Abstract

With the dynamic sharing of global resources shifted from the independent production of a single enterprise to and the development of collaborative manufacturing, today’s manufacturing industry has collaborative production among multiple enterprises. This paper extends the optimization method of the multienterprise dynamic equipment collaborative scheduling system with the dynamic manufacturing network theory approach, combining the neural network system and model predictive control theory to continuously and dynamically diagnose the changes of demand and capacity in the actual production process and design the corresponding multilayer game collaborative optimization robust model according to the uncertainty relationship. The study considers the production characteristics and management needs of multiple enterprises within the manufacturing industry, as well as the optimization of the dynamic equipment collaborative scheduling system, uncertain demand, dynamic equipment matching effectiveness, and equipment failure under the shared manufacturing model, deduces the market capacity demand for manufacturing enterprises by inverse prediction of dynamic market demand through the simple recurrent neural network (Elman network), and then maximizes the idle equipment utilization and load capacity under the shared manufacturing model in model rolling optimization. This paper gives model solutions based on big data analysis and combines improved population intelligence algorithms to determine the dynamic matching of manufacturing resources, product supply and demand paths, and transportation flows. The simulation results show that the application of model predictive control theory to the model of Elman neural network system diagnosis can effectively reduce the adverse effects of the two-way uncertainty environment on the profitability of enterprises. Meanwhile, considering the maximum performance matching of dynamic equipment scheduling and combining with robust optimization methods will reduce the cost loss of manufacturing enterprises in the worst case, and the cost loss reduction can reach 24.73%. The analysis results verify that the method is of great practical significance in the direction of intelligent production collaboration and industrial digital transformation.

1. Introduction

Economic globalization has gradually eliminated barriers between countries and regions, and factors of production have flowed freely around the world. Reasonable resource allocation has brought about major changes in the development environment of the manufacturing industry. Many manufacturing enterprises have changed their spatial layout to achieve greater economic benefits and cater to larger market demands. Negri et al. proposed that in Industry 4.0 and Smart Manufacturing research, optimization and decision-making can be achieved through digital twin (DT) technology and rely on synchronization enabled by sensors to update the same data in real-time with the physical system [1]. Villalonga et al. proposed that an important challenge for today’s cyber-physical production systems is to update dynamic production schedules through automated decisions executed at production runtime [2]. This shows that in the era of Industry 4.0, the real-time feedback and monitoring of production data will help manufacturers improve their own production efficiency and productivity. We use the existing sensor monitoring system to monitor the production data in real-time, analyze the equipment operation, and analyze the equipment failure problems and the real-time data changes in production capacity to achieve a more efficient and reliable production method. And in the process, in the face of insufficient capacity, we can dynamically realize the way of equipment scheduling to improve the production capacity of enterprises. This new manufacturing concept, which breaks through spatial restrictions and realizes physical space and cyberspace, has led the previous static resource allocation to a more flexible and dynamic resource allocation. In order to improve the problems of inconvenient communication, inefficient resource utilization, and inability to complete manufacturing tasks efficiently in the manufacturing industry, resource sharing has become an important manufacturing method to promote the transformation and upgrading of the manufacturing industry [3]. In order to better meet customer needs and respond to market demand faster, more and more manufacturing companies have begun to say goodbye to the traditional manufacturing model, and collaborative manufacturing has become a new manufacturing model adopted by manufacturing companies [4]. Collaborative communication between enterprises is an important bridge to achieve information and resource sharing [5]. Zhu et al. proposed that with the support of supply chain comanufacturing platform, the overall competitiveness of supply chain comanufacturing can be effectively improved, and the real-time interaction and information sharing of material, information, and capital flow between suppliers, manufacturers, and customers can be realized [6].

