation performance management system, and use statistical analysis methods to establish a distribution matrix of association rules for energy storage materials under the joint supply chain operation performance management system. The formula is defined as:

where \(w_{ij}\) is the first sampling node, \(d_{NN}\) is the diversified feature component of materials. Combined with the global weighted analysis method, the feature extraction model of power storage materials under the performance management system of joint supply chain is constructed. At the operation and maintenance management node I, the digital meta-sequence of the collected power storage materials under the performance management system of joint supply chain is represented as \((w_{1,j} ,w_{2,j} , \cdots ,w_{tj} )\) , where it is the number of electric storage materials under the joint supply chain operation performance management system, and \(A= A_1, A_2, \ldots A_m\) is the weighting coefficient of electric storage materials mining under the joint supply chain operation performance management system. Combining with semantic feature analysis method, the characteristic distribution model of electric storage materials mining under the joint supply chain operation performance management system is established, and the electric storage materials under the joint supply chain operation performance management system are focused on the characteristic space by multi-dimensional space reorganization method. The distribution time series \(b= b_1, b_2, \ldots b_m\) of power storage materials under the joint supply chain operation performance management system is obtained, and the spatial clustering model of power storage materials under the joint supply chain operation performance management system is defined as:

where \(\sigma\) is the dynamic parameter of power material distribution management, \(r\) is the time delay of power material logistics distribution, and \(b\) is the fuzzy degree of power material logistics distribution [ 22 ]. The fuzzy clustering characteristic coefficient of power storage materials under the joint supply chain operation performance management system is calculated, which is defined as:

The output information of power storage materials under the joint supply chain operation performance management system is automatically planned based on the fuzzy optimization method, and the multi-objective optimization ability of power storage materials under the joint supply chain operation performance management system is improved [ 23 ].

2.3 Multi-objective Feature Detection of Power Storage Materials Management

The fuzzy feature detection method is used to collect electric storage materials under the joint supply chain operation performance management system, and the feature quantity of association rules of electric storage materials under the joint supply chain operation performance management system is extracted [ 24 ], and the data fuzziness is matched, and the association rule set of electric storage materials under the joint supply chain operation performance management system is defined as:

where \(d_{m + 1} (m)\) is the predicted value of power storage materials set at point under the joint supply chain operation performance management system, and \(d_{k + 1} (m)\) is the fuzzy characteristic quantity of power storage materials under the joint supply chain operation performance management system collected at point \(m\) . According to the above analysis, the data storage structure of energy storage materials under the joint supply chain operation performance management system is optimized and reorganized, and the adaptive weighting coefficient of energy storage materials under the joint supply chain operation performance management system is obtained as follows:

where \(\max_{l} Freq_{i,j}\) is the ambiguity identification characteristic quantity of electric power storage materials under the joint supply chain operation performance management system detected between operation and maintenance management nodes, and it is:

where \(d_{i}\) and \(d_{j}\) are the similarity attributes of multi-objective optimization of power storage materials under the joint supply chain operation performance management system, fuzzy clustering method is adopted to mine power storage materials under the joint supply chain operation performance management system based on quantitative regression analysis method, a multi-objective optimization model of power storage materials under the joint supply chain operation performance management system is established to improve the optimization planning ability [ 25 ].

3 Multi-objective Optimization of Power Storage Materials

3.1 analysis of multi-objective optimization characteristics of power storage materials.

The forward regression learning method of fuzzy organizational performance is adopted to carry out multi-objective optimization management of power storage materials management [ 11 ]. The iterative calculation formula of fuzzy feature mining of power storage materials detection is as follows:

where \(d_{i}\) is the dynamic parameter of innovative power material logistics distribution, and \(d_{j}\) is the characteristic parameter of joint supply chain operation performance. Statistical information analysis method is used, the fuzzy characteristic distribution set of power storage material mining under the joint supply chain operation performance management system is established, and the following results are obtained:

where \(NB\) is the characteristic quantity of the regression analysis of the distribution of operating resources in the joint supply chain [ 12 ]. The characteristic decomposition and optimization extraction of power storage materials under the joint supply chain operation performance management system are carried out by the multi-objective optimization method of rough vector characteristic distribution set. The two-level distribution degree of multi-objective optimization of energy storage materials under the performance management system of supply chain joint operation is based on the statistical analysis of energy storage materials under the performance management system of supply chain joint operation. The method of big data information sampling is used, this paper analyzes the prior data of power storage materials under the joint supply chain operation performance management system. Assuming that the total number of nodes sampled by power storage materials under the joint supply chain operation performance management system is V, when D, the optimal grid parameter distribution model of multi-objective optimal distribution of power storage materials under the joint supply chain operation performance management system can be described as:

where \(\beta\) is the demand response of electric power materials, \(s(t)\) is the distribution set of the current situation of electric power materials logistics and distribution management of Company A, and \(i(t)\) is the current of the statistical inquiry of inventory information. The NSGA-II optimization analysis method is adopted to conduct three kinds of inventory control of electric power storage materials under the joint supply chain operation performance management system, including inductive cycle inventory, inventory coding, and computerized inventory. The dynamic integration method of electric power storage materials under the joint supply chain operation performance management system is carried out [ 13 ] based on the game correlation analysis method, and the output optimization characteristics are obtained.

where \(\alpha\) is the monthly material demand parameter of each project site, \(r(t)\) is the dynamic distribution set of material storage network layout, and \(s(t)\) is the autocorrelation characteristic component. An intelligent planning model for multi-objective optimization of power storage materials under the joint supply chain operation performance management system is established. Considering the following multi-input characteristic distribution, statistical analysis of power storage materials set under the joint supply chain operation performance management system is carried out to improve the multi-objective optimization ability of power storage materials set business.

3.2 Multi-objective Optimization Output of Power Storage Business

The demand of power materials and the supply of warehousing materials are not always in a completely matched state based on the objective reality that both the supply and demand sides of power materials are uncertain, but it keeps a stable dynamic balance according to the actual changes at both ends of supply and demand. To realize the management optimization of power material logistics and distribution in Company A, it is an extremely important optimization part to improve the matching degree between supply and demand of storage materials. The short-term deviation fluctuation between supply and demand can be kept in a minimum range by improving the matching degree between supply and demand of power materials, and the stable and efficient operation of power material logistics and distribution can be guaranteed. Therefore, improving the matching degree between supply and demand of warehousing materials is listed as one of the main optimization objectives.

The duration of power supply is an important factor that determines the efficiency of logistics distribution. To optimize logistics distribution management and improve efficiency, the first task is to shorten the duration of power supply as much as possible. The circulation of materials involves many links, such as purchasing, warehousing, material selection, packing and delivery, etc. This means that to achieve the optimization goal of shortening the supply time of electric power materials, we must focus on the overall situation of material logistics and distribution, refine the optimization goal into each circulation link by layers, and take targeted optimization measures to achieve the overall optimization goal.

Establish the reliability characteristic distribution function of multi-objective optimization of power storage materials under the joint supply chain operation performance management system, and realize the multi-objective optimization of power storage materials under the joint supply chain operation performance management system [ 2 ]. The mathematical expression of the quadratic programming problem is as follows:

where \(C_{ij}\) is the target regression distribution parameter of power storage materials under the joint supply chain operation performance management system. Combined with the association rule scheduling, the optimal calculation formula of power storage materials scheduling under the joint supply chain operation performance management system is defined as \(10^{{\vec{D}_{ij} }} = (10^{{D_{ij1} }} , \ldots ,10^{{D_{iju} }} )\) . The feature fusion analysis method is used, the statistical feature information of power storage materials under the joint supply chain operation performance management system is as follows

The above formula represents the resource scheduling set of power storage materials planning under the joint supply chain operation performance management system. Using spatial planning methods, the multi-objective optimization model for energy storage materials under the joint supply chain performance management system is:

Based on this, a multi-objective optimization model for energy storage materials was constructed under the intelligent joint supply chain operation performance management system. NSGA-II is a widely used metaheuristic multi-objective algorithm with advantages such as good solution set convergence and fast running speed.

The use of NSGA-II algorithm can help optimize the inventory control strategies for three types of energy storage materials in the joint supply chain performance management system, to achieve the best performance indicators under different constraint conditions. By optimizing and solving, the optimal inventory management plan can be found. The optimization solution process of NSGA-II algorithm is as follows:

(1) Generate initial population: \(N\) is the number of individuals in the population, and randomly produce initial population \(P_{0}\) .

(2) Fast non-dominated sorting: The fast non-dominated sorting of individuals in the population is achieved through non-dominated sorting algorithm \(O\left( {gN^{2} } \right)\) . This algorithm records the number of individuals in the population as \(N\) and the target number as \(g\) . The algorithm runs as follows: first, extract the number of advantages of each solution in the entire solution space and set it as the first layer. Then extract an individual in the first layer, traverse its corresponding dominance set, and subtract 1 from the number of dominance for each individual. Finally, if the number of advantages is 0, the second layer is obtained. Repeat this loop until all layers are obtained.

(3) Crowding distance calculation: Set as the crowding distance of bounded individuals, calculate the crowding degree of other individuals using the following formula.

where \(\delta_{d} \left( l \right)\) is the crowding distance of individual \(l\) , \(d\) is the level of individual \(l\) , \(n\) is the number of individuals \(d\) , \(E_{s}\) is the value of the \(s\) -th objective function, \(E_{s}^{\max }\) is the maximum value of the \(s\) -th objective function, and \(E_{s}^{\min }\) is the minimum value of the \(s\) -th objective function.

