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

 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

Received  July 2021 Revised  January 2022 Early access April 2022

Fund Project: 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.

Citation: Chao Zhao, Jixiang Song. Coordination of dual-channel supply chain considering differential pricing and loss-aversion based on quality control. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022053
##### References:
 [1] A. Aslani and J. Heydari, Transshipment contract for coordination of a green dual-channel supply chain under channel disruption, J. Clean. Prod., 223 (2019), 596-609. [2] J. Chen, L. Liang, D. Q. Yao and S. Sun, Price and quality decisions in dual-channel supply chains, Eur. J. Oper. Res., 259 (2017), 935-948.  doi: 10.1016/j.ejor.2016.11.016. [3] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. [4] I. Dobos and K. Richter, A production/recycling model with quality consideration, Int. J. Prod. Econ., 104 (2006), 571-579. [5] H. Felfel, W. B. Yahia, O. Ayadi and F. Masmoudi, Stochastic multi-site supply chain planning in textile and apparel industry under demand and price uncertainties with risk aversion, Ann. Oper. Res., 271 (2018), 551-574.  doi: 10.1007/s10479-018-2980-2. [6] Z. Feng and C. Tan, Pricing, Green degree and coordination decisions in a green supply chain with loss aversion, Mathematics, 7 (2019), 239. [7] T. Feng, L. R. Keller and X. Zheng, Decision making in the newsvendor problem: A cross-national laboratory study, Omega, 39 (2011), 41-50. [8] M. Fisher and A. Raman, Reducing the cost of demand uncertainty through accurate response to early sales, Oper. Res., 44 (1996), 87-99. [9] B. Hu, C. Meng, D. Xu and Y. J. Son, Three-echelon supply chain coordination with a loss-averse retailer and revenue sharing contracts, Int. J. Prod. Econ., 179 (2016), 192-202. [10] F. Huang, J. He and J. Wang, Coordination of VMI supply chain with a loss-averse manufacturer under quality-dependency and marketing-dependency, J. Ind. Manag. Optim., 15 (2019), 1753.  doi: 10.3934/jimo.2018121. [11] D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, in Handbook of the fundamentals of financial decision making: Part I, World Scientific, 2013: 99-127. doi: 10.21236/ADA045771. [12] Q. H. Li and B. Li, Dual-channel supply chain equilibrium problems regarding retail services and fairness concerns, Appl. Math. Model, 40 (2016), 7349-7367.  doi: 10.1016/j.apm.2016.03.010. [13] C. Lin, W. S. Chow, C. N. Madu, C. H. Kuei and P. P. Yu, A structural equation model of supply chain quality management and organizational performance, Int. J. Prod. Econ., 96 (2005), 355-365. [14] Y. Z. Liu and Z. P. Fan, Supply chain coordination contract model considering loss aversion and quality level, Chinese J. Manage. Sci., 25 (2017), 65-77. [15] M. Liu, E. Cao and C. K. Salifou, Pricing strategies of a dual-channel supply chain with risk aversion, Transport. Res. E-Log., 90 (2016), 108-120. [16] W. Liu, M. Wang and D. Zhu, Service capacity procurement of logistics service supply chain with demand updating and loss-averse preference, Appl. Math. Model., 66 (2019), 486-507.  