© X. Yu et al., Published by EDP Sciences 2025

1 Introduction

The high-end equipment manufacturing industry is an important part of the global manufacturing industry, involving multiple high-tech fields such as aerospace, rail transportation, and energy equipment [1,2]. This industry not only requires products to have high technical content and complex manufacturing processes [3], but also requires effective coordination of multiple supply chain nodes during the production process to ensure product quality and delivery time [4,5]. The development of globalization has made today's enterprises face more diversified market demands, increasing production complexity, and a rapidly changing external environment [6,7]. How to optimize supply chain management and improve overall efficiency has become a key issue for high-end equipment manufacturing companies to maintain their competitiveness [8,9].

Strategic resource allocation involves long-term planning and partner selection, while tactical issues focus on logistics path optimization and inventory management. Although the high-end equipment manufacturing industry is constantly developing in the direction of intelligence, the current supply chain management still faces many challenges [10,11]. Due to the complexity of products and the large scale of supply chains in high-end equipment manufacturing, traditional supply chain planning models are unable to cope with multi-objective and multi-level decision-making and are unable to cope with multi-dimensional decision-making needs in the supply chain [12,13]. In particular, when there is a high degree of uncertainty between long-term planning and short-term scheduling, the adaptability of existing models is poor, and it is impossible to achieve global optimization in a dynamic environment. The nodes in the current supply chain are numerous and widely distributed. How to efficiently coordinate the information flow, logistics, and capital flow between different nodes is also an urgent problem to be solved [14,15]. Although traditional optimization algorithms (such as genetic algorithms, particle swarm algorithms, etc.) perform well on single-objective or small-scale problems, their solution speed and efficiency drop significantly when faced with large-scale supply chain systems [16,17]. The supply chain of high-end equipment manufacturing usually involves multiple partners, production bases, storage centers, and other complex multi-party participants [18,19]. Optimization problems often present the characteristics of multiple objectives and multiple constraints [20]. Traditional algorithms are prone to falling into local optimal solutions when dealing with these problems and lack global search capabilities. With the rapid changes in the market environment and the uncertainty of customer demand, supply chain management requires real-time response and adjustment [21,22], which places higher requirements on the efficiency of traditional algorithms [23,24]. Therefore, proposing a new model and combining it with a new optimization algorithm not only meets practical needs but also provides a new solution for improving the overall efficiency of the high-end equipment manufacturing industry [25].

The purpose of this study is to propose a double-layer planning model based on artificial intelligence communication technology for the complex and multi-level supply chain service combination problem in the high-end equipment manufacturing industry, and optimize it through CGA to improve the intelligence level of supply chain management and the overall operation efficiency. When constructing a double-layer model, in the upper-level planning, this article focuses on solving strategic resource allocation and high-level decision-making problems, which play a key role in the coordination of the overall structure of the supply chain; in the lower-level planning, tactical issues such as logistics route optimization, inventory management, and supplier selection are optimized to improve the operational efficiency of each node. To cope with the complexity of multi-objective and multi-constraint problems in supply chain systems and the need for large-scale data processing, this article proposes to use the parallel processing capabilities of cloud computing to accelerate the optimization process of genetic algorithms. CGA achieves the optimal solution for supply chain service combinations in a relatively short time by simulating the selection, crossover, and mutation operations in the evolutionary process. At the same time, this article integrates artificial intelligence communication technology into supply chain management to achieve real-time monitoring and dynamic adjustment of the supply chain operation status, ensure the intelligent response capability of the supply chain system, and meet the rapidly changing market needs of the high-end equipment manufacturing industry.

2 Related work

In order to solve the problem of optimizing complex supply chain systems, many scholars and researchers have proposed a variety of optimization methods and models. Ge H proposed a coordinated beef supply chain model that can help alleviate slaughtering and processing bottlenecks, reduce operating costs, and prevent potential disruptions [26]. A virtual closed-loop supply chain network model based on multi-cycle, multi-product, and Internet of Things uses the Grey Wolf algorithm [27,28] and the Firefly algorithm to solve the fuzziness problem of supply chain demand [29]. The grey wolf optimization algorithm is mainly used for function optimization and engineering design. Its advantages in multi-objective search and global convergence are of reference significance in population diversity and the ability to jump out of local optimum. A method for setting the optimal order quantity for supply chain management through particle swarm optimization [30,31] minimizes the comprehensive cost of facility location and transportation while meeting all customer needs [32]. Although these studies provide important references for supply chain optimization, they are computationally complex and slow to optimize when dealing with large-scale supply chain networks. They still have obvious limitations in dealing with complex, dynamic, and multi-objective supply chain management.

