JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (11): 104-115.doi: 10.6040/j.issn.1671-9352.0.2022.213

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Equilibrium of dual-channel supply chain considering manufacturer online referral under different power structures

Tingting GUO1(),Zhengxiang WU2,*()   

  1. 1. School of Business Administration, Liaoning Technical University, Huludao 125105, Liaoning, China
    2. School of Marketing Management, Liaoning Technical University, Huludao 125105, Liaoning, China
  • Received:2022-04-05 Online:2023-11-20 Published:2023-11-07
  • Contact: Zhengxiang WU E-mail:guotingting8909@yeah.net;wuzhengxiang89@126.com

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Abstract:

Based on Stackelberg and Bertrand game theory, the optimization models of dual-channel supply chain with manufacturer online referral under three power structures are established, and the dual-channel supply chain equilibrium in different situations is studied. Through comparative analysis of the dual-channel supply chain equilibrium, the issue of whether the manufacturer and the physical retailer can reach an agreement on the selection of online referral method is discussed. The effect of the online referral method on product pricing, total market demand of the channel, and the first-mover advantage of the manufacturer or the physical retailer act as the supply chain leader are analyzed. The results show that the manufacturer and the physical retailer have the same preference for online referral method. Online referral method will not change the online retail price of the product, but it will change the wholesale price and the physical retail price. In addition, when the manufacturer promotes both the online direct channel and the physical retail channel, the total market demand of the online direct channel will be reduced, the total market demand of the physical retail channel will be increased. The online referral method will not affect the first-mover advantage when manufacturer or physical retailer act as supply chain leader.

Key words: dual-channel supply chain, online referral, power structure

CLC Number: 

  • F274

Table 1

Total market demand of each channel under different online referral methods"

在线推介方式 渠道类型
实体零售渠道 网络直销渠道
仅推介网络直销渠道 $\frac{(1-\delta) \alpha_{\mathrm{t}}-p_{\mathrm{r}}+\delta p_{\mathrm{e}}}{1-\delta^{2}}$ $\frac{(1-\delta) \alpha_{\mathrm{t}}-p_{\mathrm{e}}+\delta p_{\mathrm{r}}}{1-\delta^{2}}+\left(\alpha_{\mathrm{r}}-p_{\mathrm{e}}\right)$
同时推介实体零售渠道和网络直销渠道 $\frac{(1-\delta) \alpha_{\mathrm{t}}-p_{\mathrm{r}}+\delta p_{\mathrm{e}}}{1-\delta^{2}}+\frac{(1-\delta) \alpha_{\mathrm{r}}-p_{\mathrm{r}}+\delta p_{\mathrm{e}}}{1-\delta^{2}}$ $\frac{(1-\delta) \alpha_{\mathrm{t}}-p_{\mathrm{e}}+\delta p_{\mathrm{r}}}{1-\delta^2}+\frac{(1-\delta) \alpha_{\mathrm{r}}-p_{\mathrm{e}}+\delta p_{\mathrm{r}}}{1-\delta^2}$

Table 2

Equilibrium results of dual-channel supply chain dominated by manufacturer"

均衡结果 在线推介方式
仅推介网络直销渠道(i=d) 同时推介实体零售渠道和网络直销渠道(i=s)
$w^{\mathrm{M} i *}$ $\frac{\delta \alpha_{\mathrm{r}}+(2-\delta) \alpha_{\mathrm{t}}}{4} $$\frac{\alpha_{\mathrm{r}}+\alpha_t}{4}$
$p_{\mathrm{e}}^{\mathrm{M} i *}$ $\frac{\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}}{4} $$\frac{\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}}{4}$
$p_{\mathrm{r}}^{\mathrm{M} i *}$ $\frac{\delta \alpha_{\mathrm{r}}+(3-2 \delta) \alpha_{\mathrm{t}}}{4} $ $\frac{(3-\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)}{8} $
$D_{\mathrm{e}}^{\mathrm{M} i *}$ $\frac{2(1+\delta) \alpha_{\mathrm{r}}+(2+\delta) \alpha_{\mathrm{t}}}{4(1+\delta)} $ $\frac{(2+\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)}{4(1+\delta)}$
$D_{\mathrm{r}}^{\mathrm{M} i *}$ $\frac{\alpha_{\mathrm{t}}}{4(1+\delta)} $ $\frac{\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}}{4(1+\delta)} $
$\pi_{\mathrm{m}}^{\mathrm{M} i *}$ $\frac{(1+\delta) \alpha_{\mathrm{r}}^2+2(1+\delta) \alpha_{\mathrm{r}} \alpha_{\mathrm{t}}+2 \alpha_{\mathrm{t}}^2}{8(1+\delta)} $ $\frac{(3+\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)^2}{16(1+\delta)}$
$\pi_{\mathrm{r}}^{\mathrm{M} i *}$ $\frac{(1-\delta) \alpha_{\mathrm{t}}^2}{16(1+\delta)}$ $\frac{(1-\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)^2}{32(1+\delta)}$

Table 3

Equilibrium results of dual-channel supply chain dominated by physical retailer"

均衡结果 在线推介方式
仅推介网络直销渠道(i=d) 同时推介实体零售渠道和网络直销渠道(i=s)
$w^{\mathrm{R} i *}$ $\frac{\delta \alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}}{4} $ $\frac{(1+\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)}{8} $
$p_{\mathrm{e}}^{\mathrm{R} i *}$ $\frac{\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}}{4}$ $\frac{\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}}{4} $
$p_{\mathrm{r}}^{\mathrm{R} i *}$ $\frac{\delta \alpha_{\mathrm{r}}+(3-2 \delta) \alpha_{\mathrm{t}}}{4} $ $\frac{(3-\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)}{8}$
$D_{\mathrm{e}}^{\mathrm{R} i *}$ $\frac{2(1+\delta) \alpha_{\mathrm{r}}+(2+\delta) \alpha_{\mathrm{t}}}{4(1+\delta)} $ $\frac{(2+\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)}{4(1+\delta)} $
$D_{\mathrm{r}}^{\mathrm{R} i *}$ $\frac{\alpha_{\mathrm{t}}}{4(1+\delta)} $ $\frac{\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}}{4(1+\delta)} $
$\pi_{\mathrm{m}}^{\mathrm{R} i *}$ $\frac{2(1+\delta) \alpha_{\mathrm{r}}^2+4(1+\delta) \alpha_{\mathrm{r}} \alpha_{\mathrm{t}}+(3+\delta) \alpha_{\mathrm{t}}^2}{16(1+\delta)} $ $\frac{(5+3 \delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)^2}{32(1+\delta)} $
$\pi_{\mathrm{r}}^{\mathrm{R} i *}$ $\frac{(1-\delta) \alpha_{\mathrm{t}}^2}{8(1+\delta)}$ $\frac{(1-\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)^2}{16(1+\delta)}$

Table 4

Equilibrium results of dual-channel supply chain under the condition that manufacturer and physical retailer with balance channel power"

均衡结果 在线推介方式
仅推介网络直销渠道(i=d) 同时推介实体零售渠道和网络直销渠道(i=s)
$w^{\mathrm{N} i *}$ $\frac{3 \delta \alpha_{\mathrm{r}}+(4-\delta) \alpha_{\mathrm{t}}}{12}$ $\frac{(2+\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)}{12}$
$p_{\mathrm{e}}^{\mathrm{N} i *}$ $\frac{\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}}{4}$ $\frac{\alpha_{\mathrm{r}}+\alpha_t}{4} $
$p_{\mathrm{r}}^{\mathrm{N} i *}$ $\frac{3 \delta \alpha_{\mathrm{r}}+(8-5 \delta) \alpha_{\mathrm{t}}}{12}$ $\frac{(4-\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)}{12} $
$D_{\mathrm{e}}^{\mathrm{N} i *}$ $\frac{3(1+\delta) \alpha_{\mathrm{r}}+(3+\delta) \alpha_{\mathrm{t}}}{6(1+\delta)}$ $\frac{(3+\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)}{6(1+\delta)} $
$D_{\mathrm{r}}^{\mathrm{N}i*}$ $\frac{\alpha_{\mathrm{t}}}{3(1+\delta)}$ $\frac{\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}}{3(1+\delta)} $
$\pi_{\mathrm{m}}^{\mathrm{N} i *}$ $\frac{9(1+\delta) \alpha_{\mathrm{r}}^2+18(1+\delta) \alpha_{\mathrm{r}} \alpha_{\mathrm{t}}+(17+\delta) \alpha_{\mathrm{t}}^2}{72(1+\delta)}$ $\frac{(13+5 \delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)^2}{72(1+\delta)}$
$\pi_{\mathrm{r}}^{\mathrm{N} i *}$ $\frac{(1-\delta) \alpha_{\mathrm{t}}^2}{9(1+\delta)}$ $\frac{(1-\delta)\left(\alpha_{\mathrm{r}}+\alpha_{\mathrm{t}}\right)^2}{18(1+\delta)}$

Table 5

Corresponding equilibrium decision of two online recommendation methods under different power structures"

在线推介方式 变量 制造商主导(j=M) 实体零售商主导(j=R) 制造商与实体零售商权力平衡(j=N)
仅推介网络直销渠道 wjd* 53 43 46
pejd* 55 55 55
prjd* 63 63 60
Dejd* 101 101 98
Drjd* 16 16 21
πmjd* 6 363 6 206 6 328
πrjd* 156 313 278
同时推介实体零售渠道和网络直销渠道 wjs* 55 44 48
pejs* 55 55 55
prjs* 66 66 62
Dejs* 89 89 83
Drjs* 34 34 46
πmjs* 6 806 6 428 6 722
πrjs* 378 756 672
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