doi: 10.1016/j.apm.2018.09.020. [17] L. Ma, F. Liu, S. Li and H. Yan, Channel bargaining with risk-averse retailer, Int. J. Prod. Econ., 139 (2012), 155-167. [18] T. Maiti and B. C. Giri, A closed loop supply chain under retail price and product quality dependent demand, J. Manuf. Syst., 37 (2015), 624-637. [19] I. Mount, Clothing companies trying to find more direct paths to customers, The New York Times, (2013). [20] M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence, Manage. Sci., 46 (2000), 404-420. [21] H. Shi, Y. Liu and N. C. Petruzzi, Consumer Heterogeneity, Product Quality, and Distribution Channels, Manage. Sci., 59 (2013), 1162-1176. [22] C. Tang, H. Yang, E. Cao and K. K. Lai, Channel competition and coordination of a dual-channel supply chain with demand and cost disruptions, Appl. Econ., 50 (2018), 4999-5016. [23] A. A. Tsay and N. Agrawal, Channel conflict and coordination in the e-commerce age, Prod. Oper. Manag., 13 (2004), 93-110. [24] B. Vahdani, M. Zandieh and V. Roshanaei, A hybrid multi-stage predictive model for supply chain network collapse recovery analysis: a practical framework for effective supply chain network continuity management, Int. J. Prod. Res., 49 (2011), 2035-2060. [25] W. Xie, B. Chen, F. Huang and J. He, Coordination of a supply chain with a loss-averse retailer under supply uncertainty and marketing effort, J. Ind. Manag. Optim., 17 (2021), 3393.  doi: 10.3934/jimo.2020125. [26] G. Xie, W. Yue, S. Wang and K. K. Lai, Quality investment and price decision in a risk-averse supply chain, Eur. J. Oper. Res., 214 (2011), 403-410.  doi: 10.1016/j.ejor.2011.04.036. [27] X. Xu, C. K. Chan and A. Langevin, Coping with risk management and fill rate in the loss-averse newsvendor model, Int. J. Prod. Econ, 195 (2018), 296-310. [28] G. Xu, B. Dan, X. Zhang and C. Liu, Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contract, Int. J. Prod. Econ., 147 (2014), 171-179. [29] L. Xu, C. Wang and J. Zhao, Decision and coordination in the dual-channel supply chain considering cap-and-trade regulation, J. Clean. Prod., 197 (2018), 551-561. [30] N. Yan, X. He and Y. Liu, Financing the capital-constrained supply chain with loss aversion: supplier finance vs. supplier investment, Omega, 88 (2019), 162-178. [31] R. Yan and P. Zhi, Retail services and firm profit in a dual-channel market, J. Retail. Consum. Serv., 16 (2009), 306-314. [32] D. Yang and T. Xiao, Coordination of a supply chain with loss-averse consumers in service quality, Int. J. Prod. Res., 55 (2017), 3411-3430. [33] Z. Zhang, S. Liu and B. Niu, Coordination mechanism of dual-channel closed-loop supply chains considering product quality and return, J. Clean. Prod., 248 (2020), 119273. [34] C. Zhang, Y. Wang, Y. Liu and H. Wang, Coordination contracts for a dual-channel supply chain under capital constraints, J. Ind. Manag. Optim., 17 (2021), 1485.  doi: 10.3934/jimo.2020031. [35] X. Zhou, B. Xu, F. Xie and Y. Li, Research on quality decisions and coordination with reference effect in dual-channel supply chain, Sustainability, 12 (2020), 2296. [36] W. Zhuo, H. Yang, L. E. Cárdenas-Barrón and H. Wan, Loss-averse supply chain decisions with a capital constrained retailer, J. Ind. Manag. Optim., 17 (2021), 711.  doi: 10.3934/jimo.2019131.

