4. 引进低碳技术下的低碳供应链信息共享模型
4.Introduce a low-carbon supply chain information sharing model under low-carbon technology
4.1 引进低碳生产技术的情形描述
4.1 Description of the introduction of low-carbon production technologies
基于企业生产时,缴纳的碳税会给企业的生产带来巨大的压力,此外,政府出台了一系列的碳补贴政策,企业引进低碳生产技术进行生产后,可以获得一定的政府补贴,而企业在使用低碳生产技术后,生产商品所需要的消耗能量也会相对应的减少,而分摊到每件商品的碳税也会降低,进而整体的碳税也会降低。而新引进的低碳生产技术,生产出的低碳商品,对低碳商品偏好的消费者是有利于提高其整体效用的,进一步扩大市场需求,获得更多的利润。
In addition, the government has introduced a series of carbon subsidy policies, after enterprises introduce low-carbon production technology for production, they can obtain certain government subsidies, and enterprises use low-carbon production technology, the energy consumption required to produce goods will also be reduced correspondingly, and apportioned to each pieceThe carbon tax on goods will also be lowered, and the overall carbon tax will also be reduced. The newly introduced low-carbon production technology and the low-carbon goods produced are conducive to improving the overall utility of consumers who prefer low-carbon goods, further expanding market demand and obtaining more profits.
4.2 低碳生产技术下低碳偏好消费者需求
4.2 Low-carbon preference consumer demand under low-carbon production technology
在供应链中,零售商选择无差别定价,预期效用决定消费者的购买行为。因此可以利用消费者效用函数分析价格和需求的关系。
In the supply chain, retailers choose to price indiscriminately, and the expected utility determines the purchasing behavior of consumers. Therefore, the relationship between price and demand can be analyzed using the consumer utility function.
因为消费者是理性人,其效用函数受商品价格p的影响,此外,由于零售商售卖的商品是低碳商品因此,对应低碳消费者的消费者预期效用是:-*p+
Because consumers are rational people, their utility function is affected by the price of goods p, and since the goods sold by retailers are low-carbon goods, they correspond to low-carbon consumersConsumers expect utility to: - *p+
而消费者选择是否购买该商品是基于该商品的预期效用是否大于0,当商品的预期效用大于0时,消费者会选择购买该商品,而当商品的预期效用小于0时,消费者不会购买。因而当预期效用等于0时,可以得到临界的商品估值:*p-。
The consumer's choice to buy the product is based on whether the expected utility of the commodity is greater than 0, and when the expected utility of the commodity is greater than 0, the consumer willChoose to buy the product, and the consumer won't buy it when the expected utility of the product is less than 0. Thus, when the expected utility is equal to 0, the critical commodity valuation can be obtained: *p- .
因为无低碳商品偏好消费者对低碳商品不敏感,因此无低碳商品偏好消费者的预期效用为:-*p,同理可以得到无低碳商品偏好消费者的临界估值:*p
Because consumers without a preference for low-carbon goods are not sensitive to low-carbon goods, the expected utility of consumers without a preference for low-carbon goods is: - *p, the same can be done to obtain a critical valuation for consumers with no preference for low-carbon goods: *p
根据假设4-2,可以得出低碳商品偏好消费者和无低碳商品偏好消费者的总人数:y2(引进低碳生产技术后)和z:
Based on hypothesis 4-2, the total number of consumers with a preference for low-carbon goods and consumers without a preference for low-carbon goods can be obtained: y 2(after the introduction of low-carbon production technologies) and z:
y2=(1-)= (1-*p+)
z=(1- (1-)= (1- (1-*p)
相加后可以得到购买该商品的消费者总人数,即总需求为: D2= (1-)+(1- (1-) =(引进低碳生产技术后)
After summing up, we can get the total number of consumers who buy the product, that is, the total demand is: D2= (1- )+(1- (1-) = (after the introduction of low-carbon production technologies).
D2对p求导后可得。因为市场需求与价格p相关,当价格升高时,需求减小因而,即
D2 is derived from p. Because market demand is related to price p, when the price increases, the demand decreases, i.e .
4.3 引进低碳技术下选择信息不共享策略
4.3 Choose a non-sharing strategy under the introduction of low-carbon technologies
当零售商选择不共享需求信息时,制造商需要多生产σ数量的商品。而生产时所需成本和所缴纳的税收由制造商来承担。生产该商品所需要的成本原材料为c_0,同时生产一个单位的商品需要消耗(e-x)的能量,其中x为采用新技术减少的耗能,并且每单位的能耗需要缴纳c_e单位的费用,而引进新技术的费用扣除补贴后还需要T那么多的支出。因此生产成本为:
When a retailer chooses not to share demand information, manufacturers need to produce σ more quantities of goods. The cost of production and the taxes paid are borne by the manufacturer. The cost of raw materials required to produce the commodity is c_0, and the production of one unit of the commodity requires the consumption of (e-x), where x is the energy consumption reduced by the use of new technology, and each unit of energy consumption needs to pay c_e unit fee, The cost of introducing new technologies after deducting subsidies will require as much expenditure as T. Therefore, the production cost is:
c=
而制造商除了需要承担生产成本外,还需缴纳碳税,每单位能耗的碳税惩罚率为:t。由此可以得到零售商和制造商的利润分别为:
In addition to the production costs, manufacturers also need to pay a carbon tax, and the carbon tax penalty rate per unit of energy consumption is: t. From this, the profits for the retailer and the manufacturer are respectively:
=(p-w)(D3)
3=(w-)(D3+σ)-T
在引进低碳技术下零售商选择信息不共享策略,得到的最优定价和利润为:
Under the introduction of low-carbon technology, retailers choose the information non-sharing strategy, and the optimal pricing and profit obtained are:
W3=
D3=
=
3
=
证明:
Prove:
本文采用逆向归纳求导法对供应链内部的博弈进行求解。
In this paper, the reverse inductive derivation method is used to solve the game within the supply chain.
首先,将零售商的最优利润函数对价格p求二阶偏导<0,又一阶偏导,所以零售商的利润函数是销售价格p的严格凹函数。
Firstly, the retailer's optimal profit function is given the second-order partial derivative <0 for the price p, and the second-order partial derivative is obtained , so the retailer's profit function is a strictly concave function of the selling price p.
令一阶偏导的结果为0,得到p3和D3:
Let the result of the first-order partial derivative be 0, and we get p3 and D3:
P3= D3=
将上述得到的p3和D3代入,计算制造商利润:
Substituting the p3 and D3 obtained above into , the manufacturer's profit is calculated
将p3和D3代入,得:
Substituting p3 and D3 into , we get:
=
对求w的一阶偏导得:,二阶偏导为:<0, 令一阶偏导的结果为0,可以得到批发价格的最优解w3。
For finding the first-order partial derivative of w, we get: , the second-order partial derivative is: <0, so that the result of the first-order partial derivative is 0, The optimal solution for the wholesale price w3 can be obtained.
w3=
最后再将得到的w3代入p3和D3中可以得到最优价格和相对应的消费者人数为:
Finally, substituting the obtained w3 into p3 and d3 can obtain the best price and the corresponding number of consumers:
D3=
最后再将上述得到的结果分别代入和中可以得到:
Finally, the above results can be substituted into and respectively, and we can get the following
-T
将和相加可以得到供应链的最优利润:
Add up and get the optimal profit for the supply chain
=-T
4.4 引入低碳生产技术下采用信息共享策略
4.4 Adopt information sharing strategies under the introduction of low-carbon production technologies
在信息共享策略时,零售商和制造商的利润函数如下:
When it comes to information sharing strategies, the profit functions for retailers and manufacturers are as follows:
=(p-w)(D2)
4=(w-)(D2)-T
采用逆向归纳求导法求解得结果。
The results are obtained by using the reverse inductive derivation method.
观察最优解,不难发现销售价格p与制造商和零售商的利润同低碳商品偏好消费者占比关系紧密。
Observing the optimal solution, it is not difficult to find that the selling price p is the proportion of the profit of the manufacturer and retailer to the preference of consumers for low-carbon goods The relationship is close.
引进低碳生产技术下采用信息共享策略,得到的最优定价和最优利润为:
Under the introduction of low-carbon production technology, the information sharing strategy is adopted, and the optimal pricing and profit are as follows:
w4=
D
-T
=-T
4.5 信息共享决策分析与比较
4.5 Information sharing decision-making analysis and comparison
本节主要分析制造商在引进低碳生产技术后,零售商采取不同的信息共享策略时,价格敏感因子、对低碳商品敏感程度、碳排放惩罚率t以及改进后节省的能耗x的影响;对比在零售商选择共享策略的情况下,制造商引进低碳生产技术的影响,并比较均衡解,帮助零售商和制造商进行最优决策。
This section mainly analyzes the price sensitivity factors and sensitivity to low-carbon products when retailers adopt different information sharing strategies after manufacturers introduce low-carbon production technologies , carbon emission penalty rate t and the impact of energy savings x after improvement; Compare the impact of manufacturers introducing low-carbon production technologies when retailers choose a sharing strategy, and compare the equilibrium solution to help retailers and manufacturers make optimal decisions.
4.5.1 效用影响因子分析
4 5.1 Utility Impact Factor Analysis
主要分析不同价格敏感因子、对低碳商品敏感程度、碳排放惩罚率t以及改进后节省的能耗x对供应商和制造商的影响,还分析了不同信息共享策略的情况。
Mainly analyze different price sensitivity factors , sensitivity to low-carbon commodities, The impact of the carbon penalty rate t and the improved energy savings x on suppliers and manufacturers is also analyzed.
市场需求与影响因子间关系的计算结果如下所示:
The results of the calculation of the relationship between market demand and impact factors are as follows:
在制造商选择引进低碳生产技术,零售商选择何种信息共享策略,消费者总人数都随着价格敏感因子、碳排放惩罚率t以及改进后节省的能耗x的增长而降低;而市场需求随着对低碳商品敏感程度因子的增大而升高。这是因为,低碳商品偏好型消费者追求低碳商品,当对低碳商品敏感程度越大,消费者购买该商品的可能也就越大,购买该商品的总人数也会随之增加。
When manufacturers choose to introduce low-carbon production technologies, and retailers choose information sharing strategies, the total number of consumers decreases with the increase of price sensitivity factors , carbon emission penalty rates, and energy savings after improvement. The market demand increases with the increase of sensitivity to low-carbon commodities. This is because consumers who prefer low-carbon commodities pursue low-carbon commodities, and the more sensitive they are to low-carbon commodities. The more likely consumers are to buy the product, the more likely they are to buy the product, and the more people will buy the product.
制造商引进低碳生产策略时,无论零售商选择何种共享策略,最优销售价格都随着对低碳商品敏感程度、碳排放惩罚率t以及改进后节省的能耗x因子的增加而增加;最优价格p随着价格敏感因子因子的增加而减少。
When manufacturers introduce low-carbon production strategies, the optimal selling price increases with the increase of sensitivity to low-carbon goods, carbon emission penalty rate t, and energy savings after improvement, regardless of the sharing strategy chosen by retailers. The optimal price p decreases with the increase of the price sensitivity factor .
当低碳敏感程度增加时,低碳倾向消费者更愿意去购买低碳商品,而零售商选择适当提高销售价格以获得更好利润。制造商选用低碳生产技术可以降低生产成本,制造商会选择适当的提高一部分的批发价格,而零售商为了应对,也会选择提高销售价格。
When the sensitivity to low carbon increases, consumers with low carbon tendencies are more willing to buy low-carbon goods, while retailers choose to raise the selling price appropriately to obtain better profits. Manufacturers can reduce production costs by choosing low-carbon production technologies, manufacturers will choose to increase some wholesale prices appropriately, and retailers will also choose to increase sales prices in response.
计算结果如下:
The result of the calculation is as follows:
=>0
=>0
=<0
= >0
>0
>0
<0
>0
制造商采取引进低碳生产策略的政策时,批发价格并不受信息差的影响。批发价格随着对低碳商品敏感程度、碳排放惩罚率t以及改进后节省的能耗x因子的增加而增加;最优批发价格w3、w4随着价格敏感因子因子的增加而减少。当改进后减少的能耗越多时,碳税对批发价格的影响也就越小。此外,在该情况下,消费者对价格敏感过是否为低碳商品。
When manufacturers adopt policies to introduce low-carbon production strategies, wholesale prices are not affected by poor information. The wholesale price increases with the increase of the sensitivity to low-carbon commodities, the carbon emission penalty rate t, and the energy consumption saved by the improved energy consumption x-factor. The optimal wholesale prices w3 and w4 decrease with the increase of the price sensitivity factor . The more energy consumption is reduced after the improvement, the less the carbon tax will have an impact on wholesale prices. In addition, in this case, consumers are price-sensitive to whether it is a low-carbon commodity.
计算结果如下所示:
The result is as follows:
=>0
=>0
=<0
= >0
4.5.2 引进低碳生产技术下最优解比较和讨论
4 5.2 Comparison and discussion of optimal solutions under the introduction of low-carbon production technologies
本文通过计算制造商和零售商之间的博弈情况,获得零售商选择不同信息共享策略下的最优解,并比较和分析最优结果。制造商引进低碳生产技术时,计算两种情形下的差值得如下结果:
In this paper, the retailer choice is obtained by calculating the game between the manufacturer and the retailerThe optimal solution under different information sharing strategies, and the optimal results are compared and analyzed. When a manufacturer introduces a low-carbon production technology, the difference between the two scenarios is calculated as follows:
0
根据以上结果,得知制造商引进低碳生产技术时,零售商和制造商最优利润还有最优销售价格与信息差、价格敏感因子、对低碳商品敏感程度、碳排放惩罚率t、改进节约耗能x有关。而在制造商选择引进低碳生产技术的情况下,零售商无论选择何种方式,对批发价格w都没有影响。此外,市场需求,在制造商选择引进低碳生产技术且时,仅与信息差有关。
According to the above results, it is known that when manufacturers introduce low-carbon production technologies, the optimal profit of retailers and manufacturers also includes the optimal selling price and information gap , and price sensitivity factors , sensitivity to low-carbon commodities , carbon emission penalty rate t, and improvement of energy conservation x. In the case where manufacturers choose to introduce low-carbon production technologies, no matter which method retailers choose, there is no impact on wholesale prices. In addition, market demand, when manufacturers choose to introduce low-carbon production technologies , is only related to poor information.
当=4D4时, ,且;
WHEN =4D4, , AND ;
当时,,且。
When , , and .
因此当制造商与零售商之间的需求信息差大于四倍D4时,零售商不会将需求信息共享给制造商;当零售商与制造商之间的需求信息差小于四倍D4时零售商会将需求信息共享给制造商。
Therefore, when the difference in demand information between the manufacturer and the retailer is greater than four times D4, the retailer will not share the demand information with the manufacturer; When the difference in demand information between the retailer and the manufacturer is less than four times D4, the retailer shares the demand information with the manufacturer.
而最优批发价格的差值为0,说明了制造商在生产商品时,生产数量的多少与生产总成本没有关系。
The difference between the optimal wholesale price is 0, which indicates that the quantity produced by the manufacturer has no relationship with the total cost of production when producing goods.
当时,D4>D3,这说明了当信息共享时购买商品的消费者人数增多。
D4>D3, which indicates that the number of consumers who purchase goods increases when information is shared.
当0>时,,但显然信息差大于0,因此。因为无信息共享时,可以获得更高的消费者需求,又因为批发价格不变,制造商利润增加,供应链内的利润也随之增加。
When 0> , but apparently the information difference is greater than 0, therefore 。 This is because there is no information to share, there is higher consumer demand, and because the wholesale price remains the same, the manufacturer's profit increases, and the profit within the supply chain also increases.
4.5.3 信息共享策略下最优解比较和讨论
4.5.3 Comparison and discussion of optimal solutions under information sharing strategies
本文计算了制造商和零售商之间的博弈并得出在零售商采取不同信息共享行策略时的最优解,通过对比分析最优结果可知当零售商选择信息共享策略之后,两种情形之间,差值计算结果如下:
This paper calculates the game between manufacturers and retailersThe optimal solution when retailers adopt different information sharing strategies, through comparative analysis of the optimal results, we can see two scenarios when retailers choose information sharing strategies, the difference is calculated as follows: