Pricing method and system for dual-channel closed-loop green supply chain considering dominant structure

Abstract

The application discloses a double-channel closed-loop green supply chain pricing method and system considering dominant structure in the technical field of green supply chain enterprise pricing decision, S1, determining the premise assumption of constructing a model; S2, constructing a market demand function containing an online direct sales channel and an offline retail channel, and constructing a closed-loop profit function covering waste product recycling and remanufacturing; S3, constructing a supply chain pricing model under the condition of no environmental subsidy, a supply chain pricing model under the condition of innovation cost subsidy, and a supply chain pricing model under the condition of product output subsidy; S4, under the two dominant structures of manufacturer dominance and retailer dominance, the model is solved by using Stackelberg game and backstepping method respectively; S5, under the constraint that the total amount of environmental subsidies is equal, the optimal pricing strategy and the optimal subsidy strategy under different situations are output. The application provides a reference basis for the pricing and subsidy decision of environmental protection organizations, manufacturers and retailers.

Description

Technical Field

[0001] This invention relates to a dual-channel closed-loop green supply chain pricing method and system that considers the power structure in the field of green supply chain enterprise pricing decision-making technology. Background Technology

[0002] With the increasing severity of global climate change and environmental pollution, green and low-carbon development has become a common direction for countries worldwide to promote industrial upgrading and sustainable development. Green supply chain management, as an important pathway to achieving sustainable development, is receiving widespread attention from academia and industry. Against this backdrop, enterprises need to reduce the environmental impact of their products throughout their entire lifecycle through green technology innovation, and they also need to build a closed-loop supply chain system covering raw material procurement, production and processing, sales and distribution, and the recycling and remanufacturing of waste products to improve resource recycling efficiency.

[0003] However, green technology innovation requires continuous financial investment, and SMEs often face dual constraints of funding and technology. To address this, environmental organizations widely use environmental subsidies to incentivize green supply chains. Common subsidy methods fall into two main categories: first, "innovation cost subsidies," which subsidize investment costs in green innovation R&D; and second, "product output subsidies," which subsidize based on the sales or production volume of green products. Different subsidy methods exhibit significant differences in their incentive pathways and ultimate effects across different links in the supply chain.

[0004] Meanwhile, with the rapid development of e-commerce and internet technology, manufacturers are opening online direct sales channels while retaining traditional offline retail channels, thus forming a dual-channel supply chain structure of "online direct sales + offline retail." In this dual-channel environment, manufacturers are both suppliers to retailers and competitors in the end market; this "coopetition" relationship creates cross-price elasticity between channels. Furthermore, due to differences in company size, market position, and bargaining power among supply chain members, the supply chain often exhibits two typical power structures: manufacturer-led and retailer-led. The decision-making order and profit distribution mechanisms of members differ significantly under these different power structures.

[0005] The existing technologies have the following shortcomings: (1) Existing pricing methods focus on a single channel or only consider single factors such as consumer preferences and carbon emissions, and lack a method for systematically modeling environmental subsidies, dominance structures and dual-channel structures at the same time; (2) Existing methods rarely incorporate the closed-loop structure of waste product recycling and remanufacturing, the level of green innovation efforts and dual-channel competition into pricing decisions; (3) Existing methods lack a systematic solution process for comparing and switching between two environmental subsidy methods (innovation cost subsidies and product output subsidies), and cannot provide differentiated decision-making references for environmental organizations and supply chain enterprises. Summary of the Invention

[0006] The purpose of this invention is to provide a dual-channel closed-loop green supply chain pricing method and system that considers the dominant structure. It uses a backward inference method to solve for the optimal decision variables and optimal profits of each member of the supply chain, thereby providing a reference for pricing and subsidy decisions for environmental organizations, manufacturers and retailers.

[0007] To achieve the above objectives, this invention provides a dual-channel closed-loop green supply chain pricing method that considers the dominance structure, comprising the following steps:

[0008] S1. Determine the underlying assumptions for building the model;

[0009] S2. In the dual-channel closed-loop green supply chain, construct a market demand function that includes online direct sales channels and offline retail channels, and construct a closed-loop profit function that covers the recycling and remanufacturing of waste products; the market demand function is jointly affected by retail prices, direct sales prices, and the level of green innovation efforts of manufacturers;

[0010] S3. Based on the environmental protection subsidy method, construct supply chain pricing models for the following scenarios: no environmental protection subsidy, innovation cost subsidy, and product output subsidy.

