A computing power supply chain network equilibrium calculation method based on a projection algorithm

Abstract

The application discloses a computing method for balance of a computing power supply chain network based on a projection algorithm, and belongs to the field of information management and information systems. In view of the problem that existing supply chain models are difficult to depict the influence of computing power resources as a new type of production factor on enterprise decision, product quality and market demand, a multi-layer supply chain network model is constructed by fusing data flow, computing power flow and product flow. The method introduces computing power service providers to form a multi-agent decision framework covering suppliers, manufacturers, computing power service nodes and demand markets, and establishes a supply chain network balance condition. Further, the multi-agent interaction is uniformly modeled based on a variational inequality, and a projection algorithm is used to solve the balance solution. The application can reflect the effect of computing power resources on product quality and market demand through an information generation mechanism, realize collaborative optimization of computing power resource allocation and supply chain decision, improve system operation efficiency and resource allocation rationality, and is suitable for computing power driven supply chain optimization and decision scenarios.

Description

Technical Field

[0001] This invention proposes a computational power supply chain network balancing calculation method based on projection algorithm, belonging to the field of information management and information systems. Background Technology

[0002] With the rapid development of the digital economy, data, algorithms, and computing power have gradually become crucial foundational elements driving industrial upgrading. Among these, computing power, as a core resource supporting data processing and artificial intelligence applications, plays an increasingly important role in areas such as intelligent manufacturing, smart supply chains, and digital services. Simultaneously, traditional supply chain systems are evolving towards digitalization and networking, with enterprises becoming significantly more reliant on data processing capabilities and computing resources in their production, procurement, and sales processes. Current research on supply chain networks primarily focuses on optimizing raw material flows, product flows, and pricing mechanisms. This involves constructing multi-layered supply chain network models and employing optimization methods or game theory analysis to achieve resource allocation and cost control. However, these methods typically treat production efficiency, product quality, or changes in demand as exogenous variables, failing to fully consider the role of computing power resources in data processing and information generation, and thus struggling to reflect the impact of computing power as a new production factor on the supply chain's operational mechanism. On the other hand, in the field of computing resource allocation, existing research mostly focuses on task scheduling and resource allocation in cloud computing or edge computing environments. The primary goal is to reduce computing latency and improve resource utilization, emphasizing optimization within the computing system itself. However, it rarely analyzes how computing resources participate in enterprise production decisions and influence market supply and demand from the perspective of the entire supply chain system. Furthermore, while some studies attempt to introduce data or information factors into supply chain models, they typically only provide a simple description of data value or information quality, lacking a systematic model of the complete transmission mechanism of "data-computing power-information-product quality-market demand." Simultaneously, in multi-agent network environments, complex interactions exist between enterprises, computing service providers, and the market, making it difficult for traditional single optimization models to uniformly describe the collaborative decision-making and equilibrium states among these entities.

[0003] Therefore, existing technologies suffer from at least the following problems: First, they fail to embed computing resources as a key production factor into the supply chain network model, lacking a characterization of their economic attributes and impact paths; second, they lack a unified modeling method to describe the decision-making behavior of multiple stakeholders and the network equilibrium state; and third, existing methods struggle to achieve synergistic optimization of computing resource allocation and supply chain decision-making. Based on these problems, it is necessary to provide a new technical solution that introduces computing resources into the supply chain network modeling framework. By constructing a multi-stakeholder equilibrium model and designing corresponding solution methods, synergistic optimization of computing resources and the supply chain system can be achieved, thereby improving the overall system operating efficiency and the rationality of resource allocation. Summary of the Invention Technical issues:

[0004] The technical problem this invention aims to solve is that, in a computing-enabled supply chain network environment, when enterprises make production decisions and allocate computing resources, they need to simultaneously consider the differences in the distribution of computing resources among different computing service nodes, as well as the cost structure and conversion efficiency of data in the process of transmission, processing and information generation, while also taking into account the impact of product quality on market demand, so as to achieve the synergistic optimization of computing resource allocation and supply chain operation and the overall balance of the system. Technical solution:

[0005] To address the aforementioned technical problems, this invention provides a method for equilibrium modeling and optimization of supply chain networks empowered by computing power. By introducing computing resources into the supply chain network structure, a multi-layered network model integrating data flow, computing power flow, and product flow is constructed. Within this unified framework, multi-entity collaborative decision-making and system equilibrium solutions are achieved, thereby realizing the coordinated optimization of computing resource allocation and supply chain operation. In the specific implementation process, a supply chain network structure including raw material supply nodes, manufacturing nodes, computing power service nodes, and demand market nodes is first constructed. The transmission relationships of product flow, data flow, and computing power flow between nodes are defined, and a corresponding network topology model is established. By introducing computing power service nodes, computing power resources participate in the supply chain system operation as an independent element. Based on this, a production decision model for manufacturing nodes is established to describe the coupling relationship between raw material input, computing power resource input, and product output. Simultaneously, data processing and information generation functions are constructed to characterize the impact of computing power resources on information quality during data processing and further reflect the mechanism by which information quality affects product quality or market demand. Furthermore, cost and revenue functions are established for each type of node in the network, including raw material procurement costs, computing power usage costs, data transmission costs, and product sales revenue. The impact of information quality on the demand or price function is also introduced, thereby achieving a linked modeling of computing resources, production decisions, and market response. Based on the above model, a multi-agent optimization model is constructed based on the optimal decision-making behavior of each node. By unifying the optimality conditions of each node, the multi-agent decision-making problem is transformed into a variational inequality model, thus describing the overall equilibrium state of the supply chain network. For the constructed variational inequality model, a projection iteration algorithm is designed to solve it. This involves initializing resource allocation variables, constructing a gradient mapping function, performing feasible region projection operations, and iteratively updating variables until a preset convergence condition is met, thereby obtaining the network equilibrium solution. Finally, the computing resource allocation results of each node in the supply chain network under equilibrium conditions, product flow distribution, and market equilibrium parameters are output, achieving coordinated optimization of computing resource allocation and supply chain system operation. 1. Model Method 1.1 Problem Description

[0006] With the development of the digital economy, enterprises are increasingly reliant on external computing resources in their production processes to analyze, model, and optimize internally accumulated data. Computing power can significantly improve enterprise production efficiency and product quality, while reducing unit production costs, thereby impacting the enterprise's competitiveness in the demand market. However, computing power services have significant engineering characteristics: their usage cost depends not only on the price of computing power but also on the combined effects of the amount of data to be computed, the capacity limitations of computing centers, waiting time, and data transmission rates. Furthermore, enterprises need to purchase raw materials from multiple suppliers and ship products to multiple demand markets during the production process. Therefore, enterprise production decisions are constrained by multiple upstream and downstream links, each with a networked economic structure. To characterize the complex relationships in this digital production system, this study constructs a supply chain network consisting of three layers of nodes: the upstream consists of m raw material suppliers and r computing centers, the middle layer consists of n enterprises, and the downstream consists of k demand markets. The specific network structure is as follows: Figure 1 As shown.

[0007] In this supply chain network, the flow of resources and information forms a dynamic system with nested product, data, and information flows. Upstream raw material suppliers continuously provide the necessary raw materials to enterprise nodes for production. Simultaneously, the vast amounts of raw data accumulated by enterprises during their production and operations are uploaded to a computing center. Within the computing center, this data undergoes processing such as calculation, inference, or training, transforming it into information directly applicable to production optimization. After computation, this information is returned to the enterprise as an information flow. This information not only reduces the unit production cost for enterprises but also improves the quality of the final product by refining processes, increasing precision, or enhancing intelligence. After obtaining information and completing production, enterprises transport their products to the demand market. In a perfectly competitive demand market, consumer demand for high-quality products is reflected in the market's price function. We allow consumers to choose different products based on quality and determine the quantity to purchase, ensuring the product flow is cleared at the market end, completing the economic loop of the entire chain. In this multi-flow interactive system, various costs are endogenously generated at different stages of the flow: enterprises incur purchase costs and transaction costs during the raw material procurement stage; corresponding transmission costs, computing costs, and waiting costs exist during data transactions; transmission costs are also incurred due to network conditions during the information return process to enterprises; and the manufacturing costs borne by enterprises in the final production are jointly determined by the input of raw materials and the information returned by the computing center. Furthermore, logistics costs are generated during the transportation of products from enterprises to the demand market, constituting the cost structure as the supply chain extends downstream. The relevant parameters and their meanings used in the model are shown in Table 1 below, the relevant variables and their meanings in Table 2 below, and the relevant functions and their meanings in Table 3 below. Table 1. Relevant parameters and their meanings Table 2. Relevant Variables and Their Meanings Table 3. Related Functions and Their Meanings

[0008] This section will analyze the behavior and optimal conditions of the raw material supplier layer, computing center layer, enterprise layer and demand market layer under the condition of perfect competition, and establish a model of the equilibrium of the entire supply chain network. 1.2 Model Establishment 1.2.1 Behavior and Optimality Conditions of Computing Centers

[0009] In a computing-enabled supply chain network, raw material suppliers produce raw materials and sell them to manufacturers at a certain price. The following analyzes the costs and revenues of supplier i. For the raw material supplier, the main costs are as follows: firstly, the production cost f of the raw materials. i In a perfectly competitive environment, the output depends not only on supplier i's own output, but also on the output of all raw material suppliers in the market. f i =f i (Q 1 ), Second, the raw material transaction costs between raw material suppliers and manufacturers. In addition to the purchase cost of the materials themselves, there are also comprehensive transaction costs throughout the procurement, collaboration, contract, and logistics execution processes. Here, we assume that the transaction costs are related to the raw material transaction volume q. ij Positively correlated, that is c ij =c ij (q ij ), The larger the volume of raw material transactions, the higher the transaction costs.

[0010] Raw material supplier revenue The main source of revenue is the sales of raw materials, of which ρ 1ij Let be the wholesale price of raw materials between raw material supplier i and manufacturer j, which is an endogenous variable. Therefore, the profit of raw material supplier i can be expressed as: Theorem 1: In a supply chain network, raw material suppliers at the same level engage in non-cooperative competition, and their cost functions are convex. The equilibrium condition for these raw material suppliers can be expressed by the following variational inequality, with the optimal solution... satisfy Equation (2) has a good explanation in economic terms: if the price that the manufacturer is willing to pay for raw materials is exactly equal to the marginal production of the raw material supplier and the transaction costs associated with the manufacturer, the raw material supplier will ship a positive quantity of raw materials to the manufacturer, and the flow on the corresponding route will be positive; if the marginal production and transaction costs of the raw material supplier exceed the price that the manufacturer is willing to pay for the product, then the flow on that route will be zero. 1.2.2 Behavior and Optimality Conditions of Raw Material Suppliers

[0011] In supply chain networks, computing power service providers receive data from manufacturers, process it into effective information that can improve production efficiency and product quality, and act as data element processors in the supply chain network, providing computing power services. They are key intermediaries in the modern supply chain digitalization process. The following is a detailed analysis of the cost and revenue composition of computing power service providers.

[0012] For computing power service provider S, the main cost is the cost of data computation. Assume that the computation cost can be expressed as a function of the sum of all data processed by the computing power provider: Q 3 Let q represent the data transaction volume between the manufacturer and the computing power service provider, assuming that the computing cost is convex and continuously differentiable, and has bounded second-order partial derivatives. Manufacturer data q js After the calculation and processing are completed, it is converted into a certain amount of information (Info). js The relationship between data and information can be represented by a function as follows: Info js =a s q js , Where a s This refers to parameters related to the algorithms and hardware used by the computing power service provider.

[0013] The revenue of computing power service providers mainly comes from the income from providing data processing services. Therefore, in this network, the profit of computing power service provider s can be expressed as:

[0014] Assuming that computing power service providers compete in a non-cooperative manner, and that the computational cost function is continuous and convex, then based on the first-order optimality condition of convex optimization, the following theorem can be obtained: Theorem 2: The optimality condition for computing power service providers can be expressed as the following variational inequality, with the optimal solution... satisfy Equation (4) gives the equilibrium optimality condition for the computing power service provider. Its economic meaning can be interpreted as the marginal computing cost when the computing power service provider provides services to a certain manufacturer. The unit computing power price ρ payable to the manufacturer 3js Consistent; if the unit transaction price is insufficient to cover the marginal calculation cost, no transaction will occur. 1.2.3 Firm Behavior and Optimality Conditions

[0015] Manufacturers, as key players in the network, need to purchase raw materials from raw material manufacturers to produce products and sell them to the demand market. They also need to transact with computing power service providers, transmitting data to them to obtain big data information. The following section analyzes in detail the composition of manufacturers' costs and revenues.

[0016] For manufacturer J, the main costs are as follows: firstly, the cost of purchasing raw materials, using... The second is the product's manufacturing cost. j This assumes that in a perfectly competitive environment, the manufacturing cost of a product depends not only on the raw materials the manufacturer obtains from its suppliers, but also on the data the manufacturer transmits to the computing service provider for calculation. f j =f j (Q 1 Q 3 ), Among these factors, production costs increase with output and decrease with the amount of information; thirdly, there are costs associated with data transactions with computing power service providers, primarily including the cost of purchasing computing power services. and the cost of calculating response time Assuming that the response time of data computation mainly consists of the time for data transmission to the computing power service provider, the waiting time for data computation, and the time for the completed computation information to be transmitted back to the manufacturer, the data transmission time cost is... For the amount of data to be transmitted q js With transmission rate The ratio, that is in It is the bandwidth between js files B. js A function of signal-to-noise ratio M: Calculated waiting time cost Simultaneously affected by the capacity C of computing power service providers s The amount of data q sent by the manufacturer for calculation js The effect can be expressed by a function as: Here, ω is the computational latency cost coefficient, used to reflect the intensity of the impact of computing resource congestion on task waiting time costs. When multiple manufacturers submit computing tasks to the computing service provider simultaneously, the increase in the total number of tasks will intensify competition for computing resources, thus causing a non-linear increase in waiting time costs. The transmission cost of sending the processed information back to the manufacturer is the amount of information transmitted, Info. js With transmission rate The ratio, the conversion relationship between data and information, can be expressed as a function: Info js =a s q js , Right now in It is the bandwidth between sj. sj A function of signal-to-noise ratio M: Therefore, the calculated response time cost It can be represented as:

[0017] Manufacturer's revenue The revenue mainly comes from product sales, of which ρ 2jk Let $\frac{j}{k}$ be the transaction price of the product between manufacturer $j$ and the demand market $k$, which is an endogenous variable. Therefore, manufacturer $j$'s profit can be expressed as: Theorem 3 assumes that manufacturers compete in a non-cooperative manner, and that the product production cost function and the response time cost function are continuous and convex. Define the feasible set of manufacturer j. According to the first-order optimality condition of convex optimization, the manufacturer's optimality condition can be expressed as the following variational inequality, for any (q) ij q jk q js )∈K j ,have As can be seen from the optimality condition given by equation (6), manufacturers cannot simultaneously adjust the scale of raw material procurement, product deployment structure, and the transaction volume of computing power data to obtain greater profits under given resource constraints and non-negativity constraints, thus reaching a stable optimal state. From the perspective of raw material and product allocation, the optimality condition reflects the inherent consistency between production and sales. The quantity of raw material procurement and the quantity of product sales are interconnected through resource balance constraints. The implicit opportunity cost corresponding to this constraint intrinsically affects the manufacturer's allocation decisions among different suppliers and markets in the equilibrium state. Manufacturers allocate resources at the marginal level to paths with higher net returns until all feasible paths achieve an equilibrium between marginal returns and marginal costs. In terms of computing power data transactions, the optimality condition reflects the manufacturer's trade-off mechanism between computing power service costs and production efficiency improvement. In the optimal state, the marginal decrease in manufacturing costs brought about by information is exactly equal to the marginal cost constituted by the price of computing power services and response time costs, so that manufacturers have no incentive to further adjust computing power investment. 1.2.4 Demand Market Behavior and Optimality Conditions

[0018] As the downstream players in the supply chain network, consumers in the demand market not only react to product prices but also to their quality levels. j Respond accordingly. High-quality products typically offer superior functionality, higher reliability, and a better consumer experience, directly increasing consumers' willingness to pay. Assume the product's demand-price function is p. k Regarding θ j Increasing and continuously differentiable, regarding the product demand d k Decreasing. Therefore, the demand price p for product j in the demand market. k This typically depends on the overall consumption pattern and the quality level of the product, where quality θ j It is endogenous, a direct result of manufacturers submitting data to computing power service providers and obtaining processed information. The marginal improvement of quality by information is diminishing, which can be expressed as a function: Where η is the information quality conversion coefficient, used to characterize the efficiency with which information obtained by the manufacturer through the computing power service provider is transformed into improved product quality during the product manufacturing process, and e is the natural logarithm. When the amount of information is 0, the initial quality of product j is η. The inverse demand function can be expressed as: ρ 4k =p k (d k q js ).

[0019] In addition, consumers also need to bear the transaction costs with manufacturers. jkHere we assume that the transaction costs between manufacturers and the demand market are equal to the transaction volume q between them. jk Positively correlated, that is c jk =c jk (Q 2 ), The larger the transaction volume of a product, the higher the transaction costs. Therefore, the equilibrium condition for consumers in the demand market can be expressed as: Equation (8) shows that if The market price that consumers are willing to pay It must equal the wholesale price of the product plus the transaction cost of the product; if the wholesale price of the product plus the transaction cost of the product is higher than the market price, then the transaction volume of the product in this channel is 0; Equation (9) shows that if the market transaction volume Then the market price must equal the inverse demand price; if the market price is higher than the price consumers are willing to pay... The trading volume is then squeezed to 0. Next, we define the feasible set of the demand market k:

[0020] Theorem 4: In demand market k, let the market decision vector be... Equilibrium state of demand market k The optimality conditions (3.8) and (3.9) are satisfied if and only if they satisfy the following variational inequality: for any (q) 1k ,...,q nk , ρ 4k d k )∈K k ,have In the equilibrium state, any offset in any feasible direction in the demand market cannot simultaneously improve consumers' payment structure and the market clearing status, thus ensuring the stability of market operation. The first term of Equation (10) reflects the payment consistency principle when consumers choose between products manufactured by different manufacturers: when a manufacturer has a positive transaction volume in demand market k, its generalized payment price must be consistent with the market price at the marginal level; if the generalized payment price corresponding to a certain manufacturer is higher than the market price, its products will not be selected by consumers in the equilibrium state, and the transaction volume is zero. The second term characterizes the clearing condition of the demand market and its price adjustment direction: in the equilibrium state, the total supply must be consistent with the demand scale at the current price and quality level; when the supply exceeds the demand, there is downward pressure on the market price to restrain demand and restore clearing; conversely, when the supply is insufficient to meet the demand, there is an upward momentum for the price, thereby promoting the market to adjust to a new equilibrium state. Product quality enters the demand function endogenously through information input, so that manufacturers' decisions on computing power services can indirectly affect the equilibrium outcome of the demand market. A higher level of information input expands the demand scale by improving product quality, thereby increasing the market's tradable volume at a given price and changing the price-quantity equilibrium relationship. This mechanism indicates that the demand market is closely coupled with the decisions of manufacturers and computing power service providers through the quality channel. 1.2.5 Equilibrium and Variational Inequality of Supply Chain Network

[0021] In the previous sections, the equilibrium states of computing power service providers, raw material suppliers, manufacturers and the demand market are respectively characterized by their first-order optimality conditions, and all can be equivalently expressed as corresponding variational inequality forms. Since raw material transactions, computing power service transactions and product transactions all occur in the same supply chain network, and the transaction volume on each route in the equilibrium state must simultaneously meet the optimality requirements of both transaction parties, the standard processing method of network equilibrium can be adopted: use the same transaction volume variable to represent the transaction level of each transaction route, and superimpose the marginal conditions of each entity on this route at the system level, so as to unify the local optima of multiple entities into a system variational inequality on the public feasible domain. This system variational inequality integrates the production and transaction costs in the upstream of the supply chain, the computing cost and response time cost in the computing power link, the endogenous response of the manufacturer-side production cost to information and output, as well as the payment consistency and clearing mechanism of the downstream market into the same equilibrium framework.

[0022] Denote the raw material transaction volume matrix Product transaction volume matrix Data transaction volume matrix Demand market terminal price vector The product flow balance constraint of the manufacturer is Its corresponding Lagrange multiplier vector is denoted as Define system decision vector The feasible domain of the system is When the assumptions that the cost function and demand function are continuously differentiable and convex hold, the system equilibrium solution is... If and only if for any The following system variational inequalities must be satisfied: In the summation process of equation (12), price terms that appear in pairs and have opposite signs can be simplified by addition and subtraction to cancel each other out, resulting in the final simplified variational inequality of the equilibrium of the entire supply chain network:

[0023] The variational inequality (13) is rewritten in standard form as follows, for a given X * ∈K, satisfying: Where <·, ·> represent the inner product in the mn+no+nr+o+n-dimensional Euclidean space. For the equilibrium solution in the supply chain network, where the system operator The function expressions for each component are as follows:

[0024] The system variational inequality characterizes the equilibrium operation mechanism of a computing-enabled supply chain network from a unified optimality perspective. Its essence reflects the marginal consistency and constraint coordination results under multi-entity, multi-segment conditions. In this equilibrium state, raw material supply, computing service provision, manufacturer production decisions, and demand market transactions are intrinsically linked within the network through price signals, shadow prices, and information quality channels, jointly determining how resources are allocated throughout the entire supply chain network. 2. Algorithm Design

[0025] To solve the equilibrium model of the computing-enabled supply chain network, this chapter expresses the equilibrium condition as a variational inequality problem defined on the non-negative feasible region and employs a projection-based iterative algorithm for numerical solution. This algorithm approximates the equilibrium solution of the system through successive corrections and projection updates of the variational inequality operators. The specific solution steps are as follows.

[0026] Step 1: Initialization. First, determine the system's dimensional parameters based on the model structure, including the number of suppliers m, the number of manufacturers n, the number of computing power service providers r, and the number of end markets o. Simultaneously, specify the parameters related to the cost function, demand function, and quality function, as well as the convergence criterion ε and the maximum number of iterations k.max During the algorithm initialization phase, an initial feasible solution that satisfies the non-negativity constraint is selected. Furthermore, based on the Lipschitz continuity of the operator F(·), the step size parameter a = 1 / L is selected, where L is the Lipschitz constant, to ensure the stability and convergence of the algorithm.

[0027] Step 2: Iterative Update. In the k-th iteration, given the current solution X... (k) Perform the following operations in sequence:

[0028] (1) Marginal cost and marginal revenue calculation: Based on the current flow and price levels, calculate the marginal terms corresponding to each decision variable, including the marginal cost of raw material production and transaction, the marginal cost of product flow and computing power flow in the manufacturer's manufacturing process, the marginal cost of product transportation and transaction, the marginal cost of computing power service provider's computing cost and transmission and response delay, the marginal impact of the quality function on computing power requests, and its feedback effect on the manufacturer's revenue through the inverse demand function.

[0029] (2) Constructing a variational inequality operator: The marginal cost and marginal revenue mentioned above are organized into a variational inequality operator F(X). (k) )=(F 1 F 2 F 3 F p F λ ), where each component corresponds to the residuals of raw material flow, product flow, computing power flow, market price, and manufacturer equilibrium conditions, respectively.

[0030] (3) Projection Update: Based on the projection method, the current solution is corrected in one step: X (k+1) =Π K (X (k) -αF(X (k) )), Among them Π K (·) denotes the projection operator over the non-negative feasible region K, used to ensure that the updated solution always satisfies the feasibility constraints.

[0031] (4) Convergence criterion test: If ||X|| is satisfied, (k+1) -X (k) || 2 If k < ε, the algorithm is considered to have converged and the iteration stops; otherwise, let k ← k+1 and continue to the next round of iterations until the maximum number of iterations k is reached. max .

[0032] Step 3: Output the equilibrium solution. When the algorithm meets the convergence condition or reaches the maximum number of iterations, output the final solution:

[0033] The solution algorithm can be represented in pseudocode as follows:

[0034] The algorithm can be represented by a flowchart as follows: Figure 2 . Beneficial effects:

[0035] Compared with existing technologies, this invention introduces computing power service nodes into the supply chain network and constructs a multi-layered network model integrating data flow, computing power flow, and product flow. This allows for a holistic characterization of the impact mechanism of computing power resources as a new production factor on enterprise production decisions, product quality, and market demand, thus overcoming the shortcomings of traditional supply chain models in reflecting the path of computing power action. Simultaneously, this invention uses variational inequalities to uniformly model the interactive behavior of multiple stakeholders, transforming the dispersed decision-making problems of raw material suppliers, manufacturers, computing power service providers, and the demand market into a unified network equilibrium problem. This achieves a synergistic characterization of multi-stakeholder decision-making behavior and the overall system operation state. Furthermore, by designing a projection algorithm to solve for the equilibrium solution, not only is the feasibility and stability of the solution guaranteed, but the efficiency and operability of equilibrium calculation under complex network conditions are also improved. Moreover, this invention enables the synergistic optimization of computing power resource allocation and supply chain operation decisions, enhancing the rationality of resource allocation while improving the overall system operating efficiency, and providing a highly scalable technical means for computing power-driven supply chain optimization and related decision-making problems. Attached Figure Description Figure 1 A diagram of the supply chain network structure; Figure 2 Here is the algorithm flowchart; Figure 3 The diagram shows a computing network structure as an example. Detailed Implementation Example: Basic computing power network

[0036] This section considers a computing-enabled supply chain network consisting of 2 raw material suppliers, 2 computing power service providers, 2 manufacturers, and 2 demand markets to construct a numerical simulation example. In this network, each manufacturer can purchase raw materials from any raw material supplier and can choose to submit data to any computing power service provider for computation; the finished products can be distributed to multiple demand markets. The specific network structure diagram is shown below. Figure 3 As shown.

[0037] The relevant cost settings in the network are as follows: First, the raw material suppliers. The raw material production costs of the two raw material suppliers are expressed as follows: The transaction costs for the two raw material suppliers and the two manufacturers are expressed as follows: For computing power service providers, the computational costs of data are expressed as follows: The relationship between data and information can be represented as follows: For manufacturers, the manufacturing cost of raw materials can be expressed as: The response time cost of computation consists of the time it takes for data to be transmitted to the computing power service provider, the waiting time for data computation, and the time it takes for the computation completion information to be transmitted back to the manufacturer, which can be expressed as follows: In a demand market, the inverse demand function can be expressed as: The transaction costs between manufacturers and the demand market can be expressed as:

[0038] The model is solved numerically using a projection-based algorithm. Numerical results show that, under given parameter conditions, the proposed algorithm converges stably and successfully obtains a network equilibrium solution that includes raw material flow, product flow, and data flow. In this equilibrium state, the total system revenue is 157943.56, and the specific equilibrium results are shown in Table 4. Table 4: Equilibrium Results of Computing Power Empowering Supply Chain Networks

[0039] The numerical results shown in Table 4 demonstrate that the supply chain network system converges to a structurally stable equilibrium state with clear economic implications. No party can unilaterally adjust any decision variable to further reduce system costs and gain greater profits. After introducing a quality-added inverse demand structure, computing power investment is no longer merely a cost item, but rather generates positive feedback to manufacturers' revenue through information transformation and quality improvement mechanisms. Under the current parameter settings, this positive revenue is sufficient to cover data computation costs and response time costs, enabling manufacturers to actively utilize computing resources in equilibrium. Manufacturers' product quality levels are significantly positive, and the overall quality level effectively pushes up the equilibrium price in the demand market through the quality-added term. Even after considering the quantity-based price reduction effect, the market price remains at a high level, indicating that quality improvement plays a substantial role on the demand side. The numerical results, to some extent, verify the transmission mechanism depicted by the model: manufacturers submit data to computing power service providers for processing, obtaining more valuable information that helps them improve product quality, which in turn increases the market's willingness to pay. As this process continues, it eventually forms a positive cycle in equilibrium, making manufacturers' investment in computing power no longer just a technological choice, but an economically rational production decision.

Claims

1. A computational power supply chain network balancing calculation method based on projection algorithm, the method comprising the following technical features: ( 1) Obtain the raw material costs, computing service costs, data transmission costs, demand function parameters, and information generation function parameters required to build a computing power supply chain network; (2) Construct a computing power supply chain network including raw material supply nodes, manufacturing nodes, computing power service nodes and demand market nodes, and define the product flow, data flow and computing power flow relationships between nodes; (3) Establish a production decision model for manufacturing nodes, describe the functional relationship between data input, computing power processing and product output, and introduce an information generation function to characterize the impact of computing power on product quality. (4) Construct the cost function and revenue function for each node, including raw material procurement cost, computing power usage cost, data transmission cost and product sales revenue; (5) Based on the optimization decision-making behavior of each node, the equilibrium conditions of the supply chain network are established, transforming the optimal decision-making problem of multiple agents into a unified variational inequality model, which can be specifically expressed as: Where q ij q represents the volume of raw material transactions between ij; jk Indicates the product transaction volume between j and k; q js This represents the amount of data exchanged between JavaScript files. This represents the raw material transaction volume between ij under equilibrium conditions, and all transaction volumes form an mn-dimensional column vector. This represents the product transaction volume between j and k under equilibrium conditions, with all transaction volumes forming a no-dimensional column vector. This represents the data transaction volume between JavaScript servers under equilibrium conditions. All transaction volumes form an nr-dimensional column vector. f i (Q 1* f represents the production cost function of raw materials; j (Q 1* Q 3* ) is the production cost function of the product; It's a function for calculating response time costs between JavaScript instances; c jk (Q 2* () is a product transaction cost function between manufacturers and the demand market; λ represents the raw material transaction costs between raw material suppliers and manufacturers. j They are Lagrange multipliers; These are the values ​​of the Lagrange multipliers under equilibrium conditions; It is the data computation cost function of computing power service provider s; ρ 4k It is the product price in the demand market, k. It represents the product price in the demand market (k) under equilibrium conditions. It is the market demand for the product under equilibrium conditions; (6) Design a projection algorithm for solving the variational inequality model, update the resource allocation variables of each node in the network, and obtain the optimal solution that satisfies the equilibrium condition; Given the number of merchants r and the number of end markets o, along with parameters related to the cost function, demand function, and quality function, as well as the convergence criterion ε and the maximum number of iterations k. max During the algorithm initialization phase, an initial feasible solution that satisfies the non-negativity constraint is selected. In addition, based on the Lipschitz continuity of the operator F(·), the step size parameter a = 1 / L is selected, where L is the Lipschitz constant, to ensure the stability and convergence of the algorithm; (6.2) Iterative Update: In the k-th iteration, given the current solution X (k) Perform the following operations in sequence: (6.2.1) Marginal cost and marginal revenue calculation: Based on the current flow and price levels, calculate the marginal items corresponding to each decision variable, including the marginal cost of raw material production and transaction, the marginal cost of product flow and computing power flow in the manufacturer's manufacturing process, the marginal cost of product transportation and transaction, the marginal cost of computing power service provider's computing cost and transmission and response delay, the marginal impact of the quality function on computing power requests, and its feedback effect on manufacturer's revenue through the inverse demand function; (6.2.2) Constructing a variational inequality operator: Unify the above marginal cost and marginal revenue into a variational inequality operator F(X). (k) )=(F 1 F 2 F 3 F p F λ Each component corresponds to the residuals of raw material flow, product flow, computing power flow, market price, and manufacturer equilibrium conditions, respectively. (6.2.3) Projection Update: Based on the projection method, the current solution is updated in one step: X (k+1) =∏ K (X (k) -αF(X (k) )), Among them Π K (·) denotes the projection operator over the non-negative feasible region K, used to ensure that the updated solution always satisfies the feasibility constraints; (6.2.4) Convergence Criterion Test: If ||X|| is satisfied... (k+1) -X (k) || 2 If k < ε, the algorithm is considered to have converged and the iteration stops; otherwise, let k ← k+1 and continue to the next round of iterations until the maximum number of iterations k is reached. max ; (6.3) Output the equilibrium solution: When the algorithm meets the convergence condition or reaches the maximum number of iterations, the final solution is output:

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