In order to solve the problems of complex, dynamic and multi-objective supply chain network processing, some researchers have begun to try to introduce cloud computing and artificial intelligence technologies into supply chain optimization. Baryannis G proposed a research direction for the integration of supply chain risk management and AI (Artificial Intelligence), using methods within the scope of AI to solve problems related to supply chain risk management [33], but there is a lack of research on specific models and algorithms. Gammelgaard B used ICT (Information and Communication Technology) tools to achieve structural flexibility in the supply chain through simple, real-time reconfiguration of resources and capacity, which not only reduced costs but also provided effective solutions for disruptive new business models [34]. Although the model performs well in processing large-scale data, it still relies on the TGA (Traditional genetic algorithms) algorithm in the specific optimization algorithm, resulting in limited efficiency improvement when solving complex multi-objective problems.

Although the above content proposes a variety of supply chain optimization methods, current research still has many problems when facing the complex and multi-objective supply chain system of the high-end equipment manufacturing industry. Existing models have high computational complexity when dealing with large-scale supply chain networks, resulting in slow optimization speed. Although traditional models and methods effectively deal with problems in specific fields, they show obvious limitations when dealing with complex supply chains in the high-end equipment manufacturing industry, and it is difficult to handle multi-objective and multi-level requirements at the same time. Many methods focus on optimizing a single goal, such as reducing costs or optimizing order volume, and it is difficult to achieve global optimization in a complex supply chain environment. TGA, Particle Swarm Optimization (PSO), and other algorithms are prone to local optimality and insufficient response speed when facing supply chains with high real-time requirements and frequent dynamic changes. Although cloud computing and artificial intelligence technologies have begun to be applied in the field of supply chain optimization, the integrated application of these technologies is still immature, lacking specific optimization algorithm improvements, and unable to fully cope with the complex and changing supply chain environment of high-end equipment manufacturing. Therefore, it is necessary to introduce more efficient and intelligent methods to improve the optimization speed and globality.

3 Materials and methods

3.1 Construction of the double-layer programming model

3.1.1 Upper-level strategic decision-making method

In the upper level of the double-layer programming model, in order to achieve strategic resource allocation and high-level decision-making of the supply chain, mixed-integer linear programming (MILP) [35,36] combined with multi-objective optimization methods is used.

When developing a strategic resource allocation plan, a comprehensive objective function is constructed to minimize the overall cost of the supply chain, improve service quality, and optimize delivery time. The goal is to minimize the total cost C (Unit: $), which is a typical application of the mixed integer linear programming (MILP) model. Its expression is:

$$C={\displaystyle {{\displaystyle \sum }}_{i=1}^N}{c}_i{x}_i+{\displaystyle {{\displaystyle \sum }}_{j=1}^M}{d}_j{y}_j+{\displaystyle {{\displaystyle \sum }}_{k=1}^P}{f}_k{z}_k,$$(1)

c_i represents resource allocation cost, d_j is partner selection cost, and f_k is other supply chain-related costs; x_i, y_j, and z_k represent the status of resource allocation, partner selection, and other decision variables, respectively. (1 means selection, 0 means no selection).

In the resource allocation stage, constraints are introduced to ensure the reasonable allocation of resources between different supply chain nodes. The main constraints include resource availability constraints, service level constraints, and partner capability constraints, which are expressed as follows:

$${\displaystyle {{\displaystyle \sum }}_{i=1}^N}{x}_i\le R_{\text{max}},$$(2)

$${\displaystyle {{\displaystyle \sum }}_{j=1}^M}{a}_{ij}{y}_j\ge S_i,\forall i\in \left\{\mathrm{1,2},\dots ,N\right\}.$$(3)

R_max represents the total amount of available resources, a_ij is the allocation capacity of resources in partner j, and S_i is the amount of resources that meet the demand. These constraints ensure the rational allocation of resources among supply chain nodes and are common resource balance and capacity constraints in MILP models. Through these constraints, it can ensure that when selecting partners, the allocation of resources can be optimized without violating the service level requirements.

The selection of partners introduces a multi-objective decision-making method and combines it with a benefit-based evaluation system. The objective function is as follows:

$$U=\alpha \cdot U_{\text{financial}}+\beta \cdot U_{\text{quality}}+\gamma \cdot U_{\text{reliability}}.$$(4)

U_financial represents financial benefits, U_quality and U_reliability represent quality and reliability indicators respectively; α, β, and γ are target weights, and α+β+γ=1, U ∈ (0, 1). In the resource allocation process, by adjusting the weight coefficient, a flexible response to different strategic goals can be achieved. According to the objective function, the fitness value F can also be calculated to evaluate the stability of the algorithm. F can be expressed as:

$$F=\frac{1}{1+U},$$(5)

In order to optimize the selection of decision variables, the Lagrangian relaxation method is used to relax the original MILP model and obtain a Lagrangian dual problem. By constructing the Lagrangian function L:

$$L=C+{\displaystyle {{\displaystyle \sum }}_{k=1}^K}{\lambda }_k\left(b_k-g_k\left(x,y,z\right)\right),$$(6)

b_k is the upper bound of the constraint, g_k (x, y, z) represent the related constraint, and λ_k is the Lagrange multiplier. Its update rule is λ^(k+1) = λ^(k) + η ⋅ ∇ L (x, λ^(k)), where η is the step length parameter and ∇L is the gradient of the Lagrange function. By solving this dual problem, the optimal solution of the decision variables can be obtained, and the optimal solution for resource allocation can be quickly determined.

