Revenue-sharing contract is a kind of mechanism to improve performance or to achieve perfect coordination of supply chain. Considering a three-level supply chain consisting of a manufacturer, a distributor, and a retailer who faces a stochastic and sales effort dependent demand, the paper analyzes the impact of sales effort on supply chain coordination and expounds the reasons why traditional revenue-sharing contract cannot coordinate supply chain in this condition. Given three cases: only the retailer bears the sales effort cost, only the manufacturer bears the sales effort cost, and the retailer bears the sales effort cost with the manufacturer, the paper proposes an improved revenue-sharing contract based on quantity discount policy to coordinate the supply chain. It illustrates that improved revenue sharing contract can coordinate supply chain by implementing it in one transaction or two transactions of three-level supply chain. The model of improved revenue-sharing contract is optimized, respectively, by addition form and multiplication form with sales effort dependent demand. Formulas are given to determine the optimal contract parameters. Finally, numerical experiments are given to test the accuracy of the model of improved revenue-sharing contract.

Supply chain is made up of several different decision makers who pursue different objectives and may conflict among each other. Then, the contractual supply chain actually faces a “double-marginal utility”: each individual of the supply chain makes the decision, respectively, in order to achieve optimum profits. But the decision is not identical with the one in the coordinated supply chain. So we need a kind of coordinative mechanism or contract to make the whole profits of supply chain achieve the optimum and guarantee each company gets more profits than it does in the noncontractual supply chain.

Revenue-sharing contract [

The revenue-sharing contract initially appeared in the industry of video-rent and was later successfully extended to other industries, such as franchise model commonly used in China. From an economic point of view of revenue-sharing contract applications in the video rental industry (1998-1999), Mortimer [

By reviewing the extensive literature available, we can see that most of the literatures do not consider the effort activities of supply chain members that affect market demand. And it is known that there exists a wide gap between market demand and the actual situation. In reality, the effort activity of supply chain members, as important factors affecting market demand [

Cachon [

These contradictions may be resolved when all supply chain members share the effort cost. For example, Wang and Gerchak [

It should be noticed that the research object of literatures mentioned above is a two-level supply chain. Through literatures searching, we have not found the literatures that take effort into account in three-level supply chain. Therefore, the paper tries to further study in the following aspects. First, the research object is extended to three-level supply chain with sales effort dependent demand, which meets the actual circs better. Second, by analyzing the behavior of the decentralized supply chain under the traditional revenue-sharing contract with sales effort dependent demand, we find that the contract fails to coordinate the supply chain. Third, by supposing only the retailer or the manufacturer bears the effort cost, we propose an improved revenue-sharing contract based on quantity discount policy, which can coordinate the three-level supply chain. Because there are two different transaction phases in the three-level supply chain, two different conditions are discussed: implementing the improved revenue-sharing contract in one transaction phase and in two transaction phases. Further, by supposing the demand and the effort satisfy addition form or multiplication form, we characterize the optimal solution to the three-level supply chain with two decision variables (sales effort and inventory quantity), and numerical examples are given to illustrate the model and the solution process. Finally, by considering the retailer bears the effort cost together with the manufacturer, an improved revenue-sharing contract based on quantity discount policy is also discussed in this paper, which can coordinate the three-level supply.

The rest of this paper is organized as follows. Section

The supply chain studied in this paper is made up of one manufacturer

Three-level supply chain.

Suppose

Supply chain contracts often apply incentive measures to adjust the relationship among the members to coordinate supply chain and to make the entire profit of decentralized supply chain equal to that of centralized supply chain as much as possible. The goal of the analysis is to design the revenue-sharing contract so as to achieve channel coordination (maximum profit for the whole supply chain). Besides, it aims at analyzing whether and how the contract parameter can be modified so as to more evenly share the profit along the chain (win-win condition for the chain partners), guaranteeing channel coordination. So, the maximum profit of centralized supply chain should first be considered as the goal of revenue-sharing contract to coordinate supply chain. The profit function of centralized supply chain can be described as

Supposing

Supposing

Therefore, if revenue-sharing contract can coordinate supply chain, then formulae (

Giannoccaro and Pontrandolfo [

From (

Similarly, if only the distributor or the manufacturer bears the sales effort cost, the revenue-sharing contract cannot coordinate the supply chain. Then, we come to a conclusion: the traditional revenue-sharing contract cannot coordinate three-level supply chain with sales effort dependent demand.

In this paper, an improved revenue-sharing contract based on quantity discount policy is proposed to coordinate three-level supply chain when demand depends on effort.

From the discussion above, it can be seen that the optimal effort of the supply chain member under revenue-sharing contract is not equal to that of the centralized supply chain. The reasons lie in that the supply chain member only gets partial gains but bears all the effort cost

This problem can be described as follows: we implement the revenue-sharing contract based on quantity policy between the retailer and the distributor and the traditional revenue-sharing contract between the distributor and the manufacturer.

Suppose the distributor provides the retailer the revenue-sharing contract

Here,

In this condition, the profit function of retailer can be described as

According to the paper of Giannoccaro and Pontrandolfo [

From (

Because the distributor is in the middle of the supply chain, to maximize his profit, he will make his optimal order quantity equal to the optimal order quantity of retailer in perfect information symmetry condition; namely,

From (

Take (

From (

Therefore, if we implement the revenue-sharing contract based on quantity discount policy between the retailer and the distributor and the traditional revenue-sharing contract between the distributor and the manufacturer and the contract parameters which satisfy (

This problem can be described as follows: we implement both the revenue-sharing contract based on quantity discount policy between the retailer and the distributor, and between the distributor and the manufacturer.

Suppose the distributor provides the retailer the revenue-sharing contract

Here, we can also suppose that, when only the retail bears the effort cost, the ratio that his profit shares the profit of the whole supply chain is also

In this condition, the profit function of the distributor can be described as

Similarly, the optimal order quantity of the distributor should satisfy

Take (

From (

Therefore, if we implement the revenue-sharing contract based on quantity discount policy both between the retailer and the distributor and between the distributor and the manufacturer and the contract parameters which satisfy (

From the discussion mentioned above, we can come to a conclusion that the traditional revenue-sharing contract cannot coordinate three-level supply chain with sales effort dependent demand. However, the improved revenue-sharing contract based on quantity discount policy can coordinate three-level supply chain. And, in this condition, the optimal order quantity and optimal effort of retailer are equal to those of the centralized supply chain. Then, it needs to determine the optimal order quantity and the optimal effort to maximize the profit of supply chain, namely,

Suppose the market demand

When the market demand satisfies

So the profit function of supply chain can be described as

Given effort

From (

Then, the profit function of supply chain can be described as

From (

Then the optimal effort

Suppose a supply chain is made up of a retailer, a distributor, and a manufacturer, and the supply chain parameters are

Here, assume the relationship between demand and effort satisfies addition form, and

The revenue-sharing contract based on quantity discount policy.

From the discussion above, we know that the revenue-sharing contract based on quantity discount policy can coordinate the supply chain whether it is implemented in one or two transactions. According to the formulas mentioned above, it is easy to get the optimal effort, the optimal order quantity, and the profit of the whole supply chain. Here,

The traditional revenue-sharing contract.

Similarly, under the traditional revenue-sharing contract, the optimal effort and order quantity of the retailer and the profit of the whole supply chain are, respectively,

The decentralized supply chain (the wholesale price contract).

Similarly, under the traditional revenue-sharing contract, the optimal effort and order quantity of the retailer and the profit of the whole supply chain are, respectively,

Table

The parameters of supply chain in different modes with only retailer bearing effort cost.

Revenue-sharing contract based on quantity discount policy | Traditional revenue-sharing contract | Wholesale price contract | ||
---|---|---|---|---|

A | B | |||

Optimal effort |
27 | 27 | 14.85 | 16 |

Optimal order quantity |
119 | 119 | 107 | 91 |

Profit of the whole supply chain |
2272.5 | 2272.5 | 2202.7 | 2137 |

Table

This problem can be described as follows: we implement the revenue-sharing contract based on quantity policy between the manufacturer and the distributor and the traditional revenue-sharing contract between the distributor and the retailer.

Supposing the manufacturer provides the distributor the revenue-sharing contract

Here,

Taking (

According to the paper of Giannoccaro and Pontrandolfo [

From (

Taking (

From (

Therefore, if we implement the revenue-sharing contract based on quantity discount policy between the retailer and the distributor and the traditional revenue-sharing contract between the distributor and the manufacturer and the contract parameters which satisfy (

Compared with the paper of Giannoccaro and Pontrandolfo [

This problem can be described as follows: we implement both the revenue-sharing contract based on quantity discount policy between the retailer and the distributor and between the distributor and the manufacturer.

Suppose the distributor provides the retailer the revenue-sharing contract

Taking (

Here, we also suppose that the ratio that his profit shares the profit of the whole supply chain is also

Taking (

From (

Taking (

From (

From (

Similarly, suppose the market demand

When the market demand satisfies

So the profit function of supply chain can be described as

Given effort

From (

Then, the profit function of supply chain can be described as

According to the supposition,

From (

The method to solve the expression of

Suppose a supply chain is made up of a retailer, a distributor, and a manufacturer, and the supply chain parameters are

Here, assume the relationship between demand and effort satisfies multiplication form, and

The revenue-sharing contract based on quantity discount policy.

From the discussion above, we know that the revenue-sharing contract based on quantity discount policy can coordinate the supply chain whether it is implemented in one or two transactions. According to the formulas mentioned above, it is easy to get the optimal effort of the manufacturer, the optimal order quantity of the retailer, and the profit of the whole supply chain. Here,

The traditional revenue-sharing contract.

Similarly, under the traditional revenue-sharing contract, the optimal effort of the manufacturer and order quantity of the retailer and the profit of the whole supply chain are, respectively,

The decentralized supply chain (the wholesale price contract).

Similarly, under the traditional revenue-sharing contract, the optimal effort of the manufacturer and the order quantity of the retailer and the profit of the whole supply chain are, respectively,

Table

The parameters of supply chain in different modes with only manufacturer bearing effort cost.

Revenue-sharing contract based on quantity discount policy | Traditional revenue-sharing contract | Wholesale price contract | ||
---|---|---|---|---|

A | B | |||

Optimal effort |
19.62 | 19.62 | 3.97 | 3.79 |

Optimal order quantity |
1674 | 1674 | 339 | 288 |

Profit of the whole supply chain |
19246.28 | 19246.28 | 7008.33 | 6544.36 |

Table

Suppose the effort cost that the retailer bears is

In this condition, we find that the traditional revenue-sharing contract fails to coordinate the supply chain whether it is implemented in one transaction phase or in two transaction phases of the three-level supply chain. The reason lies in that the distributor does not bear the effort cost, but he can get partial profit of the whole supply chain, which is unfair for the retailer and the manufacturer. So the effort level of the retailer and the manufacturer will be lower than the effort level of the centralized supply chain. Now, the following discusses how to design the improved revenue-sharing implemented in two transaction phases to coordinate the supply chain.

Suppose the distributor provides the retailer the revenue-sharing contract

If the improved revenue-sharing contract can coordinate the supply chain, the optimal effort level

From (

Taking (

We find that (

Therefore, if we implement the revenue-sharing contract based on quantity discount policy among the supply chain members and the contract parameters which satisfy (

The method to determine the optimal order quantity

The traditional revenue-sharing contract cannot coordinate three-level supply chain with sales effort dependent demand. The paper proposes an improved revenue-sharing contract based on quantity discount policy, which can be implemented in one transaction or two transactions of three-level supply chain, to coordinate the supply chain. The paper also shows that the profit of the supply chain members depends on the value of the contract parameters which is determined by the status of the members in supply chain and their bargaining power. It also gave the method to determine the optimal order quantity and the optimal effort, which can provide the decision makers of supply chain with decision support. But it also should be noticed that this research is carried out in the symmetrical information condition. So the next step is to carry out the research in the asymmetric information condition.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This research was supported by the Ministry of Education of China: Grant-in-aid for Humanity and social Science Research (no. 10YJC630188) and the Fundamental Research Funds for the Central Universities (nos. 2012B13914 and 2012B13814).