(4) Selection: Based on the calculation results of crowding degree and ranking, all individuals in the population will be assigned two attributes: non-dominated order and crowding distance. When the non-dominated order of individuals is equal, it is determined that individuals with larger crowding distance are better.

(5) Elite strategy: Merge parent population \(P_{n}\) and offspring population \(Q_{n}\) , establish a temporary population, and set the number of individuals in this population to 2 \(N\) . Calculate the crowding distance of temporary populations through fast non-dominant sorting and rank them. Extract \(N\) best individuals and set them as the next parent population \(P_{n + 1}\) .

(6) Selection, crossover, mutation: Generate a new offspring population \(Q_{n + 1}\) through genetic operators (selection, crossover, mutation).

(7) Repeat steps (2) to (4) until the maximum number of iterations set by the algorithm is reached, and obtain the multi-objective optimization strategy for energy storage materials.

4 Simulation Analysis

4.1 simulation preparations.

To verify the application performance of this method in the evaluation and scheduling of power storage materials under the joint supply chain operation performance management system, a simulation test analysis is carried out, taking Company A as an example for empirical analysis. Company A was established on March 1, 2002, which is a municipal company under a provincial electric power corporation, and its main business is to provide safe and stable power supply services. Its business scope includes power grid operation and management, peak regulation and frequency modulation power plant operation and management; purchase and sale of electric power, electric power grid crossing and trading services, electric power engineering construction; operating information industry related to electric power, electric power equipment, sales of electric power equipment, etc. There are 122 substations under its jurisdiction, including 3500 kV substations, 21 220 kV substations and 98110 kV substations. The main capacity is 29.689 million KVA, the transmission line is 27.519 km, and the total number of customers is as high as 1.6514 million. In terms of organizational structure, Company A has ten functional departments. It has jurisdiction over 24 township power supply sub-bureaus, of which the Ministry of Science and Technology is a newly established department, whose main responsibility is to undertake the power material management and information system construction delegated by the provincial head office. At present, there are 3176 on-the-job employees, with an average age of 37.8 years. The proportion of middle and senior technical talents is 66.6%, of which information talents account for 5.3% of middle and senior technical talents. The overall composition of the organization members is relatively young, and their quality and skill level are high. The whole chain of material distribution includes ten processes, such as “collecting demand, planning, issuing shipment tasks, picking and stocking, packing and delivering, issuing delivery tasks, selecting people and vehicles, material handover, delivery in transit, receiving and receiving goods”, among which the processes involve three independent platform systems, namely, production demand, warehousing management, and delivery management, covering demand approval, plan approval, and delivery approval. According to this, the number of nodes for power storage materials evaluation information sampling is 480, the length of data sampling is 1200, and the dimension of embedded scheduling is 12.

4.2 Setting Simulation Parameters

Parameters of the experimental algorithm were set before the experiment to avoid the impact of different values of model parameters on model performance and thus on the reliability of experimental results, as shown in Table  1 .

Parameters of the multi-objective optimization model of power storage materials based on NSGA-II algorithm were set according to the values in the table to ensure the performance of the model to a certain extent.

4.3 Collection of Electrical Storage Material Information

Energy storage material information is collected according to the above parameter settings, and the results are shown in Fig.  1 .

Information collection of electric power storage materials

Rough vector feature distribution set multi-objective optimization method is used to decompose and optimize the features of electric power storage materials under the joint supply chain operation performance management system, and NSGA-II optimization analysis method is used to carry out three kinds of inventory control of electric power storage materials under the joint supply chain operation performance management system: inductive cycle inventory, inventory coding, and computerized inventory. As the upstream node of the distribution chain, the storage link is the supplier of electric power materials. As the downstream node of the distribution chain, the production link is the publisher of material requirements, while the transportation link, it as the intermediate node to undertake material storage and production site, mainly undertakes the task of material transportation. Under the current material management mode, the front-line production departments of power transformation, transmission and distribution, such as operation and maintenance, and overhaul, release material requirements according to the production requirements and the situation of the production site. The warehousing department of the company, after receiving the material requirements, check whether the materials in the warehouse can meet the demand, then arrange the picking and delivery of the materials, and at the same time, release the transportation task information to the third party logistics, and entrust it to be responsible for the transportation of the materials to ensure the timely arrival of the goods. Therefore, the demand information is not shared in the three links of warehousing, transportation, and production, but which is transmitted to the transportation link after information processing in the warehousing link. This means that when the production demand changes, the adjustment of distribution and transportation must wait for the instructions from the warehouse before the transportation scheme can be adjusted. Therefore, the autocorrelation distribution of multi-objective optimization output can be obtained using the method in this paper, as shown in Fig.  2 .

Auto-correlation distribution of multi-objective optimization output

Company A has planned 67 routes for multi-point distribution of power materials on the basis of route optimization, connecting 1 first-class warehouse with 24 working points in towns and streets. The route selection of multi-point distribution is random, which does not pay attention to the adaptability between vehicle selection, distribution route and material scale, and lacks scientific planning, resulting in overlapping of some distribution routes, low utilization rate of vehicle load space, high empty vehicle driving rate, and low overall distribution efficiency.

4.4 Analysis of Simulation Results

Based on the above data, the convergence curve of target optimization can be obtained using this method and traditional methods, and the convergence can be analyzed, as shown in Fig.  3 .

Multi-objective optimal dispatching output of power storage materials

According to the analysis in Fig.  3 , this method can effectively realize the multi-objective optimization scheduling of energy storage materials under the joint supply chain operation performance management system, and its convergence performance is higher, reaching the optimal convergence in 65 iterations, while the traditional method reaches the better convergence state in 460 iterations. Compared with the two methods, the proposed method converts faster than the traditional method. The number of iterations is reduced by 395 times. Therefore, it shows that the method in this paper improves the convergence speed and has better optimization scheduling ability of energy storage materials. This is because the method in this paper adopts the rough vector feature distribution set multi-objective optimization method to decompose and optimize the characteristics of electric storage materials in the joint supply chain operation performance management system, thus improving the scheduling capability.

The accuracy of multi-objective optimization of energy storage materials under the joint supply chain operation performance management system of different methods was tested, and the performance of the proposed method was further analyzed on the basis of the above experimental analysis. The experimental results are shown in Table  2 .

According to the data in Table  2 , the precision probability of multi-objective optimization of energy storage materials for the three methods is relatively high, reaching more than 0.800. As the number of iterations increases, the precision probability of multi-objective optimization of energy storage materials gradually increases. When the number of iterations reaches 80, the precision probability of multi-objective optimization of energy storage materials for the method proposed in this paper reaches 1.000. At this time, the accurate probability of multi-objective optimization of energy storage materials for Ref. [ 3 ] method is 0.945, and the accurate probability of multi-objective optimization of energy storage materials for Ref. [ 5 ] method is 0.921. Compared with the accurate probability of the three methods, it can be seen that the accurate probability of the method in this paper is more than 0.055 higher than that of the method in reference. Under the joint supply chain operation performance management system, the method effectively improves the accurate probability of multi-objective optimization of energy storage materials, and has a good power storage material scheduling capability.

5 Conclusion

Research on a multi-objective optimization model for energy storage materials based on the NSGA-II algorithm was performed. The association rule set of energy storage materials was extracted, and the multi-objective optimization method of rough vector feature distribution set was used to decompose and optimize the characteristics of energy storage materials. Using the NSGA-II algorithm, three types of inventory control, namely circular inventory, inventory coding, and computer inventory, were summarized for inventory materials under the performance management system of joint supply chain operations. By combining the positive regression learning method with organizational operational performance, multi-objective optimization decision-making for energy storage materials has been achieved. Through experimental analysis, it can be seen that under the joint supply chain operation performance management system, this method can reach the optimal convergence state in 65 iterations, effectively improving the convergence speed. The accurate probability of multi-objective optimization of energy storage materials can reach 1000 in 80 iterations, which means the probability can reach 100%. The results show that this method can effectively improve the accuracy probability, thereby enhancing the scheduling ability of energy storage materials and having good scheduling performance. Although the experimental results indicate that the method achieves good performance within a certain number of iterations, there may be limitations in the experimental verification process, such as the selection of datasets and the setting of experimental environments. Therefore, in the future, in-depth discussions will be conducted on these issues to further improve the effectiveness and reliability of this method.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

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State Grid Hebei Electric Power Co., Ltd., Shijiazhuang Power Supply Branch, Hebei, 050000, China

Zixi Hu, Shuang Liu & Xiaodong Geng

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State Grid Shijiazhuang Luancheng District Electric Power Supply Company, Hebei, 051430, China

State Grid Pingshan Electric Power Supply Company, Hebei, 050400, China

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Hu, Z., Liu, S., Yang, F. et al. Research on Multi-objective Optimization Model of Power Storage Materials Based on NSGA-II Algorithm. Int J Comput Intell Syst 17 , 76 (2024). https://doi.org/10.1007/s44196-024-00454-3

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Received : 24 May 2023

Accepted : 12 March 2024

Published : 02 April 2024

DOI : https://doi.org/10.1007/s44196-024-00454-3

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