_{1}

As consumers’ demand for low carbon products is growing, we develop a two-echelon supply chain with price-and-carbon-emission dependent demand consists of a dominant manufacturer and a retailer, and compare the optimal price and carbon emission and profit under the centralized and decentralized scenarios. Based on the manufacturer who wants to coordinate the whole supply chain, two different coordination contracts are proposed. We find that these two contracts not only improve profits of both sides, but also have the effect of carbon reduction. Finally we validate the effectiveness and environmental of these contracts through numerical examples.

In recent decades, increasingly serious global warming has affected all aspects of human life, even the survival of human being. The work to reduce the emissions of greenhouse gases, most of which is carbon dioxide, has risen to be a common sense of all the word, and it has brought people more green life concept. This concept has affected people’s daily lives―people are willing to buy more environmental friendly products, which means that the demand for certain products will be affected by this product’s environmental performance. Much research also confirmed that. For example Kleindorfer et al. (2005) and Sarkis et al. (2011) found that customers will continue to exert influence on companies to reduce the impact on the environment during production [

Currently, there are many scholars carry out the researches on the coordination of two-echelon supply chain with manufacturers and retailers. Wang et al. (2004) constructed a two-stage sales model, and applied the revenue sharing contract to coordinate the profit of two parties [

In the existing studies of supply chain coordination, the patterns of demand are different. Zhou et al. (2008) concerned on the demand depends on the inventory levels [

Reviewed the existing research of the coordination of supply chain, we found that the directions of the research are mainly wholesale price discount contract, revenue sharing contract, buyback contracts and credit contractual options. In this paper, the wholesale price with quantity discount contract and wholesale price are both used to coordinated the supply chain, by determining the reasonable wholesale price range and the amount of the discount, to achieve supply chain coordination, so that manufacturer and retailer got profits improved.

We study a two-echelon supply chain coordination problem, with a dominated manufacturer and a retailer, both of the manufacturer and retailer make their decision base on the of maximization of their profits. The manufacturer sell a single product to retailer by the price of w, while the retailer sell their products to customers at price p.

The market demand of retailer not only depends on the price p, but also sensitive to the carbon emissions per unit of product. That requires to set a joint demand function with price and carbon emissions per unit of product, and the demand is monotonically decreasing at product price and carbon emissions per unit of product. Therefore we set the demand function as: the same as Yalabik et al. (2011) [

At the same time, we assume that the manufacturer’s initial unit product emissions amount is g_{0}, the fixed production cost of per unit product is c, the manufacturer is able to carbon emissions per unit of product g by means of technology transformation, and the transformation cost is

Despite the growing awareness of environmental protection, compared to the price, the impact of carbon emission on product demand is still much smaller. In addition, the cost of reducing carbon emissions and the transformation is also very impressive. Therefore, we assume that the parameter b, k and t satisfy

Under centralized decision, the manufacturer and the retailer will form a unified one, its purpose is to maximize the benefits of the whole supply chain, which is mainly achieved through the supply chain coordination and cooperation. In this paper, the centralized decision model of two-echelon supply chain is to maximize the profit of the whole supply chain, and it is necessary to make the sales price p and the unit product carbon emissions g. In this case, this decision is the global optimal one, and provides the benchmark for the coordination of the manufacturer and retailer in the decentralized decision. So in the case of centralized scenario, the entire supply chain profit function is

Take the partial derivative of the formula (1) for p and g respectively and make them equal to zero:

Simultaneous (2) and (3) and solved, we get:

Put the formula (4) and (5) into the demand function, we get:

The optimal profit of supply chain under centralized scenario is:

Theorem 1. There exist optimal

In the case of decentralized scenario, manufacturer and retailer make their decisions to maximize their own profits, the profit of the retailer

Based on Stackelberg principle, we simultaneous (8) and (9), and solve, we get:

Put the formula (11) and (12) into the demand function, we get:

Theorem 2. The demand under decentralized scenario is smaller than the one under centralized scenario.

Also, with the formula above, we get the optimal profit of manufacture, retailer and the whole supply chain:

The margin profit in of the supply chain between centralized scenario and decentralized scenario is:

Theorem 3. The profit of the supply chain under centralized scenario is bigger than the one decentralized scenario.

We can find that,

So, we want to coordinate the whole supply chain, base on the centralized scenario. Therefore, how to motivate the manufacturer and retailer make their decision throughout the supply chain profit maximization, how to effectively design coordination mechanism and implementation is crucial

Manufacturer and retailer coordinate with each other is to maximize the supply chain profits , but at the same time, under coordination contracts the profits of manufacturer and retailer is not less than the profit they get under decentralized scenario. That means they all attain Pareto optimal. We mainly determine a reasonable wholesale price and quantity discount of wholesale price contract to reach the coordination.

In this case, the manufacturer develops a reasonable wholesale price to sell products to retailers, and the price and the emissions per unit of output produced are the same with centralized scenario, while their own profits are not less than the profits under decentralized scenario, Assume the wholesale price manufacturers gives is w, then the profit of retailer and manufacturer are:

Theorem 4. When the wholesale price w is with

It’s easy to prove the theorem 4, from the assumptions above, we know

That are

Then we get

Finally,

When

1) The increased profit of supply chain:

2) The increased profit of retailer:

3) The increased profit of manufacturer:

When

When

Manufacturers and retailers make the decision to maximize the profit of the supply chain the demand will also, as we can know for n the formula

Theorem 5. When the wholesale price discount

When

1) The increased profit of supply chain:

2) The increased profit of retailer:

3) The increased profit of manufacturer:

When

When

For a market whose total demand is 200, and

From

From

Centralized scenario | Decentralized scenario | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

^{ } | ||||||||||

14.33 | 10.67 | 74.67 | 653.33 | 18.55 | 15.48 | 14.03 | 36.13 | 163.16 | 316.13 | |

Contracts | Profit of chain | Profit of retailer | Profit of manufacturer | Parameter range |
---|---|---|---|---|

Wholesale price | 653.33 | (163.16, 337.20) | (316.13, 490.17) | (w_{min}, w_{max}) (9.30, 12.15) |

Wholesale price discount | 653.33 | (163.16, 337.20) | (316.129, 490.17) | When w = 13 |

With the popularity of green life, the demand for green products is being more intense. Based on this, we consider the impact of price and carbon emissions on demand, and coordination of two-echelon supply chain. The profit realized by centralized scenario is bigger than decentralized scenario, and the carbon emission is lower. To coordinate the supply chain and improve the profit of both manufacturer and retailer, we design two contracts; within the range we give, we can achieve our goals. For a more green production, it is important to use this kind of contract.

Also, there are limitations of this research. The most important is we do not give specific contracts, including the contract of wholesale price and contract of wholesale price discount, but, to a certain extent, the result of this paper provides effective suggestions.

Lu Li, (2016) Coordination Contracts for Two-Echelon Supply Chain with Price-and-Carbon-Emission Dependent Demand. Modern Economy,07,606-612. doi: 10.4236/me.2016.75066