Article Contents
Article Contents

Coordination of dual-channel supply chain considering differential pricing and loss-aversion based on quality control

• *Corresponding author: Chao Zhao

The first author is supported by the 2021 scientific research plan project of Tianjin Municipal Commission of Education grant 2021SK146

• This paper investigates the coordination of dual-channel supply chain under quality control with a loss-averse manufacturer and a loss-averse retailer. Facing various uncertain factors, supply chain members tend to show loss aversion, which makes their actual decision deviate from the optimal decision without considering loss aversion. Therefore, the loss aversion effect function is applied to characterize the loss aversion of members. Besides, under quality control, utility model is constructed under centralized decision and decentralized decision, and the optimal decisions are solved according to the principle of utility maximization. Further, by analyzing and comparing the optimal strategies of two typical decision structures, the wholesale price and the quality cost-sharing contract is designed to coordinate the dual-channel supply chain, and the contract is proved to be valid. Finally, the impacts of the parameters change on the optimal quality level and order price are presented through the sensitivity analysis. It is found that quality control strategy and loss aversion degree of supply chain members affect the setting of coordination contract parameters and utility of supply chain. Moreover, the coordination of dual-channel supply chain is conducive to improving the level of product quality and reducing the price difference between channels.

Mathematics Subject Classification: Primary: 90B06; Secondary: 91A35.

 Citation:

• Figure 1.  Relationship between $\lambda$ and ${e^*}$

Figure 2.  Relationship between $p$ and ${e^*}$

Figure 3.  Relationship between $s$ and ${e^*}$

Figure 4.  Relationship between $s$ and $\Delta {p^*}$

Figure 5.  Relationship between $\lambda$ and utility

Figure 6.  Relationship between ${p_c}$ and utility

Table 1.  Comparison of contributions from different relevant literature

 Literature Dual-channel Coordination Loss-aversion Quality Differential pricing One player Two players Quality decision Quality control Zhou and Xu [35] √ √ √ Huang and He [10] √ √ Zhang et al. [34] √ √ √ √ Xie and Chen [25] √ √ Zhuo et al. [36] √ √ Liu and Fan [14] √ √ √ This paper √ √ √ √ √ √

Table 2.  Notations defined

 Parameter Definition $w$ the wholesale price $p$ online selling price $\Delta p$ the price difference between the online channel and offline channel $c$ unit production cost $q$ order size of the retailer for the new product ${c_r}$ out of stock cost per unit shortage of the retailer ${c_d}$ out of stock cost per unit shortage of the manufacturer ${p_c}$ qualified products rate ${c_i}$ inspection cost ${c_c}$ unit compensation amount for non-conforming products $m$ retailer's income from the disposal of non-conforming products $v$ retailer's income from the disposal of unsalable products $e$ the product quality level ${c_e}$ quality effort cost ${x_r}$ stochastic demand of the product in the traditional channel ${x_d}$ stochastic demand of the product in the network channel ${\pi _M}$ profit of the manufacturer under risk-neutral ${\pi _R}$ profit of the retailer under risk-neutral $E{\pi _M}$ expected profit of the manufacturer under risk-neutral $E{\pi _R}$ expected profit of the retailer under risk-neutral $EU\left( {{\pi _M}} \right)$ the utility of the manufacturer $EU\left( {{\pi _R}} \right)$ the utility of the retailer

Table 3.  Comparison of different decision-making cases

 $\left( {w, \varepsilon } \right)$ $\Delta p$ $e$ $EU\left( {{\pi _R}} \right)$ $EU\left( {{\pi _M}} \right)$ $EU\left( \pi \right)$ Centralized decision — -32.00 13.00 — — 1564.00 Decentralized decision (30, —) 13.25 11.07 667.20 150.10 817.31 Introduction contract (15.84, 0.30) -32.00 13.00 1392.50 171.50 1564.00
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Tables(3)