Figure 1 shows the key optimization steps of supply chain management in high-end equipment manufacturing. The process starts with analyzing the supply chain and evaluating the efficiency and problems of existing operations. Then, through the problem identification stage, key issues are identified in terms of resource allocation, partner selection and logistics optimization. The system identifies and classifies the key bottlenecks in the operation of the supply chain, including unreasonable resource allocation, low logistics efficiency and supplier response delay, etc., and feeds back these problems to the strategy formulation stage to provide a clear direction for the design of subsequent optimization schemes. For each problem, the article formulates resource strategies, selects partners, and forms solutions. Integrating and implementing these strategies marks the execution of the new solution. After implementation, it enters the performance monitoring stage, and the article can evaluate the results by continuously tracking key performance indicators. If the results show that there is room for improvement, the strategy can be adjusted and returned to the analysis stage for correction; if satisfied, the strategy can be continued. The process ends after achieving the optimization goal, marking the successful improvement of supply chain management in the high-end equipment manufacturing industry. This process emphasizes the close connection between each link and ensures the flexibility and efficiency of the supply chain.

Fig. 1 Systematic process of supply chain management.

3.1.2 Lower-level tactical optimization method

In logistics route optimization, the improved Dijkstra algorithm is used to solve the shortest path problem in a complex network environment. First, by establishing a logistics network model, the nodes are defined as warehouses, distribution centers, and customer locations, and the edges represent the paths and their transportation costs. The goal is to minimize the overall transportation cost, which is expressed as:

$$\text{min}Z={\displaystyle {{\displaystyle \sum }}_{i=1}^n}{\displaystyle {{\displaystyle \sum }}_{j=1}^n}{c}_{ij}{x}_{ij},$$(7)

c_ij is the transportation cost from node i to node j, x_ij is the logistics route selection variable, and n is the total number of nodes. Based on this model, the Dijkstra algorithm is applied to calculate the shortest path from the starting point to each node and select the path with the lowest total transportation cost to improve transportation efficiency and reduce transportation costs.

In terms of inventory management, the economic order quantity model is combined with dynamic demand forecasting to optimize inventory levels. By establishing an inventory control model, the goal is to minimize the total inventory cost. The formula is:

$$TC=\frac{D}{Q}S+\frac{Q}{2}H$$(8)

TC is the total cost, D is the annual demand, Q is the order quantity, S is the cost per order, and H is the unit inventory holding cost. In order to cope with the uncertainty of demand, time series analysis and regression models are used to dynamically predict future demand, combined with the safety stock level to ensure that inventory costs are reduced while meeting customer needs.

When selecting suppliers, the article uses the MADM (Multi-attribute Decision Method) method, combined with the AHP (Analytic Hierarchy Process) and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) methods, to systematically evaluate different suppliers. When establishing a decision hierarchy, the selection criteria are divided into dimensions such as cost, quality, delivery time, and service. AHP is used to assign weights and determine the importance of each criterion. Then, a decision matrix is constructed to calculate the relative advantages and disadvantages of each supplier. The comprehensive score is evaluated using the TOPSIS method, and the best supplier is finally selected. The formula is as follows:

$$V_i=\sqrt{{\displaystyle {{\displaystyle \sum }}_{j=1}^m}{\left(x_{ij}-x_{j^{+}}\right)}^2},$$(9)

V_i is the distance between supplier i, x_ij is the score of the supplier on the jth indicator, and $x_{j^{+}}$ is the ideal solution. This method can not only ensure the selection of suitable suppliers but also effectively reduce procurement risks.

The above three optimization methods can be considered uniformly through a comprehensive optimization model. Construct a multi-objective optimization model, integrate logistics routing, inventory management, and supplier selection, and use the weight method to combine various objective functions. The optimization objectives are:

$$\text{min}Z={\alpha }_1{Z}_{path}+{\alpha }_2{Z}_{inventory}+{\alpha }_3{Z}_{supplier},$$(10)

Z_path, Z_inventory, and Z_supplier are the optimization objectives of logistics routing, inventory management, and supplier selection, respectively, and α₁, α₂, and α₃ are the corresponding weight coefficients. Through this model, multi-objective coordinated optimization can be achieved to ensure the best balance between logistics efficiency, inventory cost, and supplier quality.

In Figure 2, identifying tactical problems is the starting point of all tactical optimization methods. By identifying existing tactical problems, enterprises can clarify the direction and focus of optimization. Three main paths are divided from the identification nodes, namely logistics optimization, inventory management, and supplier selection. Each path represents a different optimization area, targeting common supply chain management challenges in high-end equipment manufacturing.

