CN113674017A - Method and system for calculating and analyzing optimal proportion of cost sharing of closed-loop supply chain of household appliance - Google Patents

Method and system for calculating and analyzing optimal proportion of cost sharing of closed-loop supply chain of household appliance Download PDF

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CN113674017A
CN113674017A CN202110826440.2A CN202110826440A CN113674017A CN 113674017 A CN113674017 A CN 113674017A CN 202110826440 A CN202110826440 A CN 202110826440A CN 113674017 A CN113674017 A CN 113674017A
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张福安
李娜
孙小兵
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Yangzhou University
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Abstract

本发明公开了一种家用电器闭环供应链成本分担最优比例计算分析方法及系统。方法包括：构建家电家电制造商主导闭环供应链的碳税政策下不同的成本分担契约决策模型；采用逆推法求解所述模型，获得各模型中决策变量最优解以及家电家电制造商、家电零售商的最优利润期望值；通过数值敏感性分析碳税税率对家电家电制造商、家电零售商的定价决策、期望利润、成本分担比率、及回收率的影响规律；根据分析结果，对不同的成本分担契约决策模型进行分析。本发明通过构建制造商主导的家用电器闭环供应链成本分担契约的不同模型，来量化分析碳税税率对闭环家电供应链成员的定价决策、期望利润、成本分担比率、及回收率的影响规律，最终获得最优成本共担方案。

Figure 202110826440

The invention discloses a method and system for calculating and analyzing the optimal proportion of cost sharing in a closed-loop supply chain of household appliances. The methods include: constructing different cost-sharing contract decision-making models under the carbon tax policy in which the home appliance manufacturer dominates the closed-loop supply chain; using the inverse method to solve the model, and obtaining the optimal solution of the decision variables in each model and the The optimal profit expectation value of retailers; through numerical sensitivity analysis of the impact of carbon tax rates on the pricing decisions, expected profits, cost sharing ratios, and recovery rates of home appliance manufacturers and home appliance retailers; The cost-sharing contract decision-making model is analyzed. The present invention quantitatively analyzes the influence law of the carbon tax rate on the pricing decision, expected profit, cost sharing ratio, and recovery rate of the members of the closed-loop household appliance supply chain by constructing different models of cost-sharing contracts in the closed-loop supply chain of household appliances led by manufacturers. Finally, the optimal cost sharing scheme is obtained.

Figure 202110826440

Description

Method and system for calculating and analyzing optimal proportion of cost sharing of closed-loop supply chain of household appliance
Technical Field
The invention relates to the technical field of big data application, in particular to a method and a system for calculating and analyzing optimal proportion of cost sharing of a closed-loop supply chain of a household appliance.
Background
Over the past few years, a great deal of research and practice has proven that reducing and controlling carbon emissions is the most direct way to address the current social problem of continued environmental degradation and climate warming, and is becoming a common consensus in international society. Governments and home electronics enterprises are taking different measures to better address this problem. The carbon tax policy is an effective policy measure for guiding household appliance enterprises to reduce and control carbon emission, is well practiced in European Union countries, and achieves preliminary results. Given the importance of Closed Loop Supply Chain (CLSC) management in practice, CLSC is also a key research topic in the academic field. In the home appliance closed-loop supply chain, home appliance manufacturers use clean technology for low-carbon production to reduce carbon tax punishment, and recycle old home appliances from consumers to reduce production costs. The household appliance manufacturer determines the discharge reduction amount, the recovery rate of old household appliances and the wholesale price of unit products according to the tax rate, the emission reduction cost and the recovery cost. The home appliance retailer develops low carbon promotion activities to increase sales in consideration of low carbon preferences of consumers. The home appliance retailer decides the selling price and the investment of the low-carbon promotion activity according to the wholesale price, the promotion activity cost and the selling quantity. Each member of the supply chain makes decisions based on his own profit maximization. But a calculation scheme for quantifying the optimal proportion of cost sharing of the closed-loop supply chain of the household appliance is not available at present.
Disclosure of Invention
In order to solve the problems, the invention discloses a closed-loop supply chain cost sharing contract mechanism calculation analysis method and system based on a carbon tax policy.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for calculating and analyzing optimal proportion of cost sharing of a closed supply chain of household appliances comprises the following steps:
step S1: establishing a non-cooperative decision model and three cooperative decision models, and respectively designing three cost sharing contract coordination supply chains aiming at the cooperative decision models;
step S2: solving each model established in the step S1 by adopting a backward-stepping method to obtain the optimal solution of decision variables in each model and the optimal profit expectation value of a manufacturer main body in a closed-loop household appliance supply chain;
step S3: on the premise of ensuring certain low-carbon preference of consumers and certain low-carbon popularization activity preference of consumers, performing numerical sensitivity analysis of numerical simulation on the model through a mathematical analysis tool according to the optimal solution of the decision variables and the optimal profit expectation value of the members of the closed-loop household appliance supply chain, and determining the influence rule of the carbon tax rate on the pricing decision, the expected profit, the cost sharing rate and the recovery rate of the members of the closed-loop household appliance supply chain;
step S4: and analyzing different cost sharing contract decision models according to the analysis result of the step S3, and obtaining an optimal cost sharing scheme.
Further, in step S3, the mathematical analysis tool uses MATLAB.
Further, in the step S3, it is assumed that the carbon tax rate is uniformly distributed within a certain interval.
Further, the analysis of the different cost sharing contract decision models in step S4 includes comparison between different cooperation models.
A closed-loop supply chain cost sharing contract mechanism calculation analysis system comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the computer program realizes the closed-loop supply chain cost sharing contract mechanism calculation analysis method when being loaded to the processor.
Further, the closed-loop supply chain cost sharing contract mechanism calculation analysis system comprises a model establishing module, a model solving module, a simulation analysis module and an analysis comparison module; the model establishing module is used for establishing a non-cooperative decision model and three cooperative decision models which are dominated by a household appliance manufacturer, and designing three cost sharing contract coordination supply chains aiming at the cooperative decision models; the model solving module is used for solving the model established in the model establishing module by adopting a reverse-thrust method to obtain the optimal solution of decision variables in each model and the optimal profit expected value of a manufacturer main body in a closed-loop household appliance supply chain; the simulation analysis module is used for carrying out numerical value sensitivity analysis of numerical value simulation on the model through a mathematical analysis tool and determining the influence rule of the carbon tax rate on the pricing decision, expected profit, cost sharing rate and recovery rate of the members of the closed-loop household appliance supply chain; and the analysis comparison module is used for comparing different cost sharing contract decision models according to the analysis result of the simulation analysis module and obtaining an optimal cost sharing scheme.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the method quantitatively analyzes the influence rule of the carbon tax rate on the pricing decision, the expected profit, the cost sharing rate and the recovery rate of the members of the closed-loop household appliance supply chain under the conditions of the carbon tax policy and the low-carbon preference of the consumer by constructing different models of the cost sharing contract of the closed-loop household appliance supply chain dominated by the manufacturer, and finally obtains the optimal cost sharing scheme; and regulating the closed-loop household appliance supply chain leading by the household appliance manufacturer according to the analysis result, effectively reducing the carbon dioxide emission of the closed-loop household appliance supply chain, and improving the cooperative operation of the closed-loop household appliance supply chain. Meanwhile, the invention provides an automatic system which can be executed in a computer and can realize the method.
