Three-level Network Research Articles

Design and Site Selection of Reverse Logistics Network for Iron and Steel Enterprises from the Perspective of Green Supply Chain

The iron and steel industry is not only one of the most important components of China's national economy, but also a typical resource-and-energy-intensive industry. Under the background of "Carbon Peaking and Carbon Neutrality Goals", it is of great significance for the iron and steel industry to improve the green closed-loop supply chain and develop circular economy. From the perspective of green supply chain, this paper puts forward the three-level network structure of waste steel reverse logistics based on the present situation of waste steel recycling in China, and uses k-means clustering algorithm and accurate center of gravity method to select locations for the primary and secondary nodes. The purpose of this paper is to provide a basis for iron and steel enterprises to carry out network optimization of reverse logistics.

Research of the optimization problem of structure hierarchical communication network with changing its parameters

The article is devoted to the study of the problem of optimizing the hierarchical structure of a multicommodity communication network with discrete flows when changing its important parameters, such as the capacity of network arcs in transport blocks and the size of the transport block for transportation of the discrete small-lot cargo or of the data transmission in a digital communication network. The network has three levels of hierarchy – a backbone, a zonal and an internal and four types of nodes - backbone nodes of the first, second and third types, forming the backbone and zonal levels of the network, and nodes of the fourth type, which subordinate to each backbone node and forming the internal levels of the network. Types of nodes differ from each other in terms of functionality. The main task of the study is to establish how the structure of the backbone network changes (the number and location of backbone nodes of the first, second, and third types), the flow processing and distribution scheme, and the technical and economic indicators of the network's functioning for different values of its parameters. The principles of organization of sorting and distribution of flows in a three-level network and its mathematical model are given. A mathematical model of the optimization problem of the backbone network structure and flow sorting and distribution scheme is formulated. Algorithms for solving the problem are based on the discrete analogue of the local descent method proposed by the authors earlier, when the neighborhoods of the metric space of possible solutions are chosen based on heuristic considerations, taking into account the specifics of the problem being solved. Computer modeling of the problem on a network containing 10 nodes at the specified change in the both parameters is carried out. The modeling was carried out on the example of the transport network of cargo transportation using a computer program that is part of the instrumental software of the Information and Analytical Decision Support System (IA DSS), which is being developed at the Institute of Telecommunications and Global Information Space of the National Academy of Sciences of Ukraine. An experimental study of solution the problem showed that the structure of the network is weakly dependent on the change in the carrying capacity of the arcs and the size of the transport block. The proposed computer technology for solving problem when the network parameters are changed allows you to interactively modeling various options of a network, changing the topology, hierarchical structure, flows, parameters and constraints of the model and from the set of the obtained solutions to choose a best option, taking into account the selected a goal function and the accepted constraints; calculate preliminary technical and economic indicators of the network's functioning, estimate the cost of additional resources and plan the amount of investment required for the modernization and construction of its structural elements, which ultimately makes it possible to increase the efficiency functioning of the network by optimizing use of its resources and reducing the operating costs for the processing and transportation of flows.

Study on primary screening technique for children with autism spectrum disorder

To explore screening tools for children with autism spectrum disorder (ASD), which are convenient for primary hospitals, it can provide basic data for formulating ASD prevention policies. This was a cross-sectional study by cluster sampling. Huyi District and Xincheng District were extracted for investigation in Xi'an City. From July 2021 to September 2022, all children aged from 3 months to 36 months who live in the two districts were subjected to primary screening. The child care physician used the routine screening tool "warning signs checklist for screening psychological, behavioral and developmental problems of children" and cartoon pictures of "early high-risk warning signs of autism", the children who were positive in the initial screening were referred to the district level maternal and child health hospital for re-screening, and those who were positive in the re-screening were referred to Xi 'an Children's Hospital for diagnosis. The results showed that a total of 17 905 children aged from 3 months to 36 months were initially screened in the two districts, including 10 588 children aged from 18 months to 36 months, 50 children who were positive in the initial screening and 50 children who were re-screened. 23 children (18 boys and 5 girls) were diagnosed with ASD. The prevalence rate of ASD in children was 2.17‰ (95% confidence interval:1.29‰-3.06‰). 42 children were positive for "warning signs checklist" at the preliminary screening, and 19 were confirmed as ASD. 27 children were positive for "cartoon pictures" in the preliminary screening, and 23 were confirmed with ASD. The "cartoon pictures" in the preliminary screening and diagnosis of consistent rate was higher than the "warning signs checklist", two kinds of screening methods comparison were statistically significant difference in the odds of consistent (χ2=11.01, P=0.001). In conclusion, relying on the three-level network of maternal and child health care, it is conducive to the whole process management of screening and diagnosis of children with ASD, and to guide the formulation of prevention policies. The cartoon pictures of "early high-risk warning signs of autism" can assist the identification of children with ASD based on the "warning signs checklist", which is simple, effective and suitable for promotion in the community health care.

Assessing Digital Teaching Competence: An Approach for International Chinese Teachers Based on Deep Learning Algorithms

Digital Teaching Competency (DTC) is an important skill in the professional development of international Chinese language teachers. This study developed a new deep learning-based assessment model of DTC for international Chinese language teachers. To build this model, the researchers first collected data on DTC from 221 international Chinese language teachers at different levels in 26 countries to ensure that these sample data are representative; secondly, clustering and feature dimensionality reduction techniques were used to preprocess the data and constructed the Siamese architectural model; and finally, the researchers confirmed through experimental validation and expert evaluations that the model has a high accuracy rate of 96.33%. The innovation of this model is to use the traditional three-level network as an improved constructed digital twin network, so as to extract some features that are more accurate and to characterize those features that are most predictive. The improved network is able to extract all the inputs globally and also locally that are of most interest to the user/researcher, the final prediction results are weighted, and those weighted results are used as the final prediction output of the model. This model not only provides systematic and adaptive support for improving teachers' DTC, but through the comprehensive result output, it can provide targeted improvement strategies for teachers to improve their DTC.

PRIDNet based Image Denoising for Underwater Images

Underwater image enhancement has become a popular research topic due to its importance in aquatic robotics and marine engineering. However, the underwater images frequently experience signal-dependent speckle noise when transmitting and acquiring data, which can limit certain applications such as detection, object tracking. In the recent years, the existing underwater image enhancement algorithms efficiency has been analysed and evaluated on a small number of carefully chosen real-world images or synthetic datasets. As such, it is challenging to predict how these algorithms might function with images acquired in the wild under various circumstances. This paper introduces a new solution for noise removal from underwater images called Pyramid Real Image Noise Removal Network (PRIDNet) with patches.PRIDNet is a three-level network design using image patches. The tests were carried out on a dataset of actual noisy images demonstrate that, in terms of quantitative metrics, our proposed denoising model reduction performs better with the exixting denoisers. We determine the effectiveness and constraints of existing algorithms using benchmark assessments and the suggested model, offering valuable information for further studies on underwater image enhancement.

Optimizing the ground intra-city express delivery network: An integrated multiple centrality assessment, multi-criteria decision-making, and multi-objective integer programming model

Optimization of an intra-city express delivery network from three to two levels is of great interest to suppliers and customers for reducing costs and improving service efficiency. One feasible solution is to identify critical nodes in the three-level network and upgrade them as transshipment facilities in the two-level one. However, traditional optimization models seldom combine empirical business data, composite metrics, and objective evaluation rules. We proposed an approach integrating empirical data, multi-criteria decision-making methods based on the real-world application of the SF Express Chengdu branch. We also developed a mathematical optimization model using statistical and operations management techniques combined with logistics expertise for a location decision. First, the appropriateness of each service point as a candidate transshipment facility is evaluated from internal and external perspectives by applying multiple centrality assessment from complex network theory and fuzzy Technique for Order Preference by Similarity to an Ideal Solution, respectively. Second, 16 candidate transshipment facilities are selected by combining these two ways. Then, a multi-objective integer programming model is built to obtain the optimal number, locations of transshipment facilities, and the corresponding service points covered by each transshipment facility. Using this multi-methodologic approach, we show that the optimized two-level network is economically feasible and simply applicable, with the total cost and average delivery time reduced by 18.41% and 6 h, respectively. This article is of practical significance and provides an important reference for optimizing ground express service networks for other large cities.

WAYS TO EFFECTIVELY ADDRESS PROBLEMS EXISTING IN THE URBAN PASSENGER TRANSPORT SYSTEM

At present, public transport needs to be managed using the different models, which will take into account health problems, passenger transport problems, refinement of technical parameters of buses and their adaptation to urban operating conditions, which would be one of the preventive measures in the context of combating the coronavirus pandemic. The article discusses the issues of optimizing the routeing scheme of buses and minibuses in the conditions of a three-level transport network in large cities. Measures for the performance of the city bus routes have been developed. It has been established that the qualification of a driver and the selection of urban passenger vehicles are central issues in terms of fuel efficiency and reducing the number of harmful substances in exhaust gases.

Research on Solving Postdisaster Material Distribution and Scheduling with Improved NSGA-II Algorithm.

After the occurrence of major sudden disasters, the dispatching and distribution of disaster relief materials are particularly important, but in the process of distribution, there may be excessive distribution of similar emergency materials, unbalanced distribution volume of relief materials in different disaster-affected points, high distribution cost, and low effective distribution rate. In order to solve the above problems, based on the application of big data, this paper proposes a three-level network postdisaster material scheduling and distribution model and an improved NSGA-II algorithm. The model takes the loss degree of the disaster area and the dynamic change rate of the demand for postdisaster relief materials as the constraints, takes the demand prediction of postdisaster relief materials, the optimization of distribution path, distribution nodes, and the satisfaction of victims as the objectives, and designs the sample average approximation method and the improved NSGA-II algorithm. In order to verify the effectiveness of the proposed model and strategy, through the comparative experiment of NSGA and PSO, it can be seen from the experimental results that the three-level network allocation model and the improved NSGA-II algorithm (nondominated sorting genetic algorithm II) proposed in this paper can not only solve the existing postdisaster relief material allocation and scheduling problem but also reduce the space-time complexity of the problem.

The vulnerability of ecosystem structure in the semi-arid area revealed by the functional trait networks

The ecosystems were characterized by complex, nonlinear interactions determined by different plant functional traits. The characteristics of the multiple relationships between ecosystem functional traits affected the vulnerability to drought. A three-level network analysis on instead of the network metrics, relationships among inter-components, and essential traits was conducted in dryland ecosystems of China. The new network of functional traits included leaf, root, and biomass components was constructed to simulate different aridity conditions. Results show that the multiple relationships of functional traits that co-regulated ecosystem biomass differ along an aridity gradient. The highest network modularity and degree centrality were observed in the semi-arid ecosystems indicating low integration and high sensitivity of semi-arid ecosystems (269% and 23.7% higher than in dry sub-humid site, and 142% and 51.1% higher than arid sites). The leaf quantity strongly affected the connection between functional traits at the semi-arid zone. The semi-arid areawas found to have relatively low resistance to environmental change because of low integration and high sensitivity of the ecosystem structure at that site. An increase of degree centrality of the root traits and trade-off relationships between roots and leaves indicated greater allocation of resources by vecgetation to underground components by the arid ecosystems to increase water absorption. The study reveals the complex relationships between leaf, root, and biomass components, and the essential traits of the ecosystem. It enhanced understanding of the vulnerability of semi-arid ecosystems to environmental change.

Relation-aware Heterogeneous Graph Transformer based drug repurposing

Drug repurposing refers to discovery of new medical instructions for existing chemical drugs, which has great pharmaceutical significance. Recently, large-scale biological datasets are increasingly available, and many graph neural network (GNN) based methods for drug repurposing have been developed. These methods often deem drug repurposing as a link prediction problem, which mines features of biological data to identify drug–disease associations (i.e., drug–disease links). Due to heterogeneity of data, we need to deeply explore heterogeneous information of biological network for drug repurposing. In this paper, we propose a Relation-aware Heterogeneous Graph Transformer (RHGT) model to capture heterogeneous information for drug repurposing. We first construct a drug–gene–disease interactive network-based on biological data, and then propose a three-level network embedding model, which learns network embeddings at fine-grained subtype-level, node-level and coarse-grained edge-level, respectively. The output of subtype-level is the input of node-level and edge-level, and the output of node-level is the input of edge level. We get edge embeddings at edge-level, which integrates edge type embeddings and node embeddings. We deem that in this way, characteristics of drug–gene–disease interactive network can be captured more comprehensively. Finally, we identify drug–disease associations (i.e., drug–disease links) based on the relationship between drug–gene edge embeddings and gene–disease edge embeddings. Experimental results show that our model performs better than other state-of-the-art graph neural network methods, which validates effectiveness of the proposed model.

A novel RUL prognosis methodology of multilevel system with cascading failure: Subsea oil and gas transportation systems as a case study

Cascading failure has a great negative impact on the operation of multilevel systems. Although the frequency of this kind of failure is lower than that of general failure, it may cause outage and considerable human and economic losses. In this paper, a novel modeling methodology of cascading failure based on position importance and function importance is proposed by using dynamic Bayesian networks, and the remaining useful life (RUL) of multilevel systems considering cascading failure is estimated. By detecting the working state of the nodes, the position and function importance of the nodes are determined, and the performance of the next layer of related nodes is calculated. Through calculating iteratively to the last level, the number of failure nodes is finally determined, and the overall performance of the multilevel systems is evaluated. A subsea transportation system with three-level network and four nodes in each level is used to demonstrate the application of the proposed methodology, and the feasibility of the methodology is analyzed. The results show that the RUL of the systems is significantly reduced when considering the cascading failure, which is quite different from the degradation of the non-cascading failure mode.

Affordance in Socio-Material Networks: A Mixed Method Study of Researchers' Groups and Analog-Digital Objects.

In this paper, we argue that we can better understand the relationship between social interaction and materiality by linking qualitative analysis of analog and digital practices, adopting Basov's model of socio-material networks. Our research questions turn about the interrogation of how social links distress the usage of analog and digital objects by researchers. We consider scientific networks with the relationship between researchers and their tools as a three-level social material network. It sheds light on how different types of researchers position their engagement with analog and digital materiality over time and its affordance and emotional attachment. This study contributes to the understanding of researchers' practices that involve new and old techniques and specific and not-specific tools.

The Use of a Three-in-One Practice-Management-Innovation Training Model in the Construction of an Infection Control Team.

ObjectiveThis study aims to explore the role of a three-in-one practice, management, and innovation training model (also called as three-in-one practice-management-innovation training model) in the construction of an infection control team.MethodsThis study retrospectively analyzed the position structure, mastery of professional knowledge, and working methods of the full-time and part-time personnel of the Changzhou Cancer Hospital, compared the training content of Jiangsu Hospital Infection Control Center with the actual situation of the hospital, and formulated and implemented a three-in-one practice-management-innovation training model. First, the team members were selected for the construction and management of the Hospital Infection Management Department according to the relevant responsibility and management requirements, and their learning and mastery of the basic knowledge and skills concerning infection control were completed based on their professional roles. In line with the regulations of the hospital and department, full-time personnel were ensured of having the opportunity to participate in provincial- and municipal-level academic exchanges and then learn from each other, through collaboration between doctors and nurses, how to exercise basic management skills. At the same time, a fair competitive incentive mechanism was established through the three-level network of the hospital infection committee, the hospital infection management department, and nosocomial infection management department to implement innovative project-based management and cultivate an awareness of hospital infection control in all employees.ResultsThe professional structure of the full-time infection control personnel has been optimized, the awareness of the infection control team concerning active participation in practice has gradually increased, and infection control management and innovation has been significantly improved.ConclusionAfter the selection of an infection control management team and the delivery of well-planned training, the quality of infection control management has improved.

Research on Intelligent Comprehensive Support Technology and Application of Complex Equipment

At present, the complex equipment logistics support system often faces the situation of local logistics support capacity surplus or insufficient, which presents the disadvantages of high cost and low efficiency. The concept of equipment autonomous logistics support and perception response support emphasizes the importance of network as the center, aiming at the crucial problems of logistics support management, it puts forward that equipment logistics support management must realize full-dimension, globally controllable, wholly-owned, and end-to-end seamless integration from the equipment platform to the entire support architecture. A three-level network architecture is designed to realize real-time perception of panoramic situation through equipment technology status sensor and resource sensor, and to carry out scheduling and management through decision support system, and to organize coordinated operation of logistics manpower, support resources and support facilities.

Selective serotonin reuptake inhibitors, and serotonin and norepinephrine reuptake inhibitors for anxiety, obsessive-compulsive, and stress disorders: A 3-level network meta-analysis.

BackgroundAnxiety, obsessive-compulsive, and stress-related disorders frequently co-occur, and patients often present symptoms of several domains. Treatment involves the use of selective serotonin reuptake inhibitors (SSRIs) and serotonin and norepinephrine reuptake inhibitors (SNRIs), but data on comparative efficacy and acceptability are lacking. We aimed to compare the efficacy of SSRIs, SNRIs, and placebo in multiple symptom domains in patients with these diagnoses over the lifespan through a 3-level network meta-analysis.Methods and findingsWe searched for published and unpublished randomized controlled trials that aimed to assess the efficacy of SSRIs or SNRIs in participants (adults and children) with diagnosis of any anxiety, obsessive-compulsive, or stress-related disorder in MEDLINE, PsycINFO, Embase, and Cochrane Library from inception to 23 April 2015, with an update on 11 November 2020. We supplemented electronic database searches with manual searches for published and unpublished randomized controlled trials registered in publicly accessible clinical trial registries and pharmaceutical companies’ databases. No restriction was made regarding comorbidities with any other mental disorder, participants’ age and sex, blinding of participants and researchers, date of publication, or study language. The primary outcome was the aggregate measure of internalizing symptoms of these disorders. Secondary outcomes included specific symptom domains and treatment discontinuation rate. We estimated standardized mean differences (SMDs) with 3-level network meta-analysis with random slopes by study for medication and assessment instrument. Risk of bias appraisal was performed using the Cochrane Collaboration’s risk of bias tool. This study was registered in PROSPERO (CRD42017069090). We analyzed 469 outcome measures from 135 studies (n = 30,245). All medications were more effective than placebo for the aggregate measure of internalizing symptoms (SMD −0.56, 95% CI −0.62 to −0.51, p < 0.001), for all symptom domains, and in patients from all diagnostic categories. We also found significant results when restricting to the most used assessment instrument for each diagnosis; nevertheless, this restriction led to exclusion of 72.71% of outcome measures. Pairwise comparisons revealed only small differences between medications in efficacy and acceptability. Limitations include the moderate heterogeneity found in most outcomes and the moderate risk of bias identified in most of the trials.ConclusionsIn this study, we observed that all SSRIs and SNRIs were effective for multiple symptom domains, and in patients from all included diagnostic categories. We found minimal differences between medications concerning efficacy and acceptability. This three-level network meta-analysis contributes to an ongoing discussion about the true benefit of antidepressants with robust evidence, considering the significantly larger quantity of data and higher statistical power when compared to previous studies. The 3-level approach allowed us to properly assess the efficacy of these medications on internalizing psychopathology, avoiding potential biases related to the exclusion of information due to distinct assessment instruments, and to explore the multilevel structure of transdiagnostic efficacy.

INVESTIGATION OF THE PROBLEM OF OPTIMIZATION OF THE HIERARCHICAL STRUCTURE OF A SPARSE AND DENSE COMMUNICATION NETWORK

The article is devoted to the study of the optimization problem for the hierarchical structure of a multicommodity communication network with discrete flows and parameters when its density changes (the ratio of the number of network arcs to the maximum possible number of arcs for a given number of nodes in the network). The network has three levels of hierarchy — a backbone, a zonal and a internal and four types of nodes — backbone nodes of the first, second and third types, forming the backbone and zonal levels of the network, and nodes of the fourth type, which subordinate to each backbone node and form the internal levels of the network. The types of nodes different from one another in functionality. The main task of the study is to establish how the structure of the backbone network changes (the number and location of backbone nodes of the first, second and third types), the scheme of processing and distribution of flows and technical and economic indicators of the network's functioning for various degrees of its density. The principles of organizing the sorting and distribution of flows in a three-level network and its mathematical model are given. A mathematical model of the problem of optimizing the structure of the backbone network and the schemes of sorting and distribution of flows is formulated. The algorithms for solving the problem are based on the discrete analogue of the local descent method proposed earlier by the authors, when the neighborhoods of the metric space of possible solutions are chosen from heuristic considerations, taking into account the peculiarities of the problem being solved. Computer modeling of the problem on a homogeneous network containing 100 nodes with a change in the degree of nodes from 2 to 99 is carried out. The modeling was carried out on the example of a road transport network for the transportation of cargo using a computer program, which is part of the instrumental software of the Information and Analytical Decision Support System (IA DSS), which is being developed at the Institute of Telecommunications and Global Information Space of the National Academy of Sciences of Ukraine. An experimental study of the solution to the problem showed that the best technical, economic and operational indicators of its functioning are achieved with a degree nodes from 9 to 14, when high network connectivity is ensured, and is significantly reduced the average and maximum time of delivery of cargos to recipients. The proposed computer technology for solving problem with changing network density allows you to interactively modeling various options of a network , changing the topology, hierarchical structure, flows, parameters and constraints of the model and from the family of the resived results choose the best option, taking into account the selected a goal function and the accepted constraints; calculate preliminary technical and economic indicators of the network's functioning, estimate the cost of additional resources and plan the amount of investment required for the modernization and construction of its structural elements, which ultimately makes it possible to increase the efficiency functioning of the network by optimizing use of its resources and reducing the operating costs for the processing and transportation of flows.

Identifying optimal location of ecotourism sites by analytic network process and genetic algorithm (GA): (Kheyroud Forest)

The development of ecotourism as one of the most economical ecosystem services requires the evaluation, planning, and management of sustainable development. By considering the challenges facing the management of touristic zones, especially in forested areas, the need to use an integrated approach to optimize “recreational activities” versus “conservation of natural resources” is inevitable. Therefore, in this study location of appropriate areas for developing ecotourism was analyzed with the use of combined analytic network process (ANP) and genetic algorithm (GA). A three-level network comprising the target, five main clusters (biodiversity, climatic and climatic resources, soil and geology, topography, and socioeconomic factors), and sub-selection criteria in the studied forest areas, are designed. Subsequently, standardized and related maps were provided as selection criteria in the GIS. Accordingly, the genetic algorithm was found to consider feasible sites and 10 optimal responses including 5 appropriate and 5 inappropriate sites. In order to ensure the optimality of the proposed GA, the desirable ratio between the superior and inappropriate sites and the comparison of the results with the zones obtained by the WLC method was used. The comparative results confirmed the efficiency of GA for identifying appropriate sites for ecotourism.

Autonomous learning of foreign language based on facial emotion recognition and cloud computing

Due to the limitations of the learning environment and unguided guidance, students’ autonomous learning of foreign languages after class is not effective. In order to improve the efficiency of autonomous learning of foreign languages, this paper builds a foreign language self-learning system based on facial emotion recognition algorithm and cloud computing platform. Moreover, this paper uses emotion recognition algorithms to identify students’ status and guide them to improve students’ autonomous learning and improve the system’s operating efficiency through cloud computing platforms. In addition, this article combines the needs of autonomous learning to perform facial emotion matching and builds the corresponding functional modules of the system according to the requirements of autonomous learning and designs a sophisticated three-level network structure to achieve a balance between detection performance and real-time performance. In order to verify the performance of the system, an experiment was carried out through the accuracy rate of student’s autonomous state emotion recognition and the English improvement of students’ autonomous learning. The research results show that the foreign language autonomous learning system constructed in this paper has good performance.

Three-level network analysis of the North American natural gas price: A multiscale perspective

With the US being the largest natural gas producer, the North America formed a mature and leading natural gas market from which emerging markets can learn to develop themselves. It also influences the global market and under various factors, the market presents multiscale characteristics. We explore North American natural gas price, from 1997 to 2018, using wavelet transform and multiscale fluctuation mode network (MFMN) where nodes are a set of fluctuating states extracted from wavelet power and edges are the transmission relationships between the set of states. The multiscale characteristics are analyzed in three levels: macro-network, meso-community and micro-motif. From macroscopic, 131 out of 474 nodes are identified as major contributors of price fluctuation states in the market by weighted out-degree and transmit nodes are identified by betweenness centrality. From mesoscopic, we find that price fluctuation states in the market could be divided into 16 groups and it could be the result of middle- or long-term factors, such as season, weather and policy. From microscopic, 13 directed three-node motifs are detected to present different price fluctuation in continuous short period. And there exist price fluctuation patterns in the market by exploring the community preference for motif containment and motif preference for characters.

A modified column generation heuristic for hybrid flow shop multiple orders per job scheduling problem

With a comprehensive consideration of multiple product types, sequence-dependent setup time constraints and two different processing modes in wafer fabrication process, a scheduling model of multiple orders per job in a hybrid flow shop with an objective function of minimising total completion time of the system is developed. On the basis of the description, a new column generation algorithm based on a three-level (job-product-machine) disjunctive network flow is put forward. Furthermore, in order to improve degradation effects of the algorithm, a Lagrangian relaxation with sub-gradient optimisation is integrated into a frame of the column generation algorithm. Therefore, a modified column generation algorithm as a combination of Lagrangian approach and column generation algorithm is proposed. Finally, theory analysis and simulation experiments demonstrate that the presented algorithm is valid and feasible.