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

Chao Zhao; Jixiang Song

doi:10.3934/jimo.2022053

Article Contents

2023, Volume 19, Issue 4: 2507-2527. Doi: 10.3934/jimo.2022053

This issue Previous Article Research on corporate social responsibility and product quality in an outsourcing supply chain Next Article

$ \alpha $

-robust portfolio optimization problem under the distribution uncertainty

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

Chao Zhao^1, , and
Jixiang Song^2,3,

1.
School of Management, Tianjin University of Commerce, Tianjin 300134, China
2.
School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
3.
Key Laboratory for Mechanics in Fluid-Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100049, China

^*Corresponding author: Chao Zhao
^*Corresponding author: Chao Zhao

Received: July 2021

Revised: January 2022

Early access: April 2022

Published: April 2023

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

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Abstract

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.

Keywords:

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

Citation:

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

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

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

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

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Figure 5. Relationship between $ \lambda $ and utility

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

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Table 1. Comparison of contributions from different relevant literature

Literature	Dual-channel	Coordination	Loss-aversion		Quality		Differential pricing
Literature	Dual-channel	Coordination	One player	Two players	Quality decision	Quality control	Differential pricing
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	√	√		√	√	√	√

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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

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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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