Current research on collaborative manufacturing focuses on supply chain collaborative manufacturing, collaborative manufacturing systems, collaborative industrial design, and collaborative production planning. In the area of collaborative manufacturing in supply chain, Li et al. studied the business process and resource interaction mode of collaborative manufacturing in supply chain by focusing on the core production enterprises and five supply chain business links from collaborative planning, collaborative procurement, collaborative production, collaborative logistics, and collaborative service; this will enhance the overall competitiveness of collaborative manufacturing in supply chain and realize the real-time interaction and information sharing among suppliers and manufacturers and real-time interaction and information sharing of material flow, information flow, and capital flow among suppliers, manufacturers, and customers [3]. Li et al. proposed a multiobjective decision model to maximize the manufacturing matching degree in a collaborative supply chain environment and validate the feasibility and effectiveness of the method [4]. In the construction of the collaborative manufacturing system, Wang et al. analyzed the production characteristics, typical production processes, and collaborative management requirements of multiroom production in discrete manufacturing enterprises and proposed the collaborative manufacturing execution system architecture for discrete manufacturing [7]. Lin et al. discussed the conceptual design of a global decision support system for SMEs actively involved in collaborative manufacturing and proposed web service-based system architecture to provide maximum interoperability among all distributed participants of the collaborative manufacturing network and their management information systems [8]. As for collaborative industrial design, Cao et al., by analyzing the basic concept and application status of collaborative product design, pointed out that collaborative innovation is an effective way to solve the weak innovation capability of small enterprises common in industrial design; the collaboration between industrial design companies and manufacturing companies will be beneficial to the collaborative integration among industrial design industry chain members [9]. Wang et al. proposed a networked collaborative design system and established a digital assembly model independent of various commercial CAD software according to the requirements of collaborative product development [10]. In the area of collaborative production planning, Shin proposed a collaborative coordination mechanism to address the problem of self-coordination faced by manufacturing entities due to different organizational practices, constraints, and conflicting goals by studying the collaborative decision-making approach to operational coordination among manufacturing facilities in a manufacturing logistics network [11]. Cheng et al. proposed a supernetwork-based model for the scheduling problem of distributed manufacturing operations and conducted group experiments to discuss the different cases of combining distributed and collaborative manufacturing [12]. Based on the analysis of the impact of product modularity on collaborative innovation, Wang and Shu constructed a customer-driven, module-based innovation carrier and sustainable collaborative innovation network model, which provides an effective way for global manufacturing companies to manage external partners [13]. As for shared manufacturing, the current research mainly focuses on manufacturing resource service sharing, manufacturing information, and knowledge sharing. In manufacturing resource service sharing, Wang et al. proposed an integrated architecture to facilitate resource allocation in shared manufacturing in view of the difficulty of adapting traditional centralized optimization methods to cross-organizational resource coordination [14]. Du et al., after analyzing the management characteristics of the manufacturing industry, proposed an order-oriented cloud service library and an order-based shared manufacturing resource model, making it easier for heterogeneous resources in different regions to collaborate remotely [15]. Liu et al. analyzed the resource and service sharing model in traditional networked manufacturing and conducted a detailed theoretical and modeling analysis on resource service utilization and demand satisfaction rate and revealed the challenges and development directions faced nowadays [16]. In the area of manufacturing information sharing, Gao and Nee provided an overview of reported research on manufacturing-related knowledge management and focused on knowledge sharing in the product development process, highlighting manufacturing knowledge sharing methods related to the product development process and pointing out future challenges and research directions [17]. Sun et al. established a platform architecture for real-time information sharing in manufacturing supply chains to improve the efficiency of information collection and sharing based on the problem that the information collection in the current stage of manufacturing supply chain information sharing platform is traditional, which affects the speed of real-time information sharing [18]. Lopez-Ortega and Ramirez analyzed relevant information systems, servers, and prototype client applications to facilitate data sharing and exchange of flexible manufacturing resources based on manufacturing systems with relevant capabilities for data sharing and exchange [19]. Song proposed to build a collaborative networked manufacturing system based on product lifecycle manufacturing cycle and manufacturing information sharing and verified the feasibility and effectiveness of the method by simulation [20]. In terms of knowledge sharing, Wang and Wan proposed a knowledge sharing mechanism among manufacturing resources based on cloud-edge collaboration; the effectiveness of the proposed method was verified by comparing manual and knowledge sharing configurations in a comparative experiment on a multivariety, low-volume manufacturing experimental platform [21]. Zhang et al. proposed a resource-centric strategy to obtain production-related data and make decisions for the management of shared resources for resource monitoring and maintenance [22]. Zhang et al. suggested that green knowledge sharing and business model innovation are important ways for new firms to achieve performance growth and provide direction for new firms within the manufacturing industry to implement green innovation strategies to improve performance [23].

The application of the Elman neural network and swarm intelligence algorithm is an important part of realizing the optimization of the dynamic equipment scheduling system. In recent years, scholars in various industries have mentioned the importance and innovation of the neural network discipline in their own research. Based on the development of the artificial neural network and the continuous improvement of swarm intelligence algorithms, the manufacturing industry has also developed rapidly. We found that swarm intelligence algorithms are superior to traditional methods in terms of speed and quality in solving large-scale problems. Some scholars have pointed out that population intelligence algorithms have certain research prospects in the fields of autonomous driving and intelligent transportation, emergency response, and environmental monitoring and are better than traditional algorithms in data transmission in the Internet of Things (IoT) [24, 25].

The neural network is an important research field for artificial intelligence applications, which is a network composed of a large number of simple computing units (artificial neurons) interconnected. The neural network is a certain degree of abstraction, simplification, and imitation of the information processing function of the human brain nervous system on the basis of human understanding of the working mechanism of the brain. Compared with traditional intelligent algorithms, neural network models have the following characteristics: First, neural networks have nonlinear mapping capabilities; they do not require accurate mathematical models; they are good at learning and integrating effective knowledge from input and output data. In the past 20 years, neural network technology has achieved great success and progress in intelligent control, pattern recognition, computer vision, nonlinear optimization, and signal processing. Zhao and Yao proposed a novel prognostic framework based on multisensory signal features and called it a multidislocation time series convolutional neural network (MDTSCNN) [26]. Cruz et al. combined an integrated convolutional neural network and an evolutionary algorithm to propose a novel image classification method [27]. Xie et al. proposed a short-term electric load forecasting method combining the Elman neural network and particle swarm optimization algorithm [28]. Fernandes Junior and Yen combined deep convolutional neural networks and particle swarm algorithms to achieve more efficient and stable image classification tasks [29]. When we build a collaborative scheduling system based on a two-way uncertainty environment, we find that this application based on the Elman neural network and improved swarm intelligence algorithm makes the system more stable and reliable. We build models by using the basic principles of neural networks to establish the link between equipment failure factors and certain common parameters in actual production processes.

The modern control theory developed and perfected in the early 1960s has the optimal performance indicators and systematic and precise theoretical design methods and has made outstanding achievements in aerospace, guidance, and other fields. Modern control theory still has room for improvement in the control of industrial processes, which will realize higher industrial value conveniently and quickly. The problem in industrial processes is that the basis of modern control theory is an accurate object parameter model, while industrial processes often have the characteristics of nonlinearity, time-varying, strong coupling, and uncertainty, and it is difficult to obtain an accurate mathematical model, so the control effect is greatly reduced. Some scholars have further optimized the model based on the evaluation process in the manufacturing mode combined with the neural network theory. Gao constructed a comprehensive performance evaluation model based on the backpropagation (BP) neural network and a rough set to improve the performance evaluation of manufacturing collaborative logistics [30]. In addition, this study obtains a set of key performance indicators by using the rough set attribute parsimony theory to screen and optimize the evaluation indicators. Then use the BP neural network to predict and evaluate the key performance data, which greatly reduces the training time and shortens the learning time. Quan and Zhang based on the background of intelligent subsidiary suppliers, used machine learning to study the evaluation method of supplier efficiency [31]. Based on the traditional backpropagation neural network, combined with the improved particle swarm optimization algorithm, this research constructs a new neural network model based on the supplier evaluation index system and evaluates the supplier efficiency of intelligent subsidiaries. Saravanan et al. proposed a new method to simulate manufacturing cost tolerance and optimize the tolerance value as well as manufacturing cost [32]. The study combined a genetic algorithm with a neural network model to optimize tolerance values. This approach will enable design and process planning engineers to make informed decisions. Wang evaluated the manufacturing capability of smart job shops based on an improved backpropagation neural network [33]. First, the study summarizes the core production factors that affect the improvement of the manufacturing capacity of the smart job shop and constructs a multilevel scale for the manufacturing capacity of the smart job shop. At the same time, based on the evaluation of job shop scheduling, this research establishes a framework for evaluating the manufacturing capability of an intelligent job shop, thereby improving the evaluation capability of the model. Shi et al. proposed a metadata replication method with a separate replication strategy, combined with the intelligent production line network platform, carried out research on a neural network-based intelligent production line network state prediction system, and designed a network [34]. The prediction system further prejudges the operation status of the intelligent production line network. Gegovska et al. analyzed the data using a multiobjective decision model with the goal of raising awareness and addressing the needs of green supplier selection [35]. Ultimately, the research achieved a better solution by incorporating artificial neural networks. Huo et al. proposed a discrete manufacturing workshop production control method based on ant colony optimization. This research describes the production management and control problems of discrete manufacturing workshops by analyzing the functions of the management and control system and then establishes the corresponding mathematical model [36]. Finally, the research solves the static multiobjective production control problem and verifies the effectiveness of the method with a numerical example. Wang built a deep learning prediction model based on a bidirectional long short-term memory network and a self-supervision mechanism and completed order management and completion date prediction [37]. Ramírez et al. developed a new fuzzy controller and applied it to the problem of nickel recovery, minimizing fuel consumption and environmental pollution [38]. Fan and Zhang set up experiments to conduct multisystem fusion of neural networks, combined with big data and artificial intelligence, to verify the efficient operation of neural networks in multisystem fusion [39]. Using the method of mathematical analysis and big data fitting, the collected data are classified to improve the comprehensive work efficiency of the system. Jiang et al. proposed an end-to-end model for the prediction of multistep machine speed [40]. The model includes a deep convolutional LSTM encoder-decoder architecture and combines examples to verify the feasibility of the method. Mawson and Hughes proposed and compared the use of two deep neural networks to predict manufacturing based on production schedules, climatic conditions, thermal characteristics of facility buildings, building behavior, and usage energy consumption patterns of the facility and plant conditions. Ultimately, the study provided a predicted building energy profile that the model can use to identify peaks in energy consumption [41]. Hu analyzed the factors affecting product design decisions based on the development of products. This research introduced the basic process of product modeling, designed a model based on image processing under the background of big data, and built a decision-making model for product modeling and designed scheme under the big data cloud environment [42]. Finally, experiments proved that the decision-making model can improve the overall design efficiency, shorten the manufacturing cycle, and provide new ideas for product modeling design. Liu and Dai constructed a quality classification model based on a data generation model and described the process of water heater lining quality classification under small sample data and unbalanced environments [43]. Beruvides et al. proposed a real-time monitoring system and implemented an adaptive neurofuzzy inference system model, resulting in high fitting accuracy and good generalization capability [44]. Wang et al. proposed a new deep learning-based machine vision inspection method for identifying and classifying defective products without loss of detection accuracy [45]. Cruz et al. combined with a convolutional neural network (CNN) proposed a structured light-based computer vision system for LPG pressure vessel welding inspection and verified the robustness of the system [46]. Xu and Zhou presented a new object detection framework, classification priority network (CPN), and a new classification network, multigroup convolutional neural network (MG-CNN), to inspect the defects of steel surface. The proposed method had yielded best performances compared with prior methods used in defect inspection [47].

With the further improvement of manufacturing capacity, new problems have emerged. The market demands faced by today’s manufacturing companies have become more complex, and market demands are susceptible to fluctuations due to environmental influences. Manufacturing enterprises themselves face problems such as low equipment load and wastage of production capacity in the manufacturing process. At the same time, with the introduction of manufacturing concepts such as shared manufacturing, cloud manufacturing, and shared manufacturing, the matching method and matching degree between idle equipment and resource agents have gradually attracted the attention of scholars. Through the analysis of the existing literature, it can be found that scholars mainly focus on the matching of supply and demand and their combination with process industry production, but lack the analysis of the matching efficiency of dynamic equipment. For the prediction method of equipment failure, the traditional prediction method is difficult to reasonably design the weight according to different equipment models, and the prediction process often has a certain degree of subjectivity. For the existing swarm intelligence algorithms, it is often easy to fall into the local optimal solution, and it is difficult to achieve the maximum optimization of the scheduling system. In addition, there are still research gaps in the construction of the scheduling platform and the matching principle of dynamic equipment. Most of the existing dispatching platforms are built by uploading only the basic information of both supply and demand without deeply integrating the production capacity and failure problems of enterprises, and the corresponding matching principle exists only on the basic capacity demand without considering the uncertainties existing in the dynamic environment, resulting in a poor matching effect from time to time. This paper studies the optimization of the dynamic equipment scheduling system in shared manufacturing mode and explores how to combine the uncertain market demand and the uncertain dynamic equipment matching relationship to maximize the benefits of manufacturing enterprises themselves. In actual operation, the reasonable matching of dynamic equipment will enhance the production capacity of manufacturing enterprises and reduce unnecessary energy, labor, and material losses. In the existing literature, the product failure rate is not considered much, but the equipment capacity considered in this paper already includes the consideration of product defect rate. When the equipment causes product failure due to its own aging or operation error, this part of the capacity is waste capacity and is not calculated in the equipment’s own production capacity. Therefore, the basic calculation of equipment failure rate and production capacity includes the problem of defective products.

Therefore, under the background of the above practice and research, this paper makes the following contributions: (1) We combine the concept of dynamic equipment scheduling under the shared manufacturing mode and take the differentiated needs of customers as the starting point to better meet the dynamic market demand. (2) In this paper, the Elman neural network model is used to diagnose the probability of equipment failure and predict the uncertain market demand and build a multilayer game robust optimization model to solve the multiple uncertain problems such as the two-way uncertainty of production capacity and market demand and the uncertainty of matching relationship. (3) We integrate the multiobjective genetic algorithm on the basis of multiobjective particle swarm, which solves the problem that the traditional swarm intelligence algorithm is easy to fall into the local optimal solution. (4) Compared with the traditional equipment matching model, we consider the dynamic equipment matching efficiency maximization under multiple uncertain environments and combine the concept of shared manufacturing to innovatively give the idea of establishing dynamic configurable equipment, which reduces the waste of equipment capacity to a greater extent. (5) By building a multilayer supply and demand matching network of the system, the precise connection between supply and demand can be realized. Any changes in customer requirements and design changes can be quickly propagated and responded to in a timely manner in the entire system network, ultimately realizing the optimal dynamic equipment scheduling scheme and production scheme under the dynamic market demand.

The text is structured as follows: Section 2 is the problem description. Section 3 is the diagnostic model based on the neural network system, which includes diagnosis of dynamic market demand based on the gray prediction neural network model (GM(1, 1)-Elman neural network), diagnosis of production capacity based on the neural network, analysis of model predictive control in the shared manufacturing model, and analysis of maximum matching effectiveness model. Section 4 is a multilayer game analysis, which includes two-way uncertainty environment analysis, impact of uncertain demand on profit, the MPC model for dynamic equipment scheduling, and the maximum matching effectiveness model. Section 5 is the multiobjective collaborative optimization model. Section 6 is the introduction of the improved swarm intelligence algorithm (NSGA-II-MOPSO) and the performance test of the algorithm, as well as the introduction of the system flow based on neural network system diagnosis and matching performance in the shared manufacturing mode. Section 7 is the model applications. Section 8 summarizes the whole text.

2. Problem Description

The self-profit of manufacturing enterprises under the sharing mode is related to the dynamic matching of idle resources. The production capacity of each manufacturing enterprise will vary with the implementation of different dynamic equipment scheduling schemes. Under the shared manufacturing mode, different from the uncertainty of market orders, the uncertainty of production capacity within the enterprise can be subdivided into two situations: uncertainty of equipment failure and uncertainty of matching efficiency. Therefore, the manufacturing capacity of manufacturing enterprises is constantly changing, and the uncertainty of internal production capacity of manufacturing enterprises and the uncertainty of demand in the market together constitute a two-way uncertainty environment. This two-way uncertainty environment will have a huge impact on the reasonable matching of dynamic resources in the manufacturing system, the profits of manufacturing enterprises, and the design of production planning schemes. In addition, in actual production, manufacturing enterprises can stimulate different degrees of manufacturing capacity through different matching schemes of idle equipment. At the same time, the matching efficiency of dynamic equipment in the production process should also be considered, so as to avoid unnecessary waste of labor and other costs, equipment damage, and other problems. In the shared manufacturing mode, the optimization principle of the dynamic equipment collaborative scheduling system is shown in Figure 1.

Figure 1 

Optimization principle of the collaborative scheduling system considering dynamic equipment matching efficiency in shared manufacturing mode.

Aiming at the market uncertain demand problem mentioned above, this paper will study the establishment of demand under an uncertain demand environment, the efficiency of dynamic equipment matching, and the optimization of the collaborative scheduling system in manufacturing enterprises. The node types in this paper are enterprise, manufacturer, and wholesaler. Suppose the area contains wholesalers. In order to better meet the large-scale personalized needs of customers, an enterprise establishes a dynamic equipment scheduling platform within the enterprise, which records the existing equipment information in the enterprise, the equipment load in the production process, and other equipment information at all times. At present, there are subsidiaries in a manufacturing enterprise , and the quantity that can be used for equipment dispatching among the subsidiaries in the manufacturing enterprise is . For the convenience of description, the following definitions are now made: the nodes in the network are represented by , respectively; among them, is the set of nodes of the manufacturing enterprise, and is the set of nodes of subsidiaries in the manufacturing enterprise. is the set of nodes in the warehouse. is the set of nodes of the wholesaler. is the set of nodes of the demand point. The collaborative scheduling system analysis model is shown in Figure 2.

Figure 2 

Cooperative scheduling system analysis model.

represent the labor costs, material costs, and other costs corresponding to the production unit product of the subsidiary in the manufacturing enterprise , respectively. represents the unit sales price corresponding to the product produced by the subsidiary in the manufacturing enterprise . represents the recycling price of the recycled product in the warehouse in the manufacturing enterprise . represents the selling price of the remaining products of product sold by wholesaler in manufacturing enterprise through other channels. the retail price of product by wholesaler in manufacturer . represents the unit product transportation unit price for the subsidiary in the manufacturing enterprise to choose the transportation method to transport the product to the wholesaler , among them: represents the set of transportation methods, . The actual arrival of goods received by the corresponding wholesaler from subsidiary is . The order quantity of the wholesaler is . denotes the forecasted demand of wholesaler for the corresponding demand point with respect to product . denotes the maximum storage capacity of the warehouse with respect to product . denotes the existing storage capacity of the warehouse with respect to product and has . denotes the actual cargo arrival of wholesaler regarding product to the warehouse , and has , among them: , denote the corresponding cargo volume and path wear rate, respectively. denotes the warehouse returns the remaining indicates the amount of goods returned by the warehouse to subsidiary within manufacturing enterprise for reprocessing. , indicate the amount of goods reprocessed by subsidiary within manufacturing enterprise about product and the amount of goods processed by the production line, respectively. and denote the time required to reprocess a unit of product at subsidiary within manufacturing firm regarding product and the time required to process it through the production line, respectively. denotes the volume of goods handled by wholesaler regarding product by other channels. denotes the time required to move equipment from subsidiary to subsidiary the sum of the transportation and adjustment times required. The total amount of products received by wholesaler , , can be handled in three ways: (1) Wholesaler sells the products to demand point at , and the quantity is recorded as . (2) Wholesaler returns the unsold products in (1) to warehouse , and the quantity is recorded as . (3) If there is still a surplus of products then wholesaler sells them at a low price of , and the quantity is recorded as

3. Neural Network System Diagnosis Model

In this section, we propose a control strategy based on Elman Neural Network-Model Predictive Control (NNMPC). To enhance the supply-demand matching ability of subsidiaries to dynamic market demand and the enterprise’s own interests, we design controllers with robust quality regarding equipment failure, equipment matching relationship, and dynamic market demand based on the shared manufacturing model.

3.1. System Diagnosis

3.1.1. GM(1, 1)-Elman Neural Network Demand Diagnosis

Combined with the market environment, we conducted a big data analysis of the terminal of the market to know that the main factors that can be used to reflect the dynamic market demand are the following categories of factors: customer purchasing power, product market share, market terminal consumption records, and customer purchasing frequency and predict the next cycle of these four categories of factors through a gray prediction model (GM(1, 1)). We simulate the mapping relationship between each factor and market demand using a neural network model in combination with previous data, and then map the market demand in the next cycle from the predicted value of each factor in the next cycle. The specific process is shown in Figure 3; among them, the solid line indicates the market demand forecasting process in the current cycle and the dashed line indicates the data processing process in preparation for the next cycle.

Figure 3 

Dynamic prediction of the Elman neural network based on gray prediction.

We continuously train the neural network by updating the actual forecasting model through the process of monitoring the data at the terminal of the market. Thus, the terminal-of-market data will be updated twice in the process of dynamically forecasting market demand: once for the historical data in the gray forecasting model and once for the historical data in the neural network model. Among them, the specific implementation of gray forecasting is as follows: Step 1: First, all gray sequences can be weakened by some kind of generation to show their randomness and regularity. We use the cumulative generation, let the initial data of each factor be , the accumulation equation is , and then there is the cumulative data as . The pro-valued generating number is obtained using , and is called the generating coefficient. In particular, when , the number is said to be the mean generating number. Step 2: Second, the data are examined. Firstly, the rank ratio of the series is calculated, , if all the rank ratios fall within the tolerable coverage interval , then the series can be modeled as GM(1, 1) for gray prediction. Otherwise, the data need to be transformed appropriately. Step 3: Build the gray prediction model: define the gray derivative of as , and let be the neighbor-valued generating series of series , that is, . Thus, the model of the gray differential equation defining GM(1, 1) is , among them, is called the development coefficient, is called the whitening background value, and is called the amount of gray action. We can obtain the set of equations as follows: Listed according to the matrix method, Then, GM(1, 1) can be represented by . Eventually, we obtain the predicted value of Step 4: Test the accuracy prediction of the gray model; we choose the posterior difference test method to test the data. The predicted is obtained using cumulative subtraction to get , . And calculate the residuals, . Calculate the variance of the original sequence and the variance of the residual, and , . Calculate the posttest ratio, and check the observation. For specific values, please refer to Table 1.

We normalize the historical data of four factors, including customer purchasing power, product market share, terminal-of-market consumption records, customer purchasing frequency, and historical market demand data as the input and output values of the neural network model and train the neural network. Finally, the mapping relationship between each factor and the demand is obtained.

Some studies have shown that, compared with the BP neural network in fault diagnosis, the Elman neural network has the characteristics of simple adjustment of structural parameters, short training time, and stable performance [48–51], and it is easier to find faults and diagnose them. The Elman neural network is a typical feedback neural network model that is widely used. It can generally be divided into four layers: input layer, hidden layer, successor layer, and output layer. The connection of its input layer, hidden layer, and output layer is similar to a feedforward network. The units of the input layer only play the role of signal transmission, and the units of the output layer play the role of weighting. The hidden layer unit has two types of excitation functions, linear and nonlinear, and the excitation function usually takes the sigmoid nonlinear function. The successor layer is used to memorize the output value of the hidden layer unit at the previous moment, which can be regarded as a delay operator with one-step delay. The output of the hidden layer is self-connected to the input of the hidden layer through the delay and storage of the successor layer. This self-connection method makes it sensitive to historical data. The addition of the internal feedback network increases the ability of the network itself to process dynamic information, so as to achieve the purpose of dynamic modeling. The Elman neural network structure is shown in Figure 4.

Figure 4 

Elman neural network structure model.

Practice has proved that Elman neural network has the following advantages:(1)It is sensitive to historical state, increases the ability to process state information, has adaptable time-varying characteristics, and can be dynamically modeled(2)It can approximate any nonlinear mapping with arbitrary precision, and it is not necessary to consider the specific form of the influence of external noise on the system(3)Effectiveness, widely used in practical problems(4)The associative memory function of the Elman neural network is better and more stable

The Elman neural network works as follows:(a)Input layer and receiver layer It is known that is the input variable of the input layer node at time , and is the node of the successor layer at time . The corresponding expression is Among them, is the weight value connecting the -th input neuron node and the -th hidden layer neuron node, and is the neuron of the hidden layer at time .(b)Hidden layer The relevant equation of the neurons in the hidden layer at time is expressed as follows: The Sigmoid function expression of the hidden layer is , and represents the weight value connecting the -th node of the hidden layer to the node of the successor layer.(c)Output layer The output layer can be expressed by the following equation: In the above equation, is the weight value connecting the -th neuron of the hidden layer neuron to the output layer neuron.

We predict data according to the basic structure of the Elman neural network system combined with MATLAB. The specific structure is shown in Figure 5.

Figure 5 

MATLAB structure diagram.

3.1.2. Elman Neural Network Productivity Diagnosis

Based on data collected from 500 enterprises, we know that the failure of most equipment is a function of time, and the typical failure curve is called the bathtub curve (failure rate curve). The bathtub curve shows that the reliability of the equipment changes with a certain law during the entire life cycle from investment to scrapping. We take the use time as the abscissa and the failure rate as a curve on the ordinate. The shape of the curve is high at both ends and low in the middle as shown in Figure 6.

Figure 6 

Bathtub curve.

The equipment fault establishment process combined with the neural network system is as follows: Step 1: Calculate the respective service age regression factors and failure rate increment factors in the historical data according to different equipment models and performances. After analysis, we establish that the main factors affecting the two factors are the degree of equipment damage, the equipment load in operation, the proficiency of workers in operating the equipment, and the number of historical maintenance. The four factors are normalized and the Elman neural network algorithm is used to train the relationship between the four factors and the two factors. In the calculation of the next cycle after the training is completed, the service age regression factor and the failure rate increment factor are calculated by inputting the values corresponding to the four factors in the neural network model. Step 2: We combine the service age regression factor and the failure rate increment factor established by the Elman neural network to determine the failure rate function of the equipment. The equipment failure rate function before and after preventive maintenance is as follows: Among them, is the number of preventive maintenance, ; is the interval for the -th preventive maintenance of the equipment; is the failure rate distribution function of the equipment before the -th preventive maintenance; is the initial failure rate distribution function of the equipment; is the failure rate increment factor, , whose value can be determined according to the historical data of the equipment operation combined with the actual situation; and is the service age regression factor, . The value of is as follows: In the equation, is the adjustment coefficient of equipment maintenance cost; is the time adjustment coefficient; and is the adjustment coefficient of learning effect, , and is the percentage of experience curve given by experts based on experience judgment or estimation. Step 3: Determine the maintenance interval of the equipment. Equipment preventive maintenance intervals in this document are based on the reliability of equipment components. First, the reliability threshold of the equipment needs to be preset according to the characteristics of the equipment. When the reliability of the equipment reaches , the equipment should be treated by preventive maintenance. According to the reliability function of the equipment, When equipment reaches its reliability threshold, then By combining equations (8) and (11), the maintenance interval of this type of equipment can be obtained. Step 4: Establish the effective service age of the equipment. After the equipment undergoes preventive maintenance, the service age of the equipment will be reduced, and the retirement of the service age is related to the number of preventive maintenance of the equipment and the effect of preventive maintenance. Example: the effective service age before and after the first preventive maintenance is as follows: The effective service age before and after the second preventive maintenance is as follows: By analogy, the effective service age before and after the -th preventive maintenance of the equipment is as follows: As shown in Figure 7, it can be seen from the analysis that the effective service age of the equipment in the -th preventive maintenance interval is as follows: The number of unexpected failures of the equipment during the -th preventive maintenance interval is as follows: The total time required for maintenance over the life of the equipment is as follows: Among them, is the total time required for equipment maintenance, and is the maintenance time of one maintenance. Step 5: Determine the validity of the equipment The effectiveness of the equipment refers to the probability that the equipment is in a usable state during its life cycle. The effectiveness of the equipment is as follows:

Figure 7 

Change in service age of equipment over its life cycle.

Combined with the equipment failure matrix, the failure probability of the corresponding type of equipment in the shared manufacturing platform is predicted. Due to the large number of equipments, the platform can set thresholds to achieve premaintenance of equipments. Assume that the threshold value corresponding to the equipment of the product model of the subsidiary in the manufacturing enterprise is , and the corresponding equipment validity is . Then, a judgment equation can be established to decide whether to perform premaintenance processing on the -th equipment of this model. The specific judgment equation is as follows:

When the output result is , the equipment needs to be premaintained. When the output result is , it is considered that the performance of the equipment is good, and there is no need to perform premaintenance processing on the equipment. However, combined with the analysis of the actual situation, we found that when , even if the equipment is prerepaired, some equipment will cause irreparable loss of production capacity due to depreciation and other reasons. That is, it is difficult for some equipment to be repaired to the previous equipment capacity. As a result, the uncertainty of equipment maintenance occurs. The specific calculation equation of equipment performance after premaintenance is as follows:

And we have . Among them, , , and , respectively, represent the equipment production capacity, maintenance efficiency, and production capacity loss of the -th model of the machine and equipment of the production product of the subsidiary in the manufacturing enterprise after premaintenance treatment, and .

4. Multilayer Game Analysis

4.1. Uncertainty about the Impact of Demand on Profits

First, based on the characteristics of the shared manufacturing model and combined with the actual production process, the profit () of the product in the manufacturing enterprise can be divided into four parts, namely, sales revenue (), equipment scheduling costs (), production costs (), and product transportation costs (). The specific equation is expressed as follows:

Sales revenue (): the sales revenue obtained by manufacturing enterprise from producing product is expressed as follows:

Equipment scheduling costs (): in the process of producing product by manufacturing enterprise , the dispatching cost of dynamic equipment between subsidiaries during the dispatching process, including: equipment transportation cost () and equipment installation cost (). The specific equation is expressed as follows:

Production costs (): in the process of producing product m by manufacturing enterprise , the production costs of each subsidiary are divided into labor costs, material costs, and other costs. The specific equation is expressed as follows:

Product transportation costs (): after the manufacturing enterprise produces the product , each subsidiary selects the transportation mode and the transportation cost incurred in the process of transporting the product to each wholesaler. The specific equation is expressed as follows:

To sum up, we have the total profit of manufacturing firm producing product :

Correspondingly, the total profit equation of manufacturing enterprise is as follows:

Composed of the profits of the abovementioned manufacturing enterprises, we found that after equipment scheduling, the manufacturing capacity of the manufacturing enterprises has been improved; but in the actual process, the predicted value often deviates from the actual value, resulting in some losses.

In the manufacturing process, as the actual demand of the demand point changes, the income and strategies of the corresponding subsidiaries and wholesalers will also change accordingly. In addition, since there is profit model analysis in the closed-loop supply chain system in the constructed model, it is necessary to establish the values of and . The specific definitions are as follows.

Definition 1. Combined with data, record the corresponding of each wholesaler as , and the corresponding probability is .
We calculate the corresponding based on past data statistics. For specific values, please refer to Table 2. Among them, the corresponding calculation equation when the demand is is as follows:Chen and Ma analyzed the marginal pricing strategy in the supply chain model and put forward the following inferences [52].

Inference 1. Combined with the uncertain demand environment, the wholesaler has a unit overstock loss and a unit shortage loss (opportunity loss) , among them, , . Then, there areLi established the wholesale price under the condition of maximum expected profit by constructing a supply chain game model. Combined with equation (29), the following inferences are drawn [53].

Inference 2. Under the premise of following the principle of the manufacturer’s maximum profit, the manufacturer’s wholesale price is as follows:

4.2. MPC Model for Dynamic Equipment Scheduling

Under the shared manufacturing mode, there is uncertainty about the matching relationship between equipment and subsidiaries in the operation of the dynamic equipment scheduling platform, and it is difficult for enterprises to select the most suitable equipment according to their own conditions to meet the market demand in an uncertain environment. Secondly, it is difficult to determine the effect of equipment premaintenance. In the actual production process, it may happen that even if the equipment is prerepaired, equipment failure still occurs. In view of the current dynamic market problems, we choose to adopt predictive control (MPC) to enhance the robustness of the system. MPC is based on a process model and introduces a feedforward effect, enabling the system to react in advance and make appropriate changes to counteract expected disturbances.

The MPC algorithm mainly relies on two basic elements, an optimization tool and a system model. The former solves an optimal control problem to find control strategies that maximize the objective function, while the latter evaluates the future response of the system to these control strategies. Figure 8 shows how the MPC algorithm works. The dashed line in Figure 8 is the reference trajectory, the dotted line is the actual evolution of the system, and the solid line is the evolution of the control action.

Figure 8 

MPC algorithm implementation diagram.

It can be seen from the above analysis that the production capacity of some equipment may change after premaintenance, and the maintenance effect of prerepaired equipment before the formal maintenance treatment is difficult to predict, so it is still prone to failure of some equipment in the production process. In addition, after some equipments are predicted, it is judged that no maintenance is required because , but there is still the possibility of failure in the production process, which will reduce the production capacity of the subsidiary. In order to solve the above problems, we propose to adopt a robust strategy for analysis, and carry out equipment scheduling with the goal of improving the subsidiary’s production capacity in the worst case, namely, . Let and represent the production capacity of product produced by subsidiary of manufacturing enterprise after the equipment is repaired under normal and worst conditions, respectively. Then, there is the following equation: