Study on the Coordination of Supply Chain Based on Carbon Emissions Trading Considering the Retailers’ Competition

This paper studies the coordination of supply chain in the context of carbon emissions trading mechanism, which considering the competition between retailers. Centralized and decentralized supply chain models were constructed to discuss the price of product, to avoid the losses of profit from the decentralized decision-making, the revenue-sharing contract was introduced to coordinate the supply chain. Research shows that the carbon emissions trading reduce emissions effectively, but the higher price of carbon emissions trading cut down the total profit of supply chain; The competition between retailers upgrades the supply chain members′ profit; Coordination was achieved by introducing the revenue-sharing contract. Finally, numerical example was given to illustrate the validity of the revenue-sharing contract, and the sensitivity analysis of parameters such as the price of the emissions trading and the retailers’ competition were presented.

process based on the newsboy model 3, on the basis, he see the quotas of the government′ carbon emission as a variable parameter, research the carbon emission′s impact on the profit of the supplier 4. Abdallah studies how to maximize the enterprises′ interests with the economic and environment influence that under the carbon trading mechanism 5. Li solves the logistics distribution routing problem under the carbon emission trading mechanism, introducing a calculation method that consider the vehicle load and speed, make some interesting observation about how to control cost and reduce carbon emissions 6. Ma assuming that a local government has launched a regional carbon trading market in the purpose of maximizing the profit of whole system, the result shows some valuable managerial insights on the decision making of the company and the government 7.
Researchers have further study on supply chain which considering the competition between retailers. Bernstein on the basis of competitive relationship between multiple retailers, studies the decentralized supply chain when faced with uncertain demand equilibrium strategies 8. Yao in the perspective of retailers provide competitive services, study the operation strategy of supply chain which is composed of one manufacturer and two competitive retailers 9. Fan presents a channel pricing strategy which is combated of the quantity discount pricing and slotting fees, on the basis of considering the retailers′ competition 10. Gao in the case of two competitive retailers face random demand, to decide the product price, quantity and the responsive to price 11. Cao study the pricing and coordination problems of closed-loop supply chain under stochastic demand, where the two retailers face the different market demand and the product recycled affected by competition price 12.
The literature on carbon trading mechanism has achieved fruitful results, but there are little literature considering the effects of competition between retailers at the same time. Therefore, this article researches the coordination of supply chain that considering retailers′ competition under carbon trading mechanism, the optimal decision of the manufacturer and retailers in the mode of centralized and decentralized are concluded, and by introducing the revenue-sharing contract to coordinate the supply chain.

Description of problem and hypothesis
This paper studies the supply chain that composed of one manufacturer and two competitive retailers. In carbon trading mechanism, the government gives carbon emission quota of E to manufacturer for free, the manufacturer response the government mechanism to reduce emission, and the manufacturer has the carbon trading with price of p c to maximize its profit. e H and e L are the carbon emission of manufacturer that before and after the reduction respectively, where λ(0≤λ<1) is the purification rate, and the cost of reduction is c L =Ɛ(λe H ) 2 /2, Ɛ(Ɛ>0) is the parameter for reduction investment. The unit producing cost of product is c. The manufacturer sales the products to two competitive retailers with wholesale price w, the sale price of two retailers are p 1 , p 2 , which are the decision variables for retailers. The market demand of two competitive retailers are expressed as: q 1 =φ 1 -p 1 +βp 2 , q 2 =φ 2 -p 2 +βp 1 , where φ 1 , φ 2 are the market demand size of two retailers respectively, β(0≤β≤1) is the degree of competition between retailers.

Decision of supply chain based on the carbon emissions trading considering the retailers′ competition
The centralized and decentralized decisions were made which based on the carbon emissions trading considering the retailers′ competition, and the reverence-sharing contract was introduced to coordinate the supply chain.

Centralized Decision-making
The centralized decision-making is a kind of ideal system structure, the decision target of the supply chain members is to maximize the total profit of supply chain. The profit of supply chain under centralized decision-making is:  , the sales price of two retailers in centralized decision-making is: Then take p 1c * and p 2c * into the demand function of market, generate the optimal order quantity of two retailers is: Table1 shows after introducing of the revenue-sharing contract, the manufacturer and the retailers′ profit are higer than the decentralized decision-making that without the contract. The manufacturer′ profit relatively increased 1.5%, the profit of the two retailers grow 48.6% and 63.6% respectivily. At the same time, the total profit of supply chain rises 14.3%, that is equal to the profit of the supply chain under the centralized decision-making, that means the revenue-sharing contract coordinate the supply chain effectively. Table 2 shows the influence of carbon emissions trading′ price on the total carbon emissions, the profit of supply chain members and the total profit of supply chain.   Table 2 shows: (1) With the risen in the price of trading, the total carbon emissions has been controlled effectively, the carbon trading mechanism plays positive role in the process of low carbon economy; (2) With the risen in the price of trading, the profit of manufacturer, retailers and the overall supply chain are both on decline, so the government needs to control the price reasonably, neither too low nor too high. The low carbon trading price can′t stimulate the manufacture to reduce the carbon emissions, on the contrary, the high carbon trading price will aggravate the burden on supply chain members. The Table3 analyzes the influence of the retailers′ competing degree on the profit of supply chain members and the total profit of supply chain after introducing of the contract. Table3 shows: with the increase of retailers′ competition, the profit of manufacturer, two retailers and the total profit of the supply chain were both promoted, it means the existence of the competition of retailers making the retailers have motivation to promote for more profit, and the effective market competition also increases the profit of manufacturer.

Conclusion
Under the background of carbon trading mechanism, this paper studies the coordination problem of supply chain. By building the centralized and decentralized decision-making model of supply chain, the optimal pricing strategy of manufacturer and retailers were obtained, and in order to solve the problem of profit losses which resulting from the decentralized dicision-making, the revenue-sharing contract was introduced to coordinate the supply chain. Research shows that: (1)With the revenue-sharing contract, the supply chain members′ profit and the pross profit of supply chain both run up to the centralized decision-making level; (2)The implementation of the carbon trading mechanism reduces carbon emissions in the process of production effectively; (3)With the risen in the price of carbon trading, the profit of the manufacturer, the retailers and the overall supply is on the decline, so the government need to control the price of carbon trading; (4)With the increase of retailers′ competition ,the profit of manufacturer, two retailers and the total profit of the supply chain were both promoted.
But we have not considered the competition between manufacturers, it will be the main content of further research.