[0011] S4. Under two dominance structures, namely manufacturer-led and retailer-led, the Stackelberg game and the backward inference method are used to solve the model to obtain the optimal equilibrium solutions for wholesale price, retail price, direct sales price and green innovation effort level under each case, as well as the optimal profit of supply chain members, consumer surplus and social welfare.

[0012] S5. Under the constraint of equal total environmental subsidies, compare the optimal equilibrium solutions under different dominance structures and different subsidy methods, and output the optimal pricing strategy and optimal subsidy strategy under different scenarios.

[0013] As a further improvement to the present invention, the underlying assumptions for constructing the model in S1 include the following:

[0014] (1) All members of the supply chain are risk-neutral and perfectly rational decision-makers who aim to maximize their own profits and have completely symmetrical information.

[0015] (2) To simplify the model without loss of generality, assume that the manufacturer has no fixed production costs and the unit production cost is zero, and the retailer's unit sales cost is also zero.

[0016] (3) The market demand for green products is linearly affected by retail prices, direct sales prices, and the level of green innovation efforts;

[0017] (4) The relationship between green innovation cost and green innovation effort level is a quadratic function, that is, the higher the green innovation effort level, the higher the unit innovation cost of a product;

[0018] (5) The manufacturer remanufacturing the waste products, the cost savings per remanufacturing unit is The manufacturer's unit recycling price to consumers is The recycling rate of waste products is ,and ;

[0019] (6) Environmental organizations’ subsidy strategies include two types: one is based on the proportion of manufacturers’ green innovation costs. Innovation cost subsidies that are subsidized Second, subsidies will be provided based on the manufacturer's output of green products, with a subsidy amount of [amount missing] per unit of output. , ;

[0020] (7) Consumer surplus equals the difference between the highest price consumers are willing to pay and the price they actually pay; social welfare is obtained by adding consumer surplus to the total profit of supply chain members and then subtracting environmental protection subsidies.

[0021] As a further improvement to the present invention, the market demand function and profit function in S2 are constructed as follows:

[0022] Market demand function for traditional offline retail channels:

[0023] ;

[0024] Market demand function for online direct sales channels:

[0025] ;

[0026] in, For potential market demand; This refers to the market share of online direct sales channels. ,but This refers to the market share of offline retail channels. The retail price for retailers; The manufacturer's direct sales price; This represents the cross-channel price sensitivity coefficient, and ; A sensitivity coefficient for consumers' level of commitment to green innovation. ; The level of green innovation efforts of manufacturers;

[0027] Manufacturer's Green Innovation Costs: ,in Cost coefficient for green innovation efforts ;

[0028] Manufacturer profit function without environmental subsidies:

[0029] ;

[0030] Retailer profit function:

[0031] ;

[0032] in, The wholesale price from manufacturer to retailer;

[0033] Total profit of the supply chain system:

[0034] ;

[0035] Consumer surplus:

[0036] ;

[0037] Social welfare: , where S is the total expenditure on environmental protection subsidies.

[0038] As a further improvement to the present invention, S3 is specifically described as follows:

[0039] (1) Supply chain pricing model without environmental subsidies, i.e., the N model:

[0040] The upper-level issue is the manufacturer's decision:

[0041] ;

[0042] The underlying issue is retailer decisions: ;

[0043] Constraints: , , ;

[0044] Total expenditure on environmental protection subsidies ;

[0045] (2) Supply chain pricing model under innovation cost subsidy scenario, i.e., C model:

[0046] Environmental organizations subsidize manufacturers' green innovation costs based on a percentage (η).

[0047] The upper-level issue is the manufacturer's decision:

[0048] ;

[0049] The underlying issue is retailer decisions: ;

[0050] Constraints: , , , ;

[0051] At this point, the total expenditure on environmental protection subsidies ;

[0052] (3) Supply chain pricing model under innovation cost subsidy scenario, i.e., S model:

[0053] Environmental organizations subsidize manufacturers based on unit output γ.

[0054] The upper-level issue is the manufacturer's decision:

[0055] ;

[0056] The underlying issue is retailer decisions: ;

[0057] Constraints: , , , ;

[0058] At this point, the total expenditure on environmental protection subsidies ;

[0059] The retailer's profit function remains consistent across the three scenarios described above: .

[0060] As a further improvement to the present invention, S3 also includes the following:

[0061] Under a retailer-dominated structure:

[0062] (1) Supply chain pricing model without environmental subsidies, i.e., the N model:

[0063] The upper-level issue is retailer decision-making: ;

[0064] The underlying issue is the manufacturer's decision-making:

[0065] ;

[0066] Constraints: , , ;

[0067] Total expenditure on environmental protection subsidies ;

[0068] (2) Supply chain pricing model under innovation cost subsidy scenario, i.e., C model:

[0069] Environmental organizations subsidize manufacturers' green innovation costs based on a percentage (η).

[0070] The upper-level issue is retailer decision-making: ;

[0071] The underlying issue is the manufacturer's decision-making:

[0072] ;

[0073] Constraints: , , , ;

[0074] At this point, the total expenditure on environmental protection subsidies ;

[0075] (3) Supply chain pricing model under innovation cost subsidy scenario, i.e., S model:

[0076] Environmental organizations subsidize manufacturers based on unit output γ.

[0077] The upper-level issue is retailer decision-making: ;

[0078] The underlying issue is the manufacturer's decision-making:

[0079] ;

[0080] Constraints: , , , ;

[0081] At this point, the total expenditure on environmental protection subsidies ;

[0082] The retailer's profit function remains consistent across the three scenarios described above: .

[0083] As a further improvement of the present invention, in S4, the solution process includes the following sub-steps based on the dominance structure and subsidy situation:

[0084] S4.1 In a manufacturer-led Stackelberg game, the manufacturer, as the leader, makes the first decision on the wholesale price. Direct sales price and level of green innovation efforts Retailers, as followers, re-determine retail prices based on the manufacturers' decisions. ;

[0085] S4.2, Retailer Profit Function about Find the first-order partial derivative, let Seeking Optimal reaction function ;

[0086] S4.3, will Substitute into the manufacturer's profit function , get about , and The composite profit function; construct the composite profit function with respect to... The Hessian matrix is ​​obtained, and it is verified that the Hessian matrix is ​​negative definite under the given premise, such that the optimal solution exists;

[0087] S4.4, Regarding the composite profit function respectively... , and Find the first-order partial derivatives, and set all the above partial derivatives to zero. Solve the system of equations to obtain the optimal wholesale price under manufacturer-led conditions. Best direct sales price and optimal level of green innovation efforts Then substitute it into Get the best retail price from the retailer ;

[0088] S4.5 In a retailer-dominated Stackelberg game, the retailer, as the leader, makes the first decision on the retail price. Manufacturers, as followers, re-determine wholesale prices based on retailers' decisions. Direct sales price and level of green innovation efforts First, consider the manufacturer's profit function with respect to... Find the Hessian matrix and verify its negative definiteness. The solution is obtained based on the first-order necessary condition. , , Substituting back into the retailer's profit function, for Find the first-order partial derivative and set it to zero to obtain the optimal retail price. ;

[0089] S4.6, Apply the above optimal decision , , as well as Substituting the market demand function, the profit functions of each member, the consumer surplus function, and the social welfare function, we obtain the optimal equilibrium solutions and optimal profits for the three scenarios of no environmental subsidies, innovation cost subsidies, and product output subsidies under the two structures of manufacturer-led and retailer-led operations.

[0090] As a further improvement to the present invention, the method for fairly comparing different subsidy models in S5 is as follows:

[0091] Innovation cost subsidy coefficient Based on the constraint that the total amount of environmental protection subsidies is equal, an equation is established. Solve for the given Corresponding product output subsidy coefficient The study then compares the wholesale price, retail price, direct sales price, green innovation effort level, market demand, member profits, consumer surplus, and social welfare under the two subsidy methods, and outputs the optimal subsidy strategy under different dominance structures and different green innovation cost coefficient ranges.

[0092] As a further improvement of the present invention, the optimal subsidy strategy in S5 is the optimal dominance structure, the optimal subsidy method, and the corresponding optimal wholesale price, optimal retail price, optimal direct sales price, and optimal green innovation effort level recommended under different green innovation effort cost coefficient ranges.

