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According to the manufacturer-leading dual-channel supply chain return problem, a linear demand function considering the change rate of product interaction between the two channels and the change rate of market demand on the return price was established. Under the premise of no cross-return, this paper analyzes the changes of the optimal profit value of the manufacturer, retailer, and supply chain of the dual-channel supply chain in the context of centralized and decentralized decision-making and through the establishment of the price discount decision model and compensation strategy to coordinate the whole supply chain profit. This paper has shown that the use of the price discount decision model and compensation policy model could make the whole supply chain profit optimum value in decentralized decision-making situations equal to profit optimum value in the centralized decision-making situations, and price discount model could make manufacturers better to maximize profit considering the same return scenario, and that compensation policy model could be more helpful to maximize profits for retailers.

With the acceleration of commodity informationization, many e-commerce platforms (Taobao, Jingdong, Vipshop and Dangdang) have launched “shopping carnival” and other marketing activities, which not only make the number of goods purchased online greatly increase but also bring into the public eye a large number of intractable return problems arising from transaction activities. Influenced by information asymmetry of commodity transaction, subjective factors of consumers, distribution and transportation of commodities, etc., the return rate of goods purchased online keeps rising. Return processing has become one of the most important links in enterprise operation management. Scholars at home and abroad have carried out a lot of relevant research studies in order to improve the efficiency of enterprise operation management.

According to the dominant position of supply chain members in the supply chain, domestic and foreign scholars study the return problem from two main bodies: manufacturer and retailer. As for the manufacturer-led supply chain, Mukhopadhyay and Setaputra [

In response to the return policies, channels, and other issues; Zaarour et al. [

Melachrinoudis and Png [

The research of the above scholars focused on the coordination of single-channel and dual-channel returns by establishing a model to calculate the optimal order quantity and return quantity, but they did not conduct a specific study on return profit. This paper mainly studies the return decision problem of the manufacturer-led dual-channel supply chain and establishes two return decision models of price discount and compensation strategy, respectively. By analyzing and demonstrating the optimal value changes of each decision variable of the two models, the optimal decision application model is obtained to improve the overall profit and decision effect of the dual-channel supply chain.

The manufacturer will distribute the goods after receiving the supply from the supplier, and its structure is shown in Figure

Return structure diagram of manufacturer’s dominant dual-channel supply chain.

For the convenience of model calculation, all symbols and meanings referenced in this paper are shown in Table

Model symbol description and meaning.

Symbol | Symbol description and interpretation |
---|---|

Product purchase loyalty coefficient of offline retail channel customers | |

1− | Product purchase loyalty coefficient of online direct sales channel customers |

Potential market demand | |

_{r} | Retailer’s sales prices in the offline retail channels |

_{d} | Manufacturer’s sales prices in the online direct marketing channels |

The change rate of product interaction between two channels | |

The change rate of dual-channel market demand with product return price | |

_{r} | Demand for products from offline retail channels |

_{d} | Customer demand for products of online direct marketing channels |

_{r} | Retailer’s profit |

_{d} | Manufacturer’s profit |

Wholesale price of products from the manufacturer to the retailer | |

Superscript | Price discount contract model |

The manufacturer’s unit cost of production | |

_{r} | Return prices for offline retail channels |

_{d} | Return prices for direct online sales channels |

_{r} | Total return volume of offline retail channels |

_{d} | Total return volume of online direct sales channel |

Basic return quantity of two channels | |

Ψ | The rate of change in product return volume due to changes in return prices in online channels |

The unit salvage value of the returned product | |

Superscript | Optimal case |

Superscript | Centralized decision model |

Superscript | Decentralized decision model |

_{T} | Total profit of the supply chain |

Superscript^{B} | Compensation strategy model |

It is assumed that the demand function of both online and offline channels is a linear relation function that only considers the influence of sales price and return price. Moreover, the quantity demanded is inversely proportional to the commodity price of the channel and is directly proportional to the return price of the channel. For the convenience of calculation, set

Since the convenience of offline return is relatively high, it is assumed that the return quantity is the base value; then, the return function of the offline retail channel is

The return of online direct sales channels is affected by a variety of factors. Due to consumers’ personal self-interest, assuming that there is a certain amount of return and there is a positive correlation with the online return price, the return function of the online direct sales channel is expressed as

According to the calculation method of profit, it can be concluded that

The total profit of the supply chain is the sum of the retailer’s profit and the manufacturer’s profit, which is expressed as

Centralized decision-making means that online and offline channels cooperate to return goods and jointly formulate return policies to achieve the goal of maximizing the overall profit of the supply chain. The decision model of centralized return is as follows:

The Hessian matrix of formula (

In formula (

By calculating the first derivative of

The optimal demand of retailers and manufacturers can be obtained by substituting formula (

By substituting formulas (

In formulas (

To simplify the expression, let

In the decentralized decision-making scenario, the dual channels of the supply chain form an antagonistic relationship, and retailers and manufacturers pursue profit maximization, respectively, in the competitive market, resulting in a fragmented situation. In this paper, the manufacturer is regarded as the market leader, and a Stackelberg game model is used to solve the problem. In the decentralized scenario, the two-channel supply chain return model is as follows:

Retailer’s profit function expression:

Manufacturer’s profit function expression:

The second stage of the game is to maximize retailers’ profits. The Hessian matrix of formula (

Substituting formula (

Formula (

By substituting equation (

First, substitute formula (

By substituting formula (

By substituting formulas (

Under the decentralized decision scenario, the overall optimal profit of the supply chain is

Comparing formulas (

In the manufacturer-led supply chain, it is assumed that the manufacturer pays the appropriate wholesale price to the retailer to promote the retailer’s sales to reach a win-win situation. The function of the wholesale price contract is as follows:

In formula (

Similarly, the optimal sales price and return price of retailers and manufacturers can be obtained by the Stackelberg game according to the decentralized decision model:

Let

Substituting formula (

By substituting formulas (

The overall optimal profit of the supply chain is

It can be seen from formula (

In the dual-channel supply chain environment, manufacturers have all the online and offline customers, occupying the absolute dominant position in the market. In order to coordinate the interests of dual-channel members, a compensation strategy model is established. In order to strengthen the cooperation between the two sides, the manufacturer compensates the retailer with the order from the direct online channel according to the proportion of

Similarly, by using the Stackelberg game to solve the decentralized decision model, the optimal sales price of the retailer can be obtained:

Let

By using the method of maximizing profits based on decentralized decision-making, formula (

The optimal sales, wholesale, and return prices obtained from formulas (

Under the compensation strategy, the overall optimal profit of the supply chain is

According to formula (

The relevant parameters are set as follows: the potential market demand

The optimal profit when

0.1 | 6.92 | 1.84 | −1.36 | 0.48 | 0.98 | 5.94 | 6.92 | 1.09 | 5.83 | 6.92 |

0.2 | 7.07 | 6.49 | −0.58 | 5.91 | 1.17 | 5.90 | 7.07 | 1.78 | 5.29 | 7.07 |

0.3 | 7.23 | 5.03 | −0.37 | 4.66 | 1.51 | 5.72 | 7.23 | 2.50 | 4.73 | 7.23 |

0.4 | 7.39 | 3.86 | −0.27 | 3.59 | 1.99 | 5.40 | 7.39 | 3.26 | 4.13 | 7.39 |

0.5 | 7.54 | 3.21 | −0.22 | 2.99 | 2.62 | 4.92 | 7.54 | 4.05 | 3.49 | 7.54 |

0.6 | 7.71 | 2.80 | −0.18 | 2.62 | 3.43 | 4.28 | 7.71 | 4.88 | 2.83 | 7.71 |

0.7 | 7.87 | 2.51 | −0.15 | 2.36 | 4.41 | 3.46 | 7.87 | 5.73 | 2.13 | 7.87 |

0.8 | 8.03 | 2.31 | −0.13 | 2.18 | 5.58 | 2.45 | 8.03 | 6.63 | 1.40 | 8.03 |

The optimal profit when

0.1 | 12.60 | 2.17 | −1.48 | 0.69 | 6.08 | 6.52 | 12.60 | 6.78 | 5.82 | 12.60 |

0.2 | 9.50 | 9.09 | −6.14 | 2.95 | 4.03 | 5.47 | 9.50 | 5.18 | 4.32 | 9.50 |

0.3 | 8.40 | 5.66 | −3.81 | 1.85 | 3.25 | 5.15 | 8.40 | 4.55 | 3.85 | 8.40 |

0.4 | 7.85 | 4.10 | −2.75 | 1.35 | 2.85 | 5.00 | 7.85 | 4.23 | 3.62 | 7.85 |

0.5 | 7.54 | 3.21 | −2.15 | 1.06 | 2.62 | 4.92 | 7.54 | 4.05 | 3.49 | 7.54 |

0.6 | 7.36 | 2.63 | −1.76 | 0.87 | 2.48 | 4.88 | 7.36 | 3.96 | 3.40 | 7.36 |

0.7 | 7.26 | 2.23 | −1.49 | 0.74 | 2.40 | 4.86 | 7.26 | 3.92 | 3.34 | 7.26 |

0.8 | 7.21 | 1.93 | −1.29 | 0.64 | 2.34 | 4.87 | 7.21 | 3.92 | 3.29 | 7.21 |

The change diagram of the optimal profit value when

The change diagram of the optimal profit value when

The change diagram of the optimal profit value when

In Figures

Set

As can be seen from Table

Figure

Figure

Figure

Set

As can be seen from Table

Figure

Figure

Figure

Set

The optimal profit when

5.0 | 7.50 | 3.21 | −2.15 | 1.06 | 2.60 | 4.90 | 7.50 | 4.00 | 3.50 | 7.50 |

5.5 | 7.49 | 3.21 | −2.15 | 1.06 | 2.59 | 4.90 | 7.49 | 3.99 | 3.50 | 7.49 |

6.0 | 7.48 | 3.21 | −2.15 | 1.06 | 2.59 | 4.89 | 7.48 | 3.98 | 3.50 | 7.48 |

6.5 | 7.48 | 3.21 | −2.15 | 1.06 | 2.59 | 4.89 | 7.48 | 3.98 | 3.50 | 7.48 |

7.0 | 7.48 | 3.21 | −2.16 | 1.05 | 2.59 | 4.89 | 7.48 | 3.98 | 3.50 | 7.48 |

7.5 | 7.47 | 3.21 | −2.16 | 1.05 | 2.58 | 4.89 | 7.47 | 3.98 | 3.50 | 7.47 |

8.0 | 7.47 | 3.22 | −2.16 | 1.06 | 2.58 | 4.89 | 7.47 | 3.97 | 3.50 | 7.47 |

8.5 | 7.46 | 3.22 | −2.16 | 1.06 | 2.58 | 4.88 | 7.46 | 3.96 | 3.50 | 7.46 |

As can be seen from Table

Figure

Figure

Figure

Theoretical analysis was carried out for the two models, and the changes of the optimal profit value of the two models were analyzed when

By analyzing the data in Table

By analyzing the data in Table

By analyzing the data in Table

From Tables

By studying the return situation of a manufacturer-led dual-channel supply chain in a competitive market environment, considering the offline retail customers to purchase the product loyalty coefficient, dual channels influence each other between the product rate, the change rate of market demand to return price, and the rate at which the amount of return in an online channel changes with the return price and other factors, the price discount model and the compensation strategy model were established in order to coordinate the profits of manufacturers, retailers, and supply chain as a whole after return and make the profits maximize. Also the validity of the model should be confirmed through a numerical example and the method of chart analysis. The results show the following: (1) in the dual-channel supply chain environment, the profit of the centralized decision return model is larger than that of the decentralized decision return model. Profit coordination can be realized through the price discount model and compensation strategy model. The overall optimal profit of the supply chain in the decentralized decision-making scenario is equal to the overall optimal profit of the supply chain in the centralized decision-making scenario, which maximizes the profit of the dual-channel supply chain. (2) When the change rate of mutual influence between products of the dual-channel supply chain, the change rate of market demand on product return price, and the change rate of online direct sales channel’s return amount with return price are changed, the overall profit of retailers, manufacturers, and supply chain will be affected, and the former two are more affected than the latter. (3) When the conditions of a manufacturer-led dual-channel supply chain are the same, the price discount model is more favorable for manufacturers to maximize profits, while the compensation strategy model is more helpful for retailers to maximize profits.

This paper mainly applies price discount and compensation strategy to solve the return problem of the dual-channel supply chain and makes use of supply chain coordination decision-making to make the overall profit of the supply chain in the return scenario reach the optimal value. In the aspect of theory, it enriches supply chain decision theory and optimizes supply chain pricing decision. In the aspect of practice, it can be widely used to solve the pricing and profit coordination decision-making problem of the enterprise’s dual-channel supply chain operation mode, which has wide applicability and strong application value. When the market demand is random, the cross-return and dual-channel supply chain pricing decision under the big data environment need to be further studied.

Suppliers and retailers are rational decision-makers who make decisions based on the principle of revenue maximization. The parameters selected in this paper meet the above assumptions. And more abundant management inspiration could be obtained through numerical simulation.

The authors declare that there are no conflicts of interest.

This research was supported by the Natural Science Foundation of China (Grant no. 71662007), Guangxi Aviation Logistics Research Centre Project (Grant nos. 2017KFJJHKWL02 and 19KFJJHKWL06), the Natural Science Foundation of Guangxi (Grant no. 2018GXNSFAA281311), and Innovation Project of GUET Graduate Education (Grant no. 2020YCXS069). The authors thank all the references’ authors.