Drawings
Fig. 1 is a closed supply chain for government carbon taxes and home appliance manufacturers to reclaim products.
Fig. 2 is a graph of the optimal wholesale price w as a function of the carbon tax rate t.
Fig. 3 is a graph of optimal carbon emission reduction Δ e as a function of carbon tax rate t.
FIG. 4 is a graph of optimal recovery θ as a function of carbon tax rate t.
FIG. 5 is a plot of the optimal retail margin h as a function of carbon tax rate t.
Fig. 6 is a function curve of the low carbon promotion activity v of the optimal home appliance retailer with respect to the carbon tax rate t.
FIG. 7 is a plot of an optimal supply chain retail price p as a function of carbon tax rate t.
FIG. 8 is the optimal supply chain total profit πTCurve of function for carbon tax rate t.
Detailed Description
The technical solutions provided by the present invention will be described in detail below with reference to specific examples, and it should be understood that the following specific embodiments are only illustrative of the present invention and are not intended to limit the scope of the present invention. Additionally, the steps illustrated in the flow charts of the figures may be performed in a computer system such as a set of computer-executable instructions and, although a logical order is illustrated in the flow charts, in some cases, the steps illustrated or described may be performed in an order different than here.
The invention discloses a method for calculating and analyzing optimal proportion of cost sharing of a closed supply chain of household appliances, which comprises the following steps:
step S1: under the conditions of carbon tax policies and low carbon preference of consumers, home appliance manufacturers in closed-loop supply chains carry out carbon emission reduction, recycling and remanufacturing, and home appliance retailers carry out low carbon popularization activities. The closed supply chain members dominated by the home appliance manufacturer include government departments, home appliance manufacturers, home appliance retailers. Based on the background, the contract coordination problem of the closed-loop household appliance supply chain is researched, a non-cooperative decision model and three cooperative decision models which are dominated by a household appliance manufacturer are established, and three cost sharing contract coordination supply chains are respectively designed aiming at the cooperative decision models. The method comprises the following substeps:
step S101: home appliance manufacturers use clean technology for low carbon production to reduce carbon tax punishment, and recycle old home appliances from consumers to reduce production costs. The household appliance manufacturer determines the discharge reduction amount, the recovery rate of old household appliances and the wholesale price of unit products according to the tax rate, the emission reduction cost and the recovery cost. The home appliance retailer develops low carbon promotion activities to increase sales in consideration of low carbon preferences of consumers. The home appliance retailer decides the selling price and the investment of the low-carbon promotion activity according to the wholesale price, the promotion activity cost and the selling quantity. Each member of the supply chain makes decisions based on his own profit maximization.
According to the analysis, a household appliance market demand function and a cost function are constructed:
in the forward sales supply chain, the market demand Q is a-b (w + h) + γ Δ e + λ v. w is the wholesale price of the appliance manufacturer, h is the retail balance of the appliance retailer, a is market capacity, b is customer consumptionThe sensitivity coefficient of a consumer to the retail price, gamma is the preference coefficient of the consumer to carbon emission reduction, lambda is the preference coefficient of the consumer to the low-carbon promotion activity of the home appliance retailer, products sold in the early stage can be recycled, new products are reproduced, and delta e is the emission reduction of carbon dioxide. Old appliance recovery Q of appliance manufacturer in reverse recovery supply chainrThe new product produced by the old household appliance cannot meet the market demand (theta is the recovery rate, 0 < theta < 1), namely: q>Qr. The home appliance manufacturer can preferentially use the old home appliances to produce when producing the products, then use the new materials to produce, and the products produced by the two modes are homogeneous, the home appliance manufacturer sells the products at the same wholesale price, and the home appliance retailer sells the products to consumers at the same retail price. The Stacklberg game which is dominated by the household appliance manufacturer is formed between the household appliance manufacturer and the retailer, and the game is a symmetrical game. The cost of producing unit products by using new materials and old household appliances by household appliance manufacturers is cm、cr. Wherein c isr＜cmLet δ be cm-cr. The government collects carbon tax on carbon dioxide emitted by household appliance manufacturers, and the tax rate is t yuan/ton; the household appliance manufacturers adopt the carbon emission reduction technology, the emission of carbon dioxide of the products of production units is reduced by delta e, and the emission reduction cost is
Figure BDA0003173784390000031
Mu is the carbon emission reduction cost coefficient corresponding to the carbon emission reduction of the household appliance manufacturer. The recovery rate of the old household appliances is a function of the recovery investment of the old household appliances, the recovery rate of the invention depends on the investment of the household appliance manufacturer on the recovery activity, the recovery rate is an increasing function of the recovery investment of the household appliance manufacturer, and the recovery rate function is as follows:
Figure BDA0003173784390000032
M＝Cb*θ2cost invested for home appliance manufacturers to recycle old home appliances, CbA recycling cost factor invested for the home appliance manufacturer corresponding to the recycling rate of the old home appliances. The household appliance retailer carries out low-carbon promotion activities with the cost function of
Figure BDA0003173784390000033
U is the cost coefficient of the low-carbon promotion activities of the household appliance retailers, and v is the effort degree of the low-carbon promotion activities of the retailers.
Figure BDA0003173784390000034
Represents the profit of the appliance manufacturer in the decision model 0, o ∈ { N, A, BP, BR }.
Step S102: according to the analysis in step S101, each profit maximization model is obtained as follows:
non-cooperative decision model (model N):
in the model, home appliance manufacturers and home appliance retailers aim to achieve the maximization of their profits, the home appliance manufacturers make decisions on carbon emission reduction levels, recovery ratios and wholesale prices, and the home appliance retailers make decisions on low-carbon popularization activity investment and retail balance. From the foregoing assumptions, the home appliance manufacturer and home appliance retailer profit functions are:
Figure BDA0003173784390000035
Figure BDA0003173784390000036
one-way cooperative decision model (model a):
on the basis of a non-cooperative decision model, the household appliance manufacturer sets a sharing ratio beta (beta is more than or equal to 0 and less than or equal to 1) to subsidize the low-carbon promotion activity cost of the household appliance retailer to a certain degree, and provides an additional subsidy K for the household appliance retailerA. From the foregoing assumptions, the home appliance manufacturer and retailer profit functions are known as:
Figure BDA0003173784390000037
Figure BDA0003173784390000038
s.t
Figure BDA0003173784390000039
a two-way collaborative decision model (model Bp) to subsidize carbon emission reduction costs:
on the basis of a non-cooperative decision model, the household appliance manufacturer sets a sharing ratio beta1(0≤β1Less than or equal to 1) subsidy low-carbon promotion activity cost of the home appliance retailer, and provide additional subsidy K for the home appliance retailerBp. Home appliance retailer setting sharing ratio beta2(0≤β2Not more than 1) subsidy the carbon emission reduction production cost of the household appliance manufacturer.
Figure BDA00031737843900000310
Figure BDA00031737843900000311
s.t
Figure BDA0003173784390000041
Two-way cooperation decision model (model Br) for subsidizing recovery cost
On the basis of a non-cooperative decision model, the household appliance manufacturer sets a sharing ratio beta1(0≤β1Less than or equal to 1) subsidy low-carbon promotion activity cost of the home appliance retailer, and provide additional subsidy K for the home appliance retailerBr. Home appliance retailer setting sharing ratio beta3(0≤β3Not more than 1) subsidizing the cost of recycling old household appliances for household appliance manufacturers.
Figure BDA0003173784390000042
Figure BDA0003173784390000043
s.t
Figure BDA0003173784390000044
Step S2: solving the models by adopting a reverse-thrust method to obtain the optimal solution of decision variables in each model and the optimal profit expectation value of a manufacturer main body in a closed-loop household appliance supply chain; the method specifically comprises the following substeps:
step S201: home appliance retailers expect the greatest profit:
model N
Hessian matrix of home appliance retailer profit function:
Figure BDA0003173784390000045
it can be known that
Figure BDA0003173784390000046
When in use
Figure BDA00031737843900000414
The home appliance retailer profit function is a concave function with respect to h and v, so there is a maximum equal to the maximum value by solving the following system of equations:
Figure BDA0003173784390000047
obtaining an expression of a maximum value point:
Figure BDA0003173784390000048
Figure BDA0003173784390000049
model A
Hessian matrix of home appliance retailer profit function:
Figure BDA00031737843900000410
it can be known that
Figure BDA00031737843900000411
When in use
Figure BDA00031737843900000412
The home appliance retailer profit function is a concave function with respect to h and v, so there is a maximum equal to the maximum value by solving the following system of equations:
Figure BDA00031737843900000413
obtaining an expression of a maximum value point:
Figure BDA0003173784390000051
Figure BDA0003173784390000052
model Bp
Hessian matrix of home appliance retailer profit function:
Figure BDA0003173784390000053
it can be known that
Figure BDA0003173784390000054
When in use
Figure BDA0003173784390000055
The home appliance retailer profit function is a concave function with respect to h and v, so there is a maximum equal to the maximum value by solving the following system of equations:
Figure BDA0003173784390000056
obtaining an expression of a maximum value point:
Figure BDA0003173784390000057
Figure BDA0003173784390000058
model Br
Hessian matrix of home appliance retailer profit function:
Figure BDA0003173784390000059
it can be known that
Figure BDA00031737843900000510
When in use
Figure BDA00031737843900000511
The home appliance retailer profit function is a concave function with respect to h and v, so there is a maximum equal to the maximum value by solving the following system of equations:
Figure BDA00031737843900000512
obtaining an expression of a maximum value point:
Figure BDA00031737843900000513
Figure BDA00031737843900000514
step S202: home appliance manufacturers expect the greatest profit: the optimal solution of the expected profit obtained in step S201 is substituted into the objective function with the maximum profit for the home appliance manufacturer, which is specifically as follows:
model N
Substituting h (w, Δ e), v (w, Δ e) into equation (1) yields a hessian matrix for the appliance manufacturer profit function for w, Δ e, θ:
Figure BDA0003173784390000061
therefore, the following steps are carried out:
Figure BDA0003173784390000062
Figure BDA0003173784390000063
therefore, when 2 λ2μ+U[γ2+2bγt+bU(bt2-4μ)]＜0
And 4Cbλ2μ+2Cb[γ2+2bγt+bU(bt2-4μ)]+b2μUδ2The profit function of the home appliance manufacturer at < 0 is a concave function with respect to w, θ, Δ e, and thus has a maximum value, i.e., a maximum value, and the following equation is solved:
Figure BDA0003173784390000064
can determine wN*，ΔeN*，θN*，hN*，vN*。
Model A
Substituting h (w, Δ e, β), v (w, Δ e, β) into equation (3) yields a hessian matrix for the appliance manufacturer profit function for w, Δ e, θ:
Figure BDA0003173784390000065
therefore, the following steps are carried out:
Figure BDA0003173784390000066
Figure BDA0003173784390000067
Figure BDA0003173784390000068
thus when
[(2-3β)λ2-4b(β-1)2U]μ+(β-1)2U(γ2+2bγt+b2t2)＜0，
And b is2δ2μU(β-1)2+2Cb{[(2-3β)λ2-4b(β-1)2U]μ+(β-1)2U(γ2+2bγt+b2t2) The profit function of the appliance manufacturer at } < 0 is a concave function with respect to w, θ, Δ e, and thus has a maximum value, i.e., a maximum value, by solving the following equation
Figure BDA0003173784390000071
From the first order conditions, w can be obtainedA(β)，ΔeA(β)，θA(β) substituting it into
Figure BDA0003173784390000072
Thereby obtaining hA(β)，vA(beta). Will wA(β)，ΔeA(β)，θA(β)，hA(β)，vA(β) substitution into equation (3) due to the second derivative
Figure BDA0003173784390000073
Making the first derivative zero to obtain
Figure BDA0003173784390000074
Will beta1 A*Substitution into wA(β)，ΔeA(β)，θA(β)，hA(β)，vA(β) then w can be determinedA*，ΔeA*，θA*，hA*，vA*. Finally, K can be obtained by satisfying the constraint condition (5)A*。
Model Bp
H (w, delta e, beta)1)，v(w,Δe,β1) Substituting equation (6) to obtain the hessian matrix for the appliance manufacturer profit function for w, Δ e, θ:
Figure BDA0003173784390000075
Figure BDA0003173784390000076
Figure BDA0003173784390000077
Figure BDA0003173784390000078
when in use
[(2-3β1)λ2-4b(β1-1)2U](β2-1)μ+(β1-1)2U(γ2+2bγt+b2t2) Is < 0 and
b2δ2μU(β1-1)2(1-β2)+2Cb{[(2-3β1)λ2-4b(β1-1)2U](β2-1)μ+(β1-1)2U(γ2+2bγt+b2t2) When the ratio is less than 0, the ratio is more than zero,
Figure BDA0003173784390000079
is a joint concave function with respect to w, Δ e, θ. Solving the following system of equations
Figure BDA00031737843900000710
From first order conditions
Figure BDA00031737843900000711
Substitute it into
Figure BDA00031737843900000712
Figure BDA00031737843900000713
Thereby obtaining
Figure BDA00031737843900000714
Will be provided with
Figure BDA00031737843900000715
Figure BDA0003173784390000081
Substitution into equations (6), (7) due to second derivative
Figure BDA0003173784390000082
Making the first derivative zero to obtain
Figure BDA0003173784390000083
Figure BDA0003173784390000084
Will be provided with
Figure BDA0003173784390000085
Substitution into
Figure BDA0003173784390000086
Then it can be determined
Figure BDA0003173784390000087
Finally, the constraint condition (8) is satisfied to obtain
Figure BDA0003173784390000088
Model Br
H (w, delta e, beta)1)，v(w,Δe,β1) Substituting equation (9) results in a hessian matrix for the appliance manufacturer profit function for w, Δ e, θ:
Figure BDA0003173784390000089
therefore, the following steps are carried out:
Figure BDA00031737843900000810
Figure BDA00031737843900000811
Figure BDA00031737843900000812
when mu [ lambda ]2(2-3β1)-4bU(1-β1)2]+(1-β1)2U(γ2+2bγt+b2t2)＜0
And b is2δ2μU(β1-1)2+2Cb(1-β3){μ[λ2(2-3β1)-4bU(1-β1)2]+(1-β1)2U(γ2+2bγt+b2t2) When the ratio is less than 0, the ratio is more than zero,
Figure BDA00031737843900000813
is a joint concave function with respect to w, Δ e, θ. Solving the following system of equations
Figure BDA00031737843900000814
From first order conditions
Figure BDA0003173784390000091
Substitute it into
Figure BDA0003173784390000092
Figure BDA0003173784390000093
Thereby obtaining
Figure BDA0003173784390000094
Will be provided with
Figure BDA0003173784390000095
Figure BDA0003173784390000096
Substitution into equations (9), (10) due to second derivative
Figure BDA0003173784390000097
Making the first derivative zero to obtain
Figure BDA0003173784390000098
Figure BDA0003173784390000099
Will be provided with
Figure BDA00031737843900000910
Substitution into
Figure BDA00031737843900000911
Then it can be determined
Figure BDA00031737843900000912
Finally, the constraint condition (11) is satisfied to obtain
Figure BDA00031737843900000913
Step S203: the optimal solution of each model obtained in step S202.
Model N
In the N model, the best decision for the appliance manufacturer and retailer is:
Figure BDA00031737843900000914
Figure BDA00031737843900000915
Figure BDA00031737843900000916
Figure BDA00031737843900000917
Figure BDA00031737843900000918
by mixing wN*，ΔeN*，θN*，hN*And vN*Substituting the values of (a) and (b) into equations (1) and (2) yields the optimum profits for the appliance manufacturer, retailer, and overall supply chain as:
Figure BDA00031737843900000919
Figure BDA00031737843900000920
Figure BDA00031737843900000921
the best decision for model a appliance manufacturers and retailers is:
Figure BDA00031737843900000922
Figure BDA00031737843900000923
Figure BDA0003173784390000101
Figure BDA0003173784390000102
Figure BDA0003173784390000103
Figure BDA0003173784390000104
by mixing betaA*，wA*，ΔeA*，θA*，hA*And vA*Substituting the values of (a) into equations (3) and (4) yields the optimum profits for the appliance manufacturer, retailer, and overall supply chain as:
Figure BDA0003173784390000105
Figure BDA0003173784390000106
Figure BDA0003173784390000107
the best decision for model Bp appliance manufacturers and retailers is:
Figure BDA0003173784390000108
Figure BDA0003173784390000109
Figure BDA00031737843900001010
Figure BDA00031737843900001011
Figure BDA00031737843900001012
Figure BDA00031737843900001013
Figure BDA00031737843900001014
by mixing
Figure BDA00031737843900001015
wBp*，ΔeBp*，θBp*，hBp*And vBp*Substituting the values of (a) into equations (6) and (7) yields the optimum profits for the appliance manufacturer, retailer, and overall supply chain as:
Figure BDA0003173784390000111
Figure BDA0003173784390000112
Figure BDA0003173784390000113
model Br
The best decision for the appliance manufacturer and appliance retailer is:
Figure BDA0003173784390000114
Figure BDA0003173784390000115
Figure BDA0003173784390000116
Figure BDA0003173784390000117
Figure BDA0003173784390000118
Figure BDA0003173784390000119
Figure BDA00031737843900001110
will be provided with
Figure BDA00031737843900001111
And
Figure BDA00031737843900001112
substituting the values of (a) into equations (9) and (10),
the optimal profit for the appliance manufacturer, retailer and the entire supply chain is obtained as:
Figure BDA00031737843900001113
Figure BDA00031737843900001114
Figure BDA00031737843900001115
step S3: under the condition of ensuring that the low-carbon preference gamma of the consumer and the low-carbon popularization activity preference lambda of the consumer are certain, performing numerical sensitivity analysis of numerical simulation on the model through a mathematical analysis tool MATLAB according to the optimal solution of the decision variable and the optimal profit expectation value of the members of the supply chain of the closed-loop household appliance, and determining the influence rule of the carbon tax rate t on the pricing decision, the expected profit, the cost sharing rate and the recovery rate of the members of the supply chain of the closed-loop household appliance. In this process, to simplify the analysis process, it is assumed that t is subject to a uniform distribution between [0,15] and that the market parameters γ is 4.5 and λ is 6.
Step S4: and analyzing different cost sharing contract decision-making models according to the analysis result of the step S3, wherein the analysis comprises comparing different cooperation models by using MATLAB software through sensitivity analysis, and obtaining an optimal cost sharing scheme and an optimal sharing proportion.
Since it is difficult to obtain an explicit solution in step S2, for further analysis, the model is simplified and the parameters are assigned a to 100, b to 1, e to 3.8, γ to 4.5, λ to 6, and c tom＝20,δ＝15,Cb300, U100, μ 300, solving the numerical solution of each decision variable and profit function, analyzing and researching the change rule of the decision variable, expected profit and social welfare expectation value when the inventory change, namely the demand uncertainty is taken as the fuzzy random change of the disturbance factor.
From the calculation results, it is found that:
when in use
Figure BDA0003173784390000121
When is beta2 *＞β3 *；
When in use
Figure BDA0003173784390000122
When is beta2 *＜β3 *
Through the analysis, the home appliance retailer is willing to share the carbon emission reduction cost of the home appliance manufacturer when the low carbon preference of the consumer, the carbon tax rate and the cost of recycling the old home appliance are high or the cost saved by producing each unit of product by the old home appliance is low; conversely, the appliance retailer is willing to share the recycling costs of the appliance manufacturer.
Carbon tax rate t for optimal wholesale price w*As shown in FIG. 2, it can be seen that the wholesale price of the home appliance manufacturer will be increased with the increase of carbon tax, when t < t*When the temperature of the water is higher than the set temperature,
Figure BDA0003173784390000123
on the contrary, the method can be used for carrying out the following steps,
Figure BDA0003173784390000124
this illustrates that in terms of price decision, when t < t*At present, home appliance manufacturers prefer to perform bidirectional cooperative carbon emission reduction with home appliance retailers; when t > t*At times, home appliance manufacturers prefer to work with home appliance retailersOne-way cooperation.
Carbon tax rate t versus optimal carbon emission reduction Δ e*As can be seen from fig. 3, the household appliance manufacturer increases the investment of carbon emission reduction as the carbon tax increases, and in the bidirectional cooperation decision model for cooperative carbon emission reduction, the marginal optimal carbon emission reduction amount of the household appliance manufacturer continuously increases as the carbon tax increases, and continuously decreases in other models.
Carbon tax rate t for optimal recovery θ*As can be seen in fig. 4, the optimum recovery rate for the appliance manufacturer decreases with increasing carbon tax, which is significantly higher in the two-way collaborative decision model for collaborative recovery than in the other models. When the tax rate is high, a growing trend occurs in the two-way collaborative decision model.
Since the appliance retailer profits are the same across different models, the carbon tax rate impact on appliance manufacturer profits is consistent with the supply chain total profits.
As can be seen from the analysis of FIGS. 1, 2 and 3, the influence of the carbon tax rate on the optimal decision of the home appliance manufacturer is shown in BpSignificant in the model, followed by BrThe model, again model a, is superior to model N, so home appliance manufacturers tend to work with home appliance retailers in both directions. The increase of carbon tax will guide home appliance manufacturers to select a bidirectional cooperation decision model for cooperative carbon emission reduction to increase carbon emission reduction, thereby reducing cost, expanding sales volume and improving competitive advantage of products. In addition, for different models, high carbon taxes cannot well guide enterprises to carry out carbon emission reduction, and governments deal with enterprises of different scales and types to make different carbon tax policies.
Carbon tax rate t for optimal retail margin h*As can be seen in fig. 5, the optimal retail balance decreases with increasing carbon tax, while the retail balance in the collaborative carbon reduction model tends to increase when the tax rate is higher. t < t*Time of day, at the same tax rate
Figure BDA0003173784390000125
On the contrary, the method can be used for carrying out the following steps,
Figure BDA0003173784390000126
therefore, in price decision, when t < t*At the same time, the home appliance retailer prefers to cooperate with the home appliance manufacturer for recycling; when t > t*At times, home appliance retailers prefer to cooperate with home appliance manufacturers for carbon emissions reduction.
Carbon tax rate t invests in low carbon promotional campaigns for optimal home appliance retailers v*As shown in fig. 6, it can be seen that the investment of low-carbon promotion activities of the optimal home appliance retailer decreases with the increase of carbon tax, and when the tax rate is higher, a growth trend appears in the cooperative carbon emission reduction model. t < t*Time of day, at the same tax rate
Figure BDA0003173784390000127
On the contrary, the method can be used for carrying out the following steps,
Figure BDA0003173784390000128
therefore, under the same tax rate, when t < t*In time, the cooperative recovery model can more motivate home appliance retailers to carry out carbon emission reduction promotion activities; when t > t*In time, the cooperation with the carbon emission reduction model can more motivate household appliance retailers to carry out carbon emission reduction promotion activities.
As can be seen from the analysis in fig. 5 and 6, when the carbon tax rate is low, the home appliance manufacturer can cooperate with the home appliance manufacturer to recover the carbon tax, which is beneficial for the home appliance retailer to make positive decisions; when the carbon tax rate is high, the carbon tax rate is reduced by cooperating with the household appliance manufacturer, which is beneficial for the household appliance retailer to make positive decisions.
Carbon tax Rate t for optimal retail price p*The influence of (2) is shown in fig. 7, it can be seen that the optimal retail price of the commodity increases with the increase of the carbon tax rate, and the optimal retail price relationship of each model under the same tax rate is
Figure BDA0003173784390000131
Total profit of carbon tax rate t for optimal decision pi*As can be seen in fig. 8, the total profit for the optimal decision for each model of the closed-loop supply chain decreases as the carbon tax rate increases. The optimal total profit relationship of each model under the same tax rate is as follows:
when t < t*When the temperature of the water is higher than the set temperature,
Figure BDA0003173784390000132
Figure BDA0003173784390000133
when t > t*When the temperature of the water is higher than the set temperature,
Figure BDA0003173784390000134
therefore, under the condition of a certain carbon tax, t < t*The home appliance manufacturer and the home appliance retailer are in bidirectional cooperation, so that the home appliance manufacturer and the whole supply chain can achieve optimal profit; t > t*In time, the home appliance manufacturer and the home appliance retailer perform bidirectional cooperation for cooperative carbon emission reduction, so that the overall profit of the supply chain and the profit of the members can be optimized.
It can be analyzed and known by combining fig. 7 and 8 that when the carbon tax rate is high, the supply chain members who mainly run high-quality and high-price products can achieve the optimal price, sales and profit by selecting a bidirectional cooperation decision model for cooperative carbon emission reduction. From the above, carbon tax can guide the closed-loop household appliance supply chain member to select the bidirectional cooperation decision model, and the high carbon tax rate selects B for the supply chain memberpThe model has strong guidance.
According to the invention, under the conditions of carbon tax policy and low carbon preference of consumers, different cooperation decision models are designed for a closed-loop household appliance supply chain consisting of a single household appliance manufacturer and a household appliance retailer, and the contract coordination problem of the closed-loop household appliance supply chain is researched on the basis. Therefore, when the household appliance enterprises are influenced by the government carbon tax policy and the low carbon preference of consumers, the most favorable cost sharing interest contract can be shared through different influence degrees of various factors and different choices of the characteristics of the household appliance products.
The increase of carbon tax can reduce the total profit of the supply chain, so the carbon tax can guide household appliance supply chain members to select the most favorable cooperative operation mode according with the requirements of the household appliance supply chain members, and the bidirectional cooperative decision model can well realize the optimal balance between the profit of the household appliance supply chain members and the energy conservation and emission reduction. Particularly, when the carbon tax rate is high, the household appliance supply chain members who mainly run high-price and low-sale products can achieve the optimal profit, price and emission reduction by selecting a bidirectional cooperation decision model for cooperative carbon emission reduction. Household appliance supply chain members who host low-price and multi-sale products can achieve optimal profit, sales volume and emission reduction by selecting a bidirectional cooperation decision model for cooperation recovery. The government can guide different household appliance enterprises to select different cooperation decision models by adopting different carbon tax rates, so that the purposes of household appliance industry optimization, energy conservation, emission reduction and green sustainable development are achieved. The following table shows the parameters used in the present invention, the meanings of which are to be read together:
TABLE 1 description of the parameters
Figure BDA0003173784390000135
Figure BDA0003173784390000141
Based on the same inventive concept, the invention also provides a system for calculating and analyzing the cost sharing optimal proportion of the closed-loop supply chain of the household appliance, which comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the computer program realizes the method for calculating and analyzing the cost sharing contract mechanism of the closed-loop supply chain when being loaded to the processor. The closed-loop supply chain cost sharing contract mechanism calculation and analysis system comprises a model establishing module, a model solving module, a simulation analysis module and an analysis comparison module. The model establishing module is used for establishing a non-cooperative decision model and three cooperative decision models which are dominated by a household appliance manufacturer, designing three cost sharing contract coordinating supply chains aiming at the cooperative decision models, and specifically realizing the content of step S1 in the closed-loop supply chain cost sharing contract mechanism calculation analysis method; the model solving module is used for solving the model established in the model establishing module by adopting a reverse-thrust method, obtaining the optimal solution of decision variables in each model and the optimal profit expectation value of a manufacturer main body in a closed-loop household appliance supply chain, and particularly realizing the content of step S2 in the cost sharing contract mechanism calculation analysis method of the closed-loop supply chain; the simulation analysis module is used for carrying out numerical value sensitivity analysis of numerical value simulation on the model through a mathematical analysis tool, determining the influence rule of the carbon tax rate on the pricing decision, expected profit, cost sharing rate and recovery rate of the members of the closed-loop household appliance supply chain, and particularly realizing the content of step S3 in the closed-loop supply chain cost sharing contract mechanism calculation analysis method; and the analysis and comparison module is used for comparing different cost sharing contract decision models according to the analysis result of the simulation analysis module, obtaining an optimal cost sharing scheme and specifically realizing the content of step S4 in the closed-loop supply chain cost sharing contract mechanism calculation and analysis method.
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and such improvements and modifications are also considered to be within the scope of the present invention.

Claims (8)

1. A method for calculating and analyzing optimal proportion of cost sharing of a closed supply chain of household appliances is characterized by comprising the following steps:
step S1: establishing a non-cooperative decision model and three cooperative decision models, and respectively designing three cost sharing contract coordination supply chains aiming at the cooperative decision models;
step S2: solving each model established in the step S1 by adopting a backward-stepping method to obtain the optimal solution of decision variables in each model and the optimal profit expectation value of a manufacturer main body in a closed-loop household appliance supply chain;
step S3: on the premise of ensuring certain low-carbon preference of consumers and certain low-carbon popularization activity preference of consumers, performing numerical sensitivity analysis of numerical simulation on the model through a mathematical analysis tool according to the optimal solution of the decision variables and the optimal profit expectation value of the members of the closed-loop household appliance supply chain, and determining the influence rule of the carbon tax rate on the pricing decision, the expected profit, the cost sharing rate and the recovery rate of the members of the closed-loop household appliance supply chain;
step S4: and analyzing different cost sharing contract decision models according to the analysis result of the step S3, and obtaining an optimal cost sharing scheme.
2. The method for computing and analyzing the optimal proportion of cost sharing in the closed supply chain of the household appliances according to claim 1, wherein the step S1 comprises the following sub-steps:
step S101: constructing a household appliance market demand function and a cost function:
in the forward sales supply chain, the market demand Q ═ a-b (w + h) + γ Δ e + λ v; w is the wholesale price of the home appliance manufacturer, h is the retail balance of the home appliance retailer, a is the market capacity, b is the sensitivity coefficient of the consumer to the retail price, gamma is the preference coefficient of the consumer to carbon emission reduction, lambda is the product sold in the early stage of the preference coefficient of the consumer to the low-carbon promotion activity of the home appliance retailer can be recycled to reproduce a new product, and delta e is the reduction of carbon dioxide emission; old appliance recovery Q of appliance manufacturer in reverse recovery supply chainrTheta is the recovery rate, theta is more than 0 and less than 1, and a new product produced by the old household appliance cannot meet the market demand, namely: q>Qr(ii) a The cost of producing unit products by using new materials and old household appliances by household appliance manufacturers is cm、cr(ii) a Wherein c isr＜cmLet δ be cm-cr(ii) a The government collects carbon tax on carbon dioxide emitted by household appliance manufacturers, and the tax rate is t yuan/ton; the household appliance manufacturers adopt the carbon emission reduction technology, the emission of carbon dioxide of the products of production units is reduced by delta e, and the emission reduction cost is
Figure FDA0003173784380000011
Mu is a carbon emission reduction cost coefficient corresponding to carbon emission reduction of a household appliance manufacturer; the recovery rate of the old household appliances is a function of the recovery investment of the old household appliances, and the recovery rate function is as follows:
Figure FDA0003173784380000012
M＝Cb*θ2cost invested for home appliance manufacturers to recycle old home appliances, CbA recycling cost coefficient invested for the home appliance manufacturer corresponding to the recycling rate of the old home appliances; the household appliance retailer carries out low-carbon promotion activities with the cost function of
Figure FDA0003173784380000013
U is a cost coefficient of low-carbon promotion activities performed by the household appliance retailer, and v is the effort degree of the low-carbon promotion activities of the retailer;
Figure FDA0003173784380000014
representing the profit of the household appliance manufacturer in a 0 decision model, and o belongs to { N, A, BP, BR };
step S102: according to the analysis in step S101, each profit maximization model is obtained as follows:
non-cooperative decision model N:
the home appliance manufacturer and home appliance retailer profit functions are:
Figure FDA0003173784380000015
Figure FDA0003173784380000016
one-way cooperative decision model a:
the home appliance manufacturer and retailer profit functions are:
Figure FDA0003173784380000021
Figure FDA0003173784380000022
s.t
Figure FDA0003173784380000023
wherein, beta is the sharing ratio of subsidizing the low-carbon promotion activity cost of the home appliance retailer to a certain degree set by the home appliance manufacturer in the model, KAProviding additional subsidies to the appliance retailer;
a bidirectional cooperative decision model Bp for subsidizing carbon emission reduction cost:
Figure FDA0003173784380000024
Figure FDA0003173784380000025
s.t
Figure FDA0003173784380000026
wherein, beta1Subsidy sharing ratio, K, for low carbon promotional activity cost of home appliance retailers set by home appliance manufacturersBpFor additional subsidies provided to the retailer of the appliance, beta2Setting a sharing ratio for subsidizing the carbon emission reduction production cost of the home appliance manufacturer for the home appliance retailer;
bidirectional cooperation decision model Br for subsidizing recovery cost
Figure FDA0003173784380000027
Figure FDA0003173784380000028
s.t
Figure FDA0003173784380000029
Wherein, on the basis of the non-cooperative decision model, KBrAdditional subsidies, beta, for home appliance manufacturers to home appliance retailers3A share ratio set for the home appliance retailer subsidizing the cost of the home appliance manufacturer's recycling of old home appliances.
3. The method for calculating and analyzing the optimal proportion of cost sharing in the closed supply chain of the household appliance according to claim 1, wherein the step 2 specifically comprises the following substeps:
step S201: home appliance retailers expect the greatest profit:
model N
Hessian matrix of home appliance retailer profit function:
Figure FDA0003173784380000031
it can be known that
Figure FDA0003173784380000032
When in use
Figure FDA0003173784380000033
The home appliance retailer profit function is a concave function with respect to h and v, so there is a maximum equal to the maximum value by solving the following system of equations:
Figure FDA0003173784380000034
obtaining an expression of a maximum value point:
Figure FDA0003173784380000035
Figure FDA0003173784380000036
model A
Hessian matrix of home appliance retailer profit function:
Figure FDA0003173784380000037
it can be known that
Figure FDA0003173784380000038
When in use
Figure FDA0003173784380000039
The home appliance retailer profit function is a concave function with respect to h and v, so there is a maximum equal to the maximum value by solving the following system of equations:
Figure FDA00031737843800000310
obtaining an expression of a maximum value point:
Figure FDA00031737843800000311
Figure FDA00031737843800000312
model Bp
Hessian matrix of home appliance retailer profit function:
Figure FDA0003173784380000041
it can be known that
Figure FDA0003173784380000042
When in use
Figure FDA0003173784380000043
The home appliance retailer profit function is a concave function with respect to h and v, so there is a maximum equal to the maximum value by solving the following system of equations:
Figure FDA0003173784380000044
obtaining an expression of a maximum value point:
Figure FDA0003173784380000045
Figure FDA0003173784380000046
model Br
Hessian matrix of home appliance retailer profit function:
Figure FDA0003173784380000047
it can be known that
Figure FDA0003173784380000048
When in use
Figure FDA0003173784380000049
The home appliance retailer profit function is a concave function with respect to h and v, so that there is a maximum equal to the maximum, allOver-solving the following system of equations:
Figure FDA00031737843800000410
obtaining an expression of a maximum value point:
Figure FDA00031737843800000411
Figure FDA00031737843800000412
step S202: home appliance manufacturers expect the greatest profit: the optimal solution of the expected profit obtained in step S201 is substituted into the objective function with the maximum profit for the home appliance manufacturer, which is specifically as follows:
model N
Substituting h (w, Δ e), v (w, Δ e) into equation (1) yields a hessian matrix for the appliance manufacturer profit function for w, Δ e, θ:
Figure FDA0003173784380000051
therefore, the following steps are carried out:
Figure FDA0003173784380000052
Figure FDA0003173784380000053
therefore, when 2 λ2μ+U[γ2+2bγt+bU(bt2-4μ)]＜0
And 4Cbλ2μ+2Cb[γ2+2bγt+bU(bt2-4μ)]+b2μUδ2At time < 0The home appliance manufacturer profit function is a concave function with respect to w, θ, Δ e, and thus has a maximum value, i.e., a maximum value, by solving the following equation:
Figure FDA0003173784380000054
can determine wN*，ΔeN*，θN*，hN*，vN*；
Model A
Substituting h (w, Δ e, β), v (w, Δ e, β) into equation (4) yields a hessian matrix for the appliance manufacturer profit function for w, Δ e, θ:
Figure FDA0003173784380000055
therefore, the following steps are carried out:
Figure FDA0003173784380000056
Figure FDA0003173784380000061
Figure FDA0003173784380000062
thus when
[(2-3β)λ2-4b(β-1)2U]μ+(β-1)2U(γ2+2bγt+b2t2)＜0，
And b is2δ2μU(β-1)2+2Cb{[(2-3β)λ2-4b(β-1)2U]μ+(β-1)2U(γ2+2bγt+b2t2) The home appliance manufacturer profit function is a concave function with respect to w, θ, Δ e when the } < 0, and thus has a maximum value, i.e., a maximum valueMaximum value by solving the following equation
Figure FDA0003173784380000063
From the first order conditions, w can be obtainedA(β)，ΔeA(β)，θA(β) substituting it into
Figure FDA0003173784380000064
Thereby obtaining hA(β)，vA(β); will wA(β)，ΔeA(β)，θA(β)，hA(β)，vA(β) substitution into equation (3) due to the second derivative
Figure FDA0003173784380000065
Making the first derivative zero to obtain
Figure FDA0003173784380000066
Will be provided with
Figure FDA0003173784380000067
Substitution into wA(β)，ΔeA(β)，θA(β)，hA(β)，vA(β) then w can be determinedA*，ΔeA*，θA*，hA*，vA*(ii) a Finally, the constraint condition (5) is satisfied to obtain
Figure FDA0003173784380000068
Model Bp
H (w, delta e, beta)1)，v(w,Δe,β1) Substituting equation (7) results in a hessian matrix for the appliance manufacturer profit function for w, Δ e, θ:
Figure FDA0003173784380000069
Figure FDA00031737843800000610
Figure FDA0003173784380000071
Figure FDA0003173784380000072
[(2-3β1)λ2-4b(β1-1)2U](β2-1)μ+(β1-1)2U(γ2+2bγt+b2t2) < 0 and b2δ2μU(β1-1)2(1-β2)+2Cb{[(2-3β1)λ2-4b(β1-1)2U](β2-1)μ+(β1-1)2U(γ2+2bγt+b2t2) When the ratio is less than 0, the ratio is more than zero,
Figure FDA0003173784380000073
is a joint concave function with respect to w, Δ e, θ; solving the following system of equations
Figure FDA0003173784380000074
From first order conditions
Figure FDA0003173784380000075
Substitute it into
Figure FDA0003173784380000076
Figure FDA0003173784380000077
Thereby obtaining
Figure FDA0003173784380000078
Will be provided with
Figure FDA0003173784380000079
Figure FDA00031737843800000710
Substitution into equations (6), (7) due to second derivative
Figure FDA00031737843800000711
Making the first derivative zero to obtain
Figure FDA00031737843800000712
Figure FDA00031737843800000713
Will be provided with
Figure FDA00031737843800000714
Substitution into
Figure FDA00031737843800000715
Then it can be determined
Figure FDA00031737843800000716
Finally, the constraint condition (8) is satisfied to obtain
Figure FDA00031737843800000717
Model Br
H (w, delta e, beta)1)，v(w,Δe,β1) Substituting equation (10) results in a hessian matrix for the appliance manufacturer profit function for w, Δ e, θ:
Figure FDA0003173784380000081
therefore, the following steps are carried out:
Figure FDA0003173784380000082
Figure FDA0003173784380000083
Figure FDA0003173784380000084
when mu [ lambda ]2(2-3β1)-4bU(1-β1)2]+(1-β1)2U(γ2+2bγt+b2t2) < 0 and b2δ2μU(β1-1)2+2Cb(1-β3){μ[λ2(2-3β1)-4bU(1-β1)2]+(1-β1)2U(γ2+2bγt+b2t2) When the ratio is less than 0, the ratio is more than zero,
Figure FDA0003173784380000085
is a joint concave function with respect to w, Δ e, θ; solving the following system of equations
Figure FDA0003173784380000086
From first order conditions
Figure FDA0003173784380000091
Substitute it into
Figure FDA0003173784380000092
Figure FDA0003173784380000093
Thereby obtaining
Figure FDA0003173784380000094
Will be provided with
Figure FDA0003173784380000095
Figure FDA0003173784380000096
Substitution into equations (9), (10) due to second derivative
Figure FDA0003173784380000097
Making the first derivative zero to obtain
Figure FDA0003173784380000098
Figure FDA0003173784380000099
Will be provided with
Figure FDA00031737843800000910
Substitution into
Figure FDA00031737843800000911
Then it can be determined
Figure FDA00031737843800000912
Finally, the constraint condition (11) is satisfied to obtain
Figure FDA00031737843800000913
Step S203: according to the optimal solution of each model obtained in step S202:
model N
In the N model, the best decision for the appliance manufacturer and retailer is:
Figure FDA00031737843800000914
Figure FDA00031737843800000915
Figure FDA00031737843800000916
Figure FDA00031737843800000917
Figure FDA00031737843800000918
by mixing wN*，ΔeN*，θN*，hN*And vN*Substituting the values of (a) and (b) into equations (1) and (2) yields the optimum profits for the appliance manufacturer, retailer, and overall supply chain:
Figure FDA00031737843800000919
Figure FDA0003173784380000101
Figure FDA0003173784380000102
the best decision for model a appliance manufacturers and retailers is:
Figure FDA0003173784380000103
Figure FDA0003173784380000104
Figure FDA0003173784380000105
Figure FDA0003173784380000106
Figure FDA0003173784380000107
Figure FDA0003173784380000108
by mixing betaA*，wA*，ΔeA*，θA*，hA*And vA*Substituting the values of (a) into equations (3) and (4) yields the optimum profits for the appliance manufacturer, retailer, and overall supply chain as:
Figure FDA0003173784380000109
Figure FDA00031737843800001010
Figure FDA00031737843800001011
the best decision for model Bp appliance manufacturers and retailers is:
Figure FDA00031737843800001012
Figure FDA0003173784380000111
Figure FDA0003173784380000112
Figure FDA0003173784380000113
Figure FDA0003173784380000114
Figure FDA0003173784380000115
Figure FDA0003173784380000116
by mixing
Figure FDA0003173784380000117
wBp*，ΔeBp*，θBp*，hBp*And vBp*Substituting the values of (a) into equations (6) and (7) yields the optimum profits for the appliance manufacturer, retailer, and overall supply chain as:
Figure FDA0003173784380000118
Figure FDA0003173784380000119
Figure FDA00031737843800001110
model Br
The best decision for the appliance manufacturer and appliance retailer is:
Figure FDA00031737843800001111
Figure FDA00031737843800001112
Figure FDA00031737843800001113
Figure FDA0003173784380000121
Figure FDA0003173784380000122
Figure FDA0003173784380000123
Figure FDA0003173784380000124
will be provided with
Figure FDA0003173784380000125
And
Figure FDA0003173784380000126
substituting the values of (a) into equations (9) and (10) yields the optimum profits for the appliance manufacturer, retailer, and overall supply chain as:
Figure FDA0003173784380000127
Figure FDA0003173784380000128
Figure FDA0003173784380000129
4. the method for computing and analyzing the cost sharing optimal proportion of the closed supply chain of the household appliances according to claim 1, wherein in the step S3, the mathematical analysis tool adopts MATLAB.
5. The method for calculating and analyzing the optimal proportion of cost sharing in the closed supply chain of home appliances as claimed in claim 1, wherein in step S3, it is assumed that the carbon tax rate is uniformly distributed within a certain interval.
6. The method for cost sharing optimal ratio calculation and analysis of closed supply chain of household appliances as claimed in claim 1, wherein the analysis of different cost sharing contract decision models in step S4 includes comparison between different cooperation models.
7. A closed-loop supply chain cost sharing contract mechanism computational analysis system comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the computer program when loaded into the processor implements the closed-loop supply chain cost sharing contract mechanism computational analysis method of any one of claims 1 to 6.
8. The closed-loop supply chain cost sharing contract mechanism calculation and analysis system of claim 1, wherein the closed-loop supply chain cost sharing contract mechanism calculation and analysis system comprises a model establishing module, a model solving module, a simulation analysis module and an analysis comparison module; the model establishing module is used for establishing a non-cooperative decision model and three cooperative decision models which are dominated by a household appliance manufacturer, and designing three cost sharing contract coordination supply chains aiming at the cooperative decision models; the model solving module is used for solving the model established in the model establishing module by adopting a reverse-thrust method to obtain the optimal solution of decision variables in each model and the optimal profit expected value of a manufacturer main body in a closed-loop household appliance supply chain; the simulation analysis module is used for carrying out numerical value sensitivity analysis of numerical value simulation on the model through a mathematical analysis tool and determining the influence rule of the carbon tax rate on the pricing decision, expected profit, cost sharing rate and recovery rate of the members of the closed-loop household appliance supply chain; and the analysis comparison module is used for comparing different cost sharing contract decision models according to the analysis result of the simulation analysis module and obtaining an optimal cost sharing scheme.
CN202110826440.2A 2021-07-21 2021-07-21 Method and system for calculating and analyzing optimal proportion of cost sharing of closed-loop supply chain of household appliance Pending CN113674017A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114549019A (en) * 2022-02-11 2022-05-27 中国科学技术大学 Decision method and system for sales commission proportion of retail platform
CN114708045A (en) * 2022-06-02 2022-07-05 华中科技大学 Multi-cycle supply chain network design method and system based on consumer preference

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114549019A (en) * 2022-02-11 2022-05-27 中国科学技术大学 Decision method and system for sales commission proportion of retail platform
CN114708045A (en) * 2022-06-02 2022-07-05 华中科技大学 Multi-cycle supply chain network design method and system based on consumer preference

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