In the process of logistics optimization, the network must be modeled first. This step is to understand the relationship between the nodes in the supply chain, and then the Dijkstra algorithm [37,38] is implemented to help find the best logistics route. By selecting the best path, it can ensure the lowest logistics cost and the highest efficiency. In terms of inventory management, it needs to establish an inventory model to monitor and adjust inventory levels. Predicting demand, understanding market changes, and finally optimizing inventory levels can ensure a quick response when demand changes. For supplier selection, it is necessary to define criteria such as cost and quality to facilitate subsequent evaluation. When evaluating suppliers, the strengths and weaknesses of different suppliers can be analyzed, and the best supplier can be selected to ensure the stability and reliability of the supply chain.

Fig. 2 Tactical optimization.

3.2 Dynamic supply chain service portfolio optimization

3.2.1 Real-time data collection and processing of artificial intelligence communication technology

Real-time data collection and processing of artificial intelligence communication technology is a key link to ensure the efficient operation of all links in the supply chain. Smart sensors and IoT devices are deployed at various nodes of the supply chain to monitor key data such as logistics status, inventory levels, and production progress in real time. In order to avoid communication delays and network congestion, the data transmission efficiency is optimized by dynamically allocating bandwidth and spectrum, and the preliminary data is filtered and preprocessed with the help of edge servers, and the filtered data is uploaded to the cloud big data platform for further analysis. Set the real-time data input to x_t [x₁ (t) , x₂ (t) , … , x_n (t)], where x_i (t) is the state data of the i th node at time t. Through the RNN time series model, the supply chain demand at future time points can be predicted:

$$h_t=\sigma \left(W_h{x}_t+U_h{h}_{t-1}+b_h\right),$$(11)

$${{\displaystyle \hat{y}}}_{t+1}=W_y{h}_t+b_y,$$(12)

h_t is the hidden state, and ${{\displaystyle \hat{y}}}_{t+1}$ is the predicted output at the next moment. This process can effectively predict potential supply chain bottlenecks or market fluctuations and provide optimization solutions for decision-makers.

In order to solve the problems of information islands and data inconsistency, blockchain technology is used to ensure the transparency and immutability of data in the upstream and downstream of the supply chain. The distributed ledger technology of blockchain can ensure the interoperability of data between different nodes and prevent data loss or tampering. Combined with the above-mentioned real-time data collection and processing methods, the supply chain management system can achieve fully automated processing from data collection to optimized decision-making, effectively improving the overall response speed and flexibility of the supply chain. Here, the article shows the data collection methods of four nodes. The devices used are IoT (Internet of Things) sensors, PLC (Programmable Logic Controller), RFID (Radio Frequency Identification), GPS (Global Position System), ERP (Enterprise Resource Planning) system, etc. The specific nodes and data types of real-time data collection are shown in Table 1.

Table 1 shows the data collection content and transmission methods at different nodes in the supply chain. At the production node, industrial IoT sensors are used to monitor production progress and equipment status in real time, and data is transmitted through 5G networks and edge computing. At the warehouse node, RFID technology ensures accurate tracking of items. At the logistics node, GPS tracks the transportation route of goods in real time and monitors the temperature of goods in transit through temperature control sensors. Supplier nodes use intelligent quality inspection equipment to monitor the quality of raw materials and inventory levels, and data is processed and transmitted through edge computing to ensure timely and transparent supply chain information. The above equipment status collection frequency can be adjusted appropriately to ensure the normal operation of the equipment.

3.2.2 Adaptive optimization and dynamic resource adjustment

After collecting real-time data, the system can use the dynamic optimization model to perform adaptive resource allocation adjustments. In the process of model optimization, in order to achieve dynamic adjustment, the segmented dynamic programming method is used to decompose the optimization problem of the supply chain into multiple short-term optimization sub-problems. Set the period t, and in each period, update the resource allocation decision through the following dynamic programming formula:

$$V\left(t\right)=\text{min}\left\{C\left(x_t,S_t\right)+V\left(t-1\right)\right\},$$(13)

V (t) is the optimal decision value at time t, and C (x_t, S_t) can minimize the cost for the current state variables S_t in each period and adjust resource allocation in real time. State variables S_t include inventory (unit: pieces), order delay days (unit: days) and other quantifiable indicators. Such variables can be obtained through real-time data acquisition system and used in dynamic optimization decision-making process.

Combined with the ROS strategy (Rolling Optimization Strategy), a rolling window W is defined to achieve more flexible optimization and adjustment. In each rolling window, the resource allocation strategy is updated based on the latest status feedback data. Set the optimization cycle to T_w, and in each time window, the optimization decision formula is:

$$\text{min}{\displaystyle {{\displaystyle \sum }}_{k=t}^{t+T_w}}T{C}_k.$$(14)

This strategy ensures that within each time window, the model can reflect the latest market demand and resource allocation. By analyzing the real-time feedback of each window, the resource allocation strategy can be corrected and optimized to improve the dynamic response capability and operating efficiency of the overall supply chain. This adaptive optimization mechanism can ensure the flexibility and responsiveness of the supply chain in a dynamic environment and improve the overall operational efficiency.

3.3 Parallel computing implementation of CGA

3.3.1 Parallel population initialization and distributed evaluation

In the parallel population initialization and distributed evaluation of CGA, the population refers to a collection of multiple individuals, each of which represents a possible solution.

This article implements distributed generation of populations on a cloud platform. By designing a modular population generation algorithm, each computing node is used to independently generate individuals of the initial population. The parameter initialization of these individuals follows certain range restrictions to ensure that the characteristics of each individual are within the feasible solution space. This process is implemented by the following formula:

$$x_i=\text{rand}\left(L_{min},L_{max}\right),$$(15)

x_i represents the eigenvalue of the ith individual, L_min and L_max are the lower and upper limits of the eigenvalue, respectively. A uniformly distributed random number generator is used to ensure the diversity of the population and avoid premature convergence.

Fitness evaluation is performed locally on each computing node, and the evaluation function is set as a weighted function of the total cost and response time of the supply chain service combination:

$$F\left(x\right)=w_1\cdot C_{total}\left(x\right)+w_2\cdot T_{response}\left(x\right).$$(16)

During the evaluation process, each node independently calculates the fitness value of its population individuals, avoiding delays and bottlenecks caused by global data transmission. Using distributed database technology, nodes can access and update their fitness values in real time to ensure the timeliness of the evaluation results.

Table 2 shows sample data for population initialization in CGA, reflecting the performance of different individuals in the high-end equipment manufacturing supply chain in resource allocation optimization. Each row represents an individual, whose characteristics are raw material cost, logistics time, and supplier reliability. These characteristic values are obtained by analyzing historical data or market research to simulate different supply chain strategies. The raw material cost of individual 1 is $5.2, the logistics time is 10.5 days, and the supplier reliability is 3.1. The combination of these values makes its fitness value reach 95.0, indicating that this configuration is optimal in terms of the overall performance of the supply chain. Relatively speaking, although the characteristic value of individual 2 has an advantage in logistics time and supplier reliability, its higher raw material cost leads to a fitness value of 88.5. This analysis process emphasizes the impact of each characteristic on fitness. By evaluating these individuals, better resource allocation plans can be identified, which in turn provides a basis for subsequent selection, crossover, and mutation operations, helping to achieve efficient supply chain management and optimization.

3.3.2 Parallel selection and crossover operation

In the parallel selection and crossover operation of CGA, it is necessary to implement an individual selection mechanism based on local fitness. Each computing node selects a certain number of high-quality individuals from the generated individuals by roulette wheel selection or tournament selection according to its local fitness value. These high-quality individuals can generate a new generation of individuals in the subsequent crossover operation. The probability calculation formula for roulette wheel selection is:

$$P\left(i\right)=\frac{F\left(i\right)}{{{\displaystyle \sum }}_{j=1}^{N}F\left(j\right)},$$(17)

P (i) is the probability of selecting individual i, F (i) is the fitness of individual i, and N is the total number of individuals. This mechanism can effectively retain individuals with higher fitness and improve the convergence speed of the algorithm.

The crossover adopts single-point crossover and multi-point crossover strategies. In a single-point crossover, two parent individuals are selected, and a crossover point is randomly picked; the part before that point is retained, and the subsequent part is replaced from the other parent individual. For two parent individuals A = [a₁, a₂, a₃, a₄] and B = [b₁, b₂, b₃, b₄], if the crossover point is randomly selected as 2, the offspring individuals after crossover are C = [a₁, a₂, b₃, b₄] and D = [b₁, b₂, a₃, a₄].

To further enhance diversity, a mutation operation is introduced after the crossover operation, and a random mutation mechanism is used to make small random adjustments to the generated offspring individuals. The mutation operation can be described by the following formula:

$$X_{new}=X_{old}+\mathrm{\Delta }X,$$(18)

ΔX is a random perturbation value that follows a normal distribution. The disturbance value is ϵ∼N(0,0.1), the mean value is 0, and the standard deviation is 0.1. Mutation helps prevent the algorithm from falling into a local optimum and enhances the diversity of the population.

Table 3 shows an example of a mutation operation. Each row represents an original individual, its corresponding mutation rate, and the individual after mutation. The data generation process determines the probability of mutation at each gene locus by setting the mutation rate. The mutation rate of individuals [1,2,3,4] in the first row is 0.1, which means that each site has a 10% chance of mutation, and locus 3 is mutated to 4, thus generating the mutated individuals [1,2,4,4]. For the second row, the mutation rate of individuals [5,6,7,8] is 0.2, where locus 3 is mutated to 6, generating the mutated individuals [5,6,6,8]. In the third row, due to the low mutation rate (0.15), the individual does not mutate and remains unchanged. In the fourth row, the value of gene locus 4 changes from 16 to 17. This random mutation helps increase the diversity of the population, thereby improving the ability of the genetic algorithm in global search.