[0093] To achieve the above objectives, the present invention also provides a dual-channel closed-loop green supply chain pricing system that considers the dominance structure, including a processor and a memory. The memory stores a computer program for calculating a dual-channel closed-loop green supply chain pricing method that considers the dominance structure, and the processor executes the computer program to obtain the optimal subsidy strategy.

[0094] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0095] (1) This invention simultaneously considers environmental subsidies from environmental organizations, supply chain dominance structure, dual-channel competition, and recycling and remanufacturing of waste products, and constructs a dual-channel closed-loop green supply chain pricing model with multiple coupled factors. Compared with existing pricing methods that only consider a single factor, it is closer to the real green supply chain operation scenario.

[0096] (2) Under the two dominance structures of manufacturer-led and retailer-led, this invention systematically compares three typical scenarios: no environmental subsidies, innovation cost subsidies, and product output subsidies. It can provide quantitative basis for environmental organizations to choose the better subsidy method in different green innovation cost ranges.

[0097] (3) The present invention adopts a solution strategy that combines Stackelberg game theory and reverse reasoning. The theoretical derivation is clear and can quickly calculate the optimal decision variables, optimal profit, consumer surplus and social welfare of each member of the supply chain under given parameters, which is convenient for embedding into computer-aided decision-making systems.

[0098] (4) This invention provides a comparison method for “equal total amount of environmental protection subsidies”, which avoids unfair comparison caused by differences in the scale of subsidies under different subsidy mechanisms, and can provide more practical reference for green supply chain related enterprises to formulate wholesale prices, retail prices, direct sales prices and green innovation investment levels. Attached Figure Description

[0099] Figure 1 This is a flowchart of the method of the present invention.

[0100] Figure 2 This is a schematic diagram of the dual-channel closed-loop green supply chain described in this invention. Detailed Implementation

[0101] The present invention will be further described below with reference to the accompanying drawings:

[0102] like Figure 1-2 The dual-channel closed-loop green supply chain pricing method shown, which considers the dominance structure, includes the following steps:

[0103] S1. Determine the underlying assumptions for building the model;

[0104] (1) All members of the supply chain are risk-neutral and perfectly rational decision-makers who aim to maximize their own profits and have completely symmetrical information.

[0105] (2) To simplify the model without loss of generality, assume that the manufacturer has no fixed production costs and the unit production cost is zero, and the retailer's unit sales cost is also zero.

[0106] (3) The market demand for green products is linearly affected by retail prices, direct sales prices, and the level of green innovation efforts;

[0107] (4) The relationship between green innovation cost and green innovation effort level is a quadratic function, that is, the higher the green innovation effort level, the higher the unit innovation cost of a product;

[0108] (5) The manufacturer remanufacturing the waste products, the cost savings per remanufacturing unit is The manufacturer's unit recycling price to consumers is The recycling rate of waste products is ,and ;

[0109] (6) Environmental organizations’ subsidy strategies include two types: one is based on the proportion of manufacturers’ green innovation costs. Innovation cost subsidies that are subsidized Second, subsidies will be provided based on the manufacturer's output of green products, with a subsidy amount of [amount missing] per unit of output. , ;

[0110] (7) Consumer surplus equals the difference between the highest price consumers are willing to pay and the price they actually pay; social welfare is obtained by adding consumer surplus to the total profit of supply chain members and then subtracting environmental protection subsidies.

[0111] S2. In the dual-channel closed-loop green supply chain, construct a market demand function that includes online direct sales channels and offline retail channels, and construct a closed-loop profit function that covers the recycling and remanufacturing of waste products; the market demand function is jointly affected by retail prices, direct sales prices, and the level of green innovation efforts of manufacturers;

[0112] The market demand function and profit function are constructed as follows:

[0113] Market demand function for traditional offline retail channels:

[0114] ;

[0115] Market demand function for online direct sales channels:

[0116] ;

[0117] in, For potential market demand; This refers to the market share of online direct sales channels. ,but This refers to the market share of offline retail channels. The retail price for retailers; The manufacturer's direct sales price; This represents the cross-channel price sensitivity coefficient, and ; A sensitivity coefficient for consumers' level of commitment to green innovation. ; The level of green innovation efforts of manufacturers;

[0118] Manufacturer's Green Innovation Costs: ,in Cost coefficient for green innovation efforts ;

[0119] Manufacturer profit function without environmental subsidies:

[0120] ;

[0121] Retailer profit function:

[0122] ;

[0123] in, The wholesale price from manufacturer to retailer;

[0124] Total profit of the supply chain system:

[0125] ;

[0126] Consumer surplus:

[0127] ;

[0128] Social welfare: , where S is the total expenditure on environmental protection subsidies.

[0129] S3. Based on the environmental protection subsidy method, construct supply chain pricing models for the following scenarios: no environmental protection subsidy, innovation cost subsidy, and product output subsidy.

[0130] (1) Supply chain pricing model without environmental subsidies, i.e., the N model:

[0131] The upper-level issue is the manufacturer's decision:

[0132] ;

[0133] The underlying issue is retailer decisions: ;

[0134] Constraints: , , ;

[0135] Total expenditure on environmental protection subsidies ;

[0136] (2) Supply chain pricing model under innovation cost subsidy scenario, i.e., C model:

[0137] Environmental organizations subsidize manufacturers' green innovation costs based on a percentage (η).

[0138] The upper-level issue is the manufacturer's decision:

[0139] ;

[0140] The underlying issue is retailer decisions: ;

[0141] Constraints: , , , ;

[0142] At this point, the total expenditure on environmental protection subsidies ;

[0143] (3) Supply chain pricing model under innovation cost subsidy scenario, i.e., S model:

[0144] Environmental organizations subsidize manufacturers based on unit output γ.

[0145] The upper-level issue is the manufacturer's decision:

[0146] ;

[0147] The underlying issue is retailer decisions: ;

[0148] Constraints: , , , ;

[0149] At this point, the total expenditure on environmental protection subsidies ;

[0150] The retailer's profit function remains consistent across the three scenarios described above: .

[0151] Under a retailer-dominated structure:

[0152] (1) Supply chain pricing model without environmental subsidies, i.e., the N model:

[0153] The upper-level issue is retailer decision-making: ;

[0154] The underlying issue is the manufacturer's decision-making:

[0155] ;

[0156] Constraints: , , ;

[0157] Total expenditure on environmental protection subsidies ;

[0158] (2) Supply chain pricing model under innovation cost subsidy scenario, i.e., C model:

[0159] Environmental organizations subsidize manufacturers' green innovation costs based on a percentage (η).

[0160] The upper-level issue is retailer decision-making: ;

[0161] The underlying issue is the manufacturer's decision-making:

[0162] ;

[0163] Constraints: , , , ;

[0164] At this point, the total expenditure on environmental protection subsidies ;

[0165] (3) Supply chain pricing model under innovation cost subsidy scenario, i.e., S model:

[0166] Environmental organizations subsidize manufacturers based on unit output γ.

[0167] The upper-level issue is retailer decision-making: ;

[0168] The underlying issue is the manufacturer's decision-making:

[0169] ;

[0170] Constraints: , , , ;

[0171] At this point, the total expenditure on environmental protection subsidies ;

[0172] The retailer's profit function remains consistent across the three scenarios described above: .

[0173] S4. Under two dominance structures, namely manufacturer-led and retailer-led, the Stackelberg game and the backward inference method are used to solve the model to obtain the optimal equilibrium solutions for wholesale price, retail price, direct sales price and green innovation effort level under each case, as well as the optimal profit of supply chain members, consumer surplus and social welfare.

[0174] Based on the power structure and subsidy situation, the solution process includes the following sub-steps:

[0175] S4.1 In a manufacturer-led Stackelberg game, the manufacturer, as the leader, makes the first decision on the wholesale price. Direct sales price and level of green innovation efforts Retailers, as followers, re-determine retail prices based on the manufacturers' decisions. ;

[0176] S4.2, Retailer Profit Function about Find the first-order partial derivative, let Seeking Optimal reaction function ;

[0177] S4.3, will Substitute into the manufacturer's profit function , get about , and The composite profit function; construct the composite profit function with respect to... The Hessian matrix is ​​obtained, and it is verified that the Hessian matrix is ​​negative definite under the given premise, such that the optimal solution exists;

[0178] S4.4, Regarding the composite profit function respectively... , and Find the first-order partial derivatives, and set all the above partial derivatives to zero. Solve the system of equations to obtain the optimal wholesale price under manufacturer-led conditions. Best direct sales price and optimal level of green innovation efforts Then substitute it into Get the best retail price from the retailer ;

[0179] S4.5 In a retailer-dominated Stackelberg game, the retailer, as the leader, makes the first decision on the retail price. Manufacturers, as followers, re-determine wholesale prices based on retailers' decisions. Direct sales price and level of green innovation efforts First, consider the manufacturer's profit function with respect to... Find the Hessian matrix and verify its negative definiteness. The solution is obtained based on the first-order necessary condition. , , Substituting back into the retailer's profit function, for Find the first-order partial derivative and set it to zero to obtain the optimal retail price. ;

[0180] S4.6, Apply the above optimal decision , , as well as Substituting the market demand function, the profit functions of each member, the consumer surplus function, and the social welfare function, we obtain the optimal equilibrium solutions and optimal profits for the three scenarios of no environmental subsidies, innovation cost subsidies, and product output subsidies under the two structures of manufacturer-led and retailer-led operations.

[0181] S5. Under the constraint of equal total environmental subsidies, compare the optimal equilibrium solutions under different dominance structures and different subsidy methods, and output the optimal pricing strategy and optimal subsidy strategy under different scenarios.

[0182] The following are methods for fairly comparing different subsidy models:

[0183] Innovation cost subsidy coefficient Based on the constraint that the total amount of environmental protection subsidies is equal, an equation is established. Solve for the given Corresponding product output subsidy coefficient The study then compares the wholesale price, retail price, direct sales price, green innovation effort level, market demand, member profits, consumer surplus, and social welfare under the two subsidy methods, and outputs the optimal subsidy strategy under different dominance structures and different green innovation cost coefficient ranges.

[0184] The optimal subsidy strategy is the recommended optimal dominance structure, optimal subsidy method, and corresponding optimal wholesale price, optimal retail price, optimal direct sales price, and optimal level of green innovation effort under different green innovation effort cost coefficient ranges.

[0185] The dual-channel closed-loop green supply chain pricing system considering the dominance structure includes a processor and a memory. The memory stores a computer program for calculating the dual-channel closed-loop green supply chain pricing method considering the dominance structure, and the processor executes the computer program to obtain the optimal subsidy strategy.

[0186] In this invention, when the manufacturer is in control, the condition for the existence of an equilibrium solution is: and ,

[0187] The commercial subsidy amount under the innovation cost subsidy model is

[0188] ,

[0189] Under the product output subsidy model, the commercial subsidy amount is

[0190]

[0191] .

[0192] When retailers dominate, the condition for the existence of an equilibrium solution is: and ,

[0193] The commercial subsidy amount under the innovation cost subsidy model is

[0194] ,

[0195] Under the product output subsidy model, the commercial subsidy amount is

[0196]

[0197] .

[0198] By analyzing changes in wholesale prices, green innovation efforts, retail prices, manufacturer and retailer profits, total supply chain system profits, consumer surplus, and social welfare under two different environmental subsidy mechanisms when environmental subsidy expenditures are equal, the optimal business subsidy strategy for a given subsidy ratio can be determined. The corresponding parameter values ​​are set as follows: , , , , , , By varying the step size by 0.1, we can obtain the corresponding values ​​of the two subsidy coefficients when the commercial subsidy expenditures are equal under different cost conditions (see Table 1).

[0199]

[0200] Substituting the corresponding parameter values ​​into the equilibrium solution yields the corresponding values. Based on this, we can compare three scenarios under two structures: manufacturer-led and retailer-led, with no subsidies, innovation cost subsidies, and product output subsidies. This provides a quantitative basis for relevant departments to select the better subsidy method within different green innovation cost ranges. At the same time, it can also provide more practical reference for green supply chain related enterprises to formulate wholesale prices, retail prices, direct sales prices, and green innovation investment levels.

[0201] This invention is not limited to the above embodiments. Based on the technical solutions disclosed herein, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.

Claims

1. A dual-channel closed-loop green supply chain pricing method considering the dominant power structure, characterized by: Includes the following steps, S1. Determine the underlying assumptions for building the model; S2. In the dual-channel closed-loop green supply chain, construct a market demand function that includes online direct sales channels and offline retail channels, and construct a closed-loop profit function that covers the recycling and remanufacturing of waste products; the market demand function is jointly affected by retail prices, direct sales prices, and the level of green innovation efforts of manufacturers; S3. Based on the environmental protection subsidy method, construct supply chain pricing models for the following scenarios: no environmental protection subsidy, innovation cost subsidy, and product output subsidy. S4. Under two dominance structures, namely manufacturer-led and retailer-led, the Stackelberg game and the backward inference method are used to solve the model to obtain the optimal equilibrium solutions for wholesale price, retail price, direct sales price and green innovation effort level under each case, as well as the optimal profit of supply chain members, consumer surplus and social welfare. S5. Under the constraint of equal total environmental subsidies, compare the optimal equilibrium solutions under different dominance structures and different subsidy methods, and output the optimal pricing strategy and optimal subsidy strategy under different scenarios.

2. The dual-channel closed-loop green supply chain pricing method considering the dominance structure according to claim 1, characterized in that: The underlying assumptions for building the model in S1 include the following: (1) All members of the supply chain are risk-neutral and perfectly rational decision-makers who aim to maximize their own profits and have completely symmetrical information. (2) To simplify the model without loss of generality, assume that the manufacturer has no fixed production costs and the unit production cost is zero, and the retailer's unit sales cost is also zero. (3) The market demand for green products is linearly affected by retail prices, direct sales prices, and the level of green innovation efforts; (4) The relationship between green innovation cost and green innovation effort level is a quadratic function, that is, the higher the green innovation effort level, the higher the unit innovation cost of a product; (5) The manufacturer remanufacturing the waste products, the cost savings per remanufacturing unit is The manufacturer's unit recycling price to consumers is The recycling rate of waste products is ,and ; (6) Environmental organizations’ subsidy strategies include two types: one is based on the proportion of manufacturers’ green innovation costs. Innovation cost subsidies that are subsidized Second, subsidies will be provided based on the manufacturer's output of green products, with a subsidy amount of [amount missing] per unit of output. , ; (7) Consumer surplus equals the difference between the highest price consumers are willing to pay and the price they actually pay; social welfare is obtained by adding consumer surplus to the total profit of supply chain members and then subtracting environmental protection subsidies.

3. The dual-channel closed-loop green supply chain pricing method considering the dominance structure according to claim 2, characterized in that: The market demand function and profit function for S2 construction are constructed as follows: Market demand function for traditional offline retail channels: ； Market demand function for online direct sales channels: ； in, For potential market demand; This refers to the market share of online direct sales channels. ,but This refers to the market share of offline retail channels. The retail price for retailers; The manufacturer's direct sales price; This represents the cross-channel price sensitivity coefficient, and ; A sensitivity coefficient for consumers' level of commitment to green innovation. ; The level of green innovation efforts of manufacturers; Manufacturer's Green Innovation Costs: ,in Cost coefficient for green innovation efforts ; Manufacturer profit function without environmental subsidies: ； Retailer profit function: ； in, The wholesale price from manufacturer to retailer; Total profit of the supply chain system: ； Consumer surplus: ； Social welfare: , where S is the total expenditure on environmental protection subsidies.

4. The dual-channel closed-loop green supply chain pricing method considering the dominance structure according to claim 3, characterized in that: The specific details of S3 are as follows. Under a manufacturer-dominated structure: (1) Supply chain pricing model without environmental subsidies, i.e., the N model: The upper-level issue is the manufacturer's decision: ; The underlying issue is retailer decisions: ; Constraints: , , ; Total expenditure on environmental protection subsidies ; (2) Supply chain pricing model under innovation cost subsidy scenario, i.e., C model: Environmental organizations subsidize manufacturers' green innovation costs based on a percentage (η). The upper-level issue is the manufacturer's decision: ； The underlying issue is retailer decisions: ; Constraints: , , , ; At this point, the total expenditure on environmental protection subsidies ; (3) Supply chain pricing model under innovation cost subsidy scenario, i.e., S model: Environmental organizations subsidize manufacturers based on unit output γ. The upper-level issue is the manufacturer's decision: ； The underlying issue is retailer decisions: ; Constraints: , , , ; At this point, the total expenditure on environmental protection subsidies ; The retailer's profit function remains consistent across the three scenarios described above: .

5. The dual-channel closed-loop green supply chain pricing method considering the dominance structure according to claim 4, characterized in that: S3 also includes the following: Under a retailer-dominated structure: (1) Supply chain pricing model without environmental subsidies, i.e., the N model: The upper-level issue is retailer decision-making: ; The underlying issue is the manufacturer's decision-making: ; Constraints: , , ; Total expenditure on environmental protection subsidies ; (2) Supply chain pricing model under innovation cost subsidy scenario, i.e., C model: Environmental organizations subsidize manufacturers' green innovation costs based on a percentage (η). The upper-level issue is retailer decision-making: ; The underlying issue is the manufacturer's decision-making: ； Constraints: , , , ; At this point, the total expenditure on environmental protection subsidies ; (3) Supply chain pricing model under innovation cost subsidy scenario, i.e., S model: Environmental organizations subsidize manufacturers based on unit output γ. The upper-level issue is retailer decision-making: ; The underlying issue is the manufacturer's decision-making: ； Constraints: , , , ; At this point, the total expenditure on environmental protection subsidies ; The retailer's profit function remains consistent across the three scenarios described above: .

6. The dual-channel closed-loop green supply chain pricing method considering the dominance structure according to claim 5, characterized in that: In S4, based on the dominance structure and subsidy situation, the solution process includes the following sub-steps: S4.1 In a manufacturer-led Stackelberg game, the manufacturer, as the leader, makes the first decision on the wholesale price. Direct sales price and level of green innovation efforts Retailers, as followers, re-determine retail prices based on the manufacturers' decisions. ; S4.2, Retailer Profit Function about Find the first-order partial derivative, let Seeking Optimal reaction function ; S4.3, will Substitute into the manufacturer's profit function , get about , and The composite profit function; construct the composite profit function with respect to... The Hessian matrix is ​​obtained, and it is verified that the Hessian matrix is ​​negative definite under the given premise, such that the optimal solution exists; S4.4, Regarding the composite profit function respectively... , and Find the first-order partial derivatives, and set all the above partial derivatives to zero. Solve the system of equations to obtain the optimal wholesale price under manufacturer-led conditions. Best direct sales price and optimal level of green innovation efforts Then substitute it into Get the best retail price from the retailer ; S4.5 In a retailer-dominated Stackelberg game, the retailer, as the leader, makes the first decision on the retail price. Manufacturers, as followers, re-determine wholesale prices based on retailers' decisions. Direct sales price and level of green innovation efforts First, consider the manufacturer's profit function with respect to... Find the Hessian matrix and verify its negative definiteness. The solution is obtained based on the first-order necessary condition. , , Substituting back into the retailer's profit function, for Find the first-order partial derivative and set it to zero to obtain the optimal retail price. ; S4.6, Apply the above optimal decision , , as well as Substituting the market demand function, the profit functions of each member, the consumer surplus function, and the social welfare function, we obtain the optimal equilibrium solutions and optimal profits for the three scenarios of no environmental subsidies, innovation cost subsidies, and product output subsidies under the two structures of manufacturer-led and retailer-led operations.

7. The dual-channel closed-loop green supply chain pricing method using a dominant structure as described in claim 6, characterized in that: The method for fairly comparing different subsidy models in S5 is as follows. Innovation cost subsidy coefficient Based on the constraint that the total amount of environmental protection subsidies is equal, an equation is established. Solve for the given Corresponding product output subsidy coefficient The study then compares the wholesale price, retail price, direct sales price, green innovation effort level, market demand, member profits, consumer surplus, and social welfare under the two subsidy methods, and outputs the optimal subsidy strategy under different dominance structures and different green innovation cost coefficient ranges.

8. The dual-channel closed-loop green supply chain pricing method using a dominant structure as described in claim 7, characterized in that: The optimal subsidy strategy in S5 is the recommended optimal dominance structure, optimal subsidy method, and corresponding optimal wholesale price, optimal retail price, optimal direct sales price, and optimal level of green innovation effort under different green innovation effort cost coefficient ranges.

9. A dual-channel closed-loop green supply chain pricing system considering a dominant power structure, characterized in that: The dual-channel closed-loop green supply chain pricing method considering the dominance structure, applied to any one of claims 1-8, includes a processor and a memory. The memory stores a computer program for calculating the dual-channel closed-loop green supply chain pricing method considering the dominance structure, and the processor executes the computer program to obtain the optimal subsidy strategy.

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