These offspring individuals that have been selected and crossed can be evaluated for their fitness, ensuring that the new population is improved in each generation. After parallel selection and crossover operations, CGA achieves efficient individual generation and optimization, and promotes the evolution of supply chain service combination solutions to the global optimal solution.

4 Results

4.1 Supply chain service efficiency evaluation

In the evaluation of supply chain service efficiency, total operating cost and service response time are used as key indicators to comprehensively evaluate the actual benefits of the optimized service portfolio. The total operating cost of the optimized supply chain is achieved by accurately calculating the various expenses involved, including the costs of raw material procurement, logistics transportation, inventory holding, and distribution. The advantages and disadvantages of the double-layer model are analyzed by comparing the cost of raw material procurement with that of the traditional single-layer model.

Figure 3 compares the total operating cost of the single-layer model and the double-layer model in different months. The horizontal axis represents the supply month, which gradually decreases from 1 to 12. The vertical axis represents the total operating cost (unit: 1 thousand US dollars). The total operating cost of the single-layer model is $50,000 in January, and the cost gradually decreases as the month increases, and finally drops to $32,000 in December. Comparatively speaking, total operating costs for a double-layer model also start at $50,000, but drop more significantly, ultimately to $23,000 in December. The double-layer model is superior to the single-tier model in its ability to manage and optimize the supply chain. As the months increase, the flexibility and resource allocation efficiency of the double-layer model make cost control more effective, demonstrating its advantages in complex supply chain management. This comparison reveals that in the high-end equipment manufacturing industry, the adoption of a double-layer planning model can not only reduce total operating costs but also improve overall operational efficiency, providing important support for the sustainable development of enterprises.

Minimizing service response time is also an important dimension of evaluation. Through real-time monitoring and dynamic adjustment, the optimized supply chain can quickly respond to market changes and improve order fulfillment speed.

In Figure 4, the horizontal axis represents the time point, from 1 to 10 represents different periods, and the vertical axis represents the response time (unit: hour). Through the two broken lines drawn, it can be seen intuitively that the changes in the response time of the single-layer model and the double-layer model occur at different time points. The response time of the single-layer model is higher than that of the double-layer model as a whole. In the initial stage, the response time of the single-layer model is 15 h, while the response time of the double-layer model is 18 h. The double-layer model has a longer response time. As time goes by, the double-layer model shows obvious optimization effects, and its response time gradually decreases from the initial 18 h to 6 h, which reflects the advantages of the double-layer model in dealing with the complexity and dynamics of the supply chain. In contrast, the response time of the single-layer model has also been reduced, but its efficiency improvement is relatively small, from 15 h to 10 h. This shows that the double-layer model can more effectively adapt to market changes and customer needs when optimizing the supply chain service portfolio, and improve the overall response efficiency.

The response efficiency of the traditional single-layer model system is low, and it is difficult to cope with the complex supply chain environment of the high-end equipment manufacturing industry. The double-layer model is optimized through hierarchical optimization mechanism and real-time data feedback. The initial response time is slightly higher because the upper-level strategic decision needs to evaluate the global resource coordination, but with the rapid iterative optimization of lower-level tactical problems (such as logistics path and inventory adjustment), the overall response efficiency of the system is significantly improved, and the optimization effect is finally realized.

Fig. 3 Total operating cost comparison.

Fig. 4 Service response time comparison.

4.2 Performance evaluation of CGA

In this study, the performance of CGA was evaluated through multiple indicators, especially in large-scale optimization problems, and specific comparisons were made with different algorithms.

First, the convergence speed was analyzed to compare the impact of different algorithms on the performance of the overall supply chain. Here, the CGA of this study was used for comparative experiments with TGA and PSO.

Figure 5 shows the convergence time comparison of three optimization algorithms, namely TGA, PSO, and CGA, at 40 iterations. The horizontal axis represents the number of iterations, and the vertical axis represents the time required for each generation (in seconds). TGA showed a high calculation time in the early stage, which then gradually decreased and finally approached 95 s in the 39th generation, indicating that the algorithm converged slowly during the multi-generation optimization process; PSO showed a faster convergence speed than TGA in most generations, but also converged in the 39th generation. The convergence time of CGA is relatively low in the early stage, and with the increase of generations, the convergence time steadily decreases, and finally tends to 90 s in the 35th generation, with a faster convergence speed, showing its superior convergence characteristics and global search capabilities. It can be seen that the convergence time and convergence speed of CGA in dealing with large-scale optimization problems are significantly better than TGA and PSO, and can better adapt to the complex supply chain optimization needs of high-end equipment manufacturing industry. CGA uses the parallel processing capability of cloud computing to realize the distributed evaluation and evolution of the population, which significantly reduces the time cost of each generation optimization. Its adaptive crossover and mutation mechanism enhances the global search ability, so that the algorithm can approach the optimal solution in fewer iterations, thus improving the convergence speed and efficiency.

In terms of optimization precision, CGA can generate more candidate solutions and perform efficient evaluation by making full use of cloud computing resources, thereby improving the quality of the final solution. Compared with PSO, CGA can usually obtain higher fitness values when dealing with complex constraints and objective functions. CGA can more effectively explore and utilize information in a high-dimensional solution space, avoiding the risk of falling into local optimality. The data performance is shown in Figure 6.

Figure 6 shows the comparison of optimization precision of the three algorithms in 40 iterations. The horizontal axis represents the number of iterations, ranging from 1 to 40, and the vertical axis represents the optimization precision, in percentage, ranging from 65% to 100%.

The optimization precision of TGA gradually increased from 75% in the first generation to 95% in the 40th generation. Although the overall trend is upward, the increase is relatively slow, reflecting the limitations of the algorithm on accuracy during the optimization process, especially when dealing with complex problems. The PSO optimization precision starts at 70% and increases to 96% after 40 iterations, which is similar to TGA. The CGA optimization precision starts at 80% and reaches more than 95% after 21 iterations, with the highest being 99%. The algorithm shows the highest accuracy and the smoothest rising curve, indicating that it has obvious advantages in dealing with complex multi-objective optimization problems, can effectively avoid the trap of local optimal solutions, and achieve higher optimization precision. By comparison, it can be clearly seen that CGA is superior to TGA and PSO in overall accuracy, showing its potential application value in the optimization of complex supply chain services in high-end equipment manufacturing. This result supports the necessity and effectiveness of applying CGA to practical optimization problems.

From the perspective of algorithm stability, the fitness value can be calculated according to Formula 5, and the stability of the algorithm can be analyzed by comparing the fitness value distribution of the three algorithms in different cases.

Figure 7 shows the fitness distribution of CGA, TGA, and PSO in four specific cases, including supply chain network optimization, inventory management optimization, logistics route optimization, and supplier selection optimization. The horizontal axis represents the algorithm used, and the vertical axis represents the fitness value of each algorithm.

In the supply chain network optimization case (Figure a), CGA's fitness values range from 0.93 to 0.96, demonstrating significant global search capabilities. However, TGA and PSO have lower fitness distributions, ranging from 0.85 to 0.88 and 0.88 to 0.91, respectively, indicating poor performance. In the inventory management optimization case (Figure b), CGA performs well, with fitness values concentrated in the range of 0.92 to 0.95, while TGA and PSO have lower fitness values, ranging from 0.79 to 0.82 and 0.83 to 0.86, respectively. In the logistics route optimization cases (Figure c) and supplier selection optimization cases (Figure d), CGA's fitness values also surpass those of other algorithms, demonstrating its clear advantage in handling dynamic and complex supply chain systems. Overall, CGA outperforms TGA and PSO in all cases, with overall fitness values ranging from 0.92 to 0.97, demonstrating its strength in large-scale, multi-objective supply chain optimization problems.

Fig. 5 Convergence speed comparison of optimization algorithms.

Fig. 6 Comparison of optimization precision.

Fig. 7 Comparison of fitness values of algorithms in different cases.

5 Discussion

The two-level programming model and cloud genetic algorithm based on artificial intelligence communication technology have shown significant advantages in the optimization of the supply chain in the high-end equipment manufacturing industry. The following discussion is carried out from three aspects: theoretical contribution, practical significance, and future research direction.

In terms of theoretical contribution, This study further advances this approach by constructing a two-level programming model, integrating strategic resource allocation with tactical optimization through a hierarchical approach. Compared to traditional genetic algorithms, cloud genetic algorithms fully leverage the parallel processing capabilities of cloud computing. Experimental results show that they approach convergence within 35 generations, with a convergence time stabilizing at approximately 90 s, demonstrating a faster solution speed. Furthermore, this study deeply integrates artificial intelligence communication technology with blockchain technology, not only enabling real-time monitoring of the supply chain but also fundamentally addressing data inconsistencies and information silos through distributed ledger technology, a feature that has not been fully explored in existing research. Therefore, through innovative model architecture and improved optimization algorithms, this study provides a more efficient and intelligent solution to complex supply chain issues such as those in high-end equipment manufacturing.

In terms of practical significance, in the high-end equipment manufacturing industry, the dynamics and complexity of the supply chain put forward higher requirements for management. The model of this study solves the problems of information islands and data consistency through real-time data collection and blockchain technology, and enhances the transparency and responsiveness of the supply chain. By leveraging real-time data collection and blockchain technology, the model resolved information silos and data consistency issues, reduced information verification time, and significantly improved responsiveness. Experimental results showed that within 12 months, the model reduced total operating costs from $50,000 to $23,000 and shortened service response time from 18 h to 6 h, demonstrating its adaptability and efficiency in dynamic environments. In addition, the stability and global search capabilities of cloud genetic algorithm provide enterprises with reliable tools in multi-objective optimization scenarios, which helps enterprises to achieve efficient decision-making in key links such as resource allocation and logistics path selection. The parallel computing characteristics of cloud genetic algorithm significantly reduce the energy consumption per optimization task, providing technical support for green supply chain management.

In terms of future research directions, although this study has achieved certain results, there are still some directions worthy of in-depth exploration. The robustness of the model in extreme market fluctuations or sudden events (such as supply chain disruptions) needs to be further verified. Secondly, the current research mainly focuses on a single industry, which can be expanded to other high-complexity manufacturing industries (such as automobiles or electronics industries) in the future to verify the universality of the model. In addition, the rapid development of artificial intelligence technology provides more possibilities for supply chain optimization, such as combining reinforcement learning or large language models to further improve the intelligence level of prediction and decision-making. Finally, how to balance the complexity of the algorithm with the computing resource constraints in practical applications is also an important topic for future research.

In summary, this study provides an effective solution for supply chain optimization in the high-end equipment manufacturing industry through theoretical innovation and technology integration, and at the same time lays an important foundation for subsequent research. Future work can focus on model expansion, technology integration, and deepening of practical application scenarios.

6 Conclusions

This article proposes a double-layer planning model based on artificial intelligence communication technology for complex supply chain management problems in high-end equipment manufacturing industry, and combines it with CGA for optimization. Research results show that this model can effectively cope with multi-level decision-making and dynamic adjustment needs in modern supply chains. The overall operational efficiency and intelligence level of the supply chain have been improved. CGA uses the parallel processing capabilities of cloud computing to accelerate the optimization process and significantly improve the convergence speed and optimization precision of the algorithm. This study achieves real-time monitoring and dynamic adjustment of the supply chain's operational status. By leveraging blockchain's distributed ledger to ensure data immutability, it reduces information verification time and addresses the issues of delayed information transmission and silos in traditional supply chain management. Although this research focuses on high-end equipment manufacturing, its modular design allows for scalability to small and medium-sized enterprises. By adjusting resource constraint parameters, it can adapt to supply chain networks of different scales. Although this study focuses on high-end equipment manufacturing industry, the modular design of the model makes it scalable to small and medium-sized enterprises, and can be adapted to supply chain networks of different sizes by adjusting resource constraint parameters. The experiment shows that the total operating cost of the proposed two-layer model is reduced from $50,000 to $23,000 within 12 months, the service response time is shortened from the original 18 h to 6 h, the convergence speed of CGA is close to 90 s in 35 generations, and the optimization accuracy remains above 95% after 21 optimizations. The model proposed in this article provides new ideas and methods for supply chain optimization in the high-end equipment manufacturing industry, promotes the development of intelligent supply chain management, and has important theoretical and practical application value.

Funding

This work was supported by the Natural Science Foundation of Guangxi Province (No.2021GXNSFAA075019); Philosophy and Social Science Foundation of Guangxi (No.25KSF232); Higher Education Undergraduate Teaching Reform Project of Guangxi (No.2024JGA258); The “14th Five Year Plan” of Guangxi Education and Science special project of college innovation and entrepreneurship education (No.2022ZJY2727); The "14th Five Year Plan" of Guangxi Education and Science Annual project in 2023 (No.2023A028). This study acknowledge the support of Guangxi Academy of Artificial Intelligence; the National First-class Undergraduate Major - The Major of Logistics Management; Demonstrative Modern Industrial School of Guangxi University - Smart Logistics Industry School Construction Project; Guangxi Colleges and Universities Key laboratory of Intelligent Logistics Technology; Engineering Research Center of Guangxi Universities and Colleges for Intelligent Logistics Technology; Demonstrative Modern Industrial School of Guangxi University - Smart Logistics Industry School Construction Project, Nanning Normal University.

Conflicts of interest

The author(s) declare(s) that there are no conflicts of interest regarding the publication of this paper

Data availability statement

This article does not cover data research. No data were used to support this study.

Author contribution statement

The following statements should be used “Conceptualization, X.Y. and J.M.; Methodology, M.Z.; Software, J.L.; Validation, X.Y., J.M. and Z.Z.; Formal Analysis, X.Y.; Investigation, J.M.; Resources, M.Z.; Data Curation, J.M.; Writing − Original Draft Preparation, M.Z.; Writing − Review & Editing, X.Y.; Visualization, J.L.; Supervision, J.L.; Project Administration, M.Z.; Funding Acquisition, J.M.”.

References

All Tables

All Figures

	Fig. 1 Systematic process of supply chain management.
In the text

	Fig. 2 Tactical optimization.
In the text

	Fig. 3 Total operating cost comparison.
In the text

	Fig. 4 Service response time comparison.
In the text

	Fig. 5 Convergence speed comparison of optimization algorithms.
In the text

	Fig. 6 Comparison of optimization precision.
In the text

	Fig. 7 Comparison of fitness values of algorithms in different cases.
In the text