show all references

##### References:
 [1] A. Aslani and J. Heydari, Transshipment contract for coordination of a green dual-channel supply chain under channel disruption, J. Clean. Prod., 223 (2019), 596-609. [2] J. Chen, L. Liang, D. Q. Yao and S. Sun, Price and quality decisions in dual-channel supply chains, Eur. J. Oper. Res., 259 (2017), 935-948.  doi: 10.1016/j.ejor.2016.11.016. [3] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. [4] I. Dobos and K. Richter, A production/recycling model with quality consideration, Int. J. Prod. Econ., 104 (2006), 571-579. [5] H. Felfel, W. B. Yahia, O. Ayadi and F. Masmoudi, Stochastic multi-site supply chain planning in textile and apparel industry under demand and price uncertainties with risk aversion, Ann. Oper. Res., 271 (2018), 551-574.  doi: 10.1007/s10479-018-2980-2. [6] Z. Feng and C. Tan, Pricing, Green degree and coordination decisions in a green supply chain with loss aversion, Mathematics, 7 (2019), 239. [7] T. Feng, L. R. Keller and X. Zheng, Decision making in the newsvendor problem: A cross-national laboratory study, Omega, 39 (2011), 41-50. [8] M. Fisher and A. Raman, Reducing the cost of demand uncertainty through accurate response to early sales, Oper. Res., 44 (1996), 87-99. [9] B. Hu, C. Meng, D. Xu and Y. J. Son, Three-echelon supply chain coordination with a loss-averse retailer and revenue sharing contracts, Int. J. Prod. Econ., 179 (2016), 192-202. [10] F. Huang, J. He and J. Wang, Coordination of VMI supply chain with a loss-averse manufacturer under quality-dependency and marketing-dependency, J. Ind. Manag. Optim., 15 (2019), 1753.  doi: 10.3934/jimo.2018121. [11] D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, in Handbook of the fundamentals of financial decision making: Part I, World Scientific, 2013: 99-127. doi: 10.21236/ADA045771. [12] Q. H. Li and B. Li, Dual-channel supply chain equilibrium problems regarding retail services and fairness concerns, Appl. Math. Model, 40 (2016), 7349-7367.  doi: 10.1016/j.apm.2016.03.010. [13] C. Lin, W. S. Chow, C. N. Madu, C. H. Kuei and P. P. Yu, A structural equation model of supply chain quality management and organizational performance, Int. J. Prod. Econ., 96 (2005), 355-365. [14] Y. Z. Liu and Z. P. Fan, Supply chain coordination contract model considering loss aversion and quality level, Chinese J. Manage. Sci., 25 (2017), 65-77. [15] M. Liu, E. Cao and C. K. Salifou, Pricing strategies of a dual-channel supply chain with risk aversion, Transport. Res. E-Log., 90 (2016), 108-120. [16] W. Liu, M. Wang and D. Zhu, Service capacity procurement of logistics service supply chain with demand updating and loss-averse preference, Appl. Math. Model., 66 (2019), 486-507.  doi: 10.1016/j.apm.2018.09.020. [17] L. Ma, F. Liu, S. Li and H. Yan, Channel bargaining with risk-averse retailer, Int. J. Prod. Econ., 139 (2012), 155-167. [18] T. Maiti and B. C. Giri, A closed loop supply chain under retail price and product quality dependent demand, J. Manuf. Syst., 37 (2015), 624-637. [19] I. Mount, Clothing companies trying to find more direct paths to customers, The New York Times, (2013). [20] M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence, Manage. Sci., 46 (2000), 404-420. [21] H. Shi, Y. Liu and N. C. Petruzzi, Consumer Heterogeneity, Product Quality, and Distribution Channels, Manage. Sci., 59 (2013), 1162-1176. [22] C. Tang, H. Yang, E. Cao and K. K. Lai, Channel competition and coordination of a dual-channel supply chain with demand and cost disruptions, Appl. Econ., 50 (2018), 4999-5016. [23] A. A. Tsay and N. Agrawal, Channel conflict and coordination in the e-commerce age, Prod. Oper. Manag., 13 (2004), 93-110. [24] B. Vahdani, M. Zandieh and V. Roshanaei, A hybrid multi-stage predictive model for supply chain network collapse recovery analysis: a practical framework for effective supply chain network continuity management, Int. J. Prod. Res., 49 (2011), 2035-2060. [25] W. Xie, B. Chen, F. Huang and J. He, Coordination of a supply chain with a loss-averse retailer under supply uncertainty and marketing effort, J. Ind. Manag. Optim., 17 (2021), 3393.  doi: 10.3934/jimo.2020125. [26] G. Xie, W. Yue, S. Wang and K. K. Lai, Quality investment and price decision in a risk-averse supply chain, Eur. J. Oper. Res., 214 (2011), 403-410.  doi: 10.1016/j.ejor.2011.04.036. [27] X. Xu, C. K. Chan and A. Langevin, Coping with risk management and fill rate in the loss-averse newsvendor model, Int. J. Prod. Econ, 195 (2018), 296-310. [28] G. Xu, B. Dan, X. Zhang and C. Liu, Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contract, Int. J. Prod. Econ., 147 (2014), 171-179. [29] L. Xu, C. Wang and J. Zhao, Decision and coordination in the dual-channel supply chain considering cap-and-trade regulation, J. Clean. Prod., 197 (2018), 551-561. [30] N. Yan, X. He and Y. Liu, Financing the capital-constrained supply chain with loss aversion: supplier finance vs. supplier investment, Omega, 88 (2019), 162-178. [31] R. Yan and P. Zhi, Retail services and firm profit in a dual-channel market, J. Retail. Consum. Serv., 16 (2009), 306-314. [32] D. Yang and T. Xiao, Coordination of a supply chain with loss-averse consumers in service quality, Int. J. Prod. Res., 55 (2017), 3411-3430. [33] Z. Zhang, S. Liu and B. Niu, Coordination mechanism of dual-channel closed-loop supply chains considering product quality and return, J. Clean. Prod., 248 (2020), 119273. [34] C. Zhang, Y. Wang, Y. Liu and H. Wang, Coordination contracts for a dual-channel supply chain under capital constraints, J. Ind. Manag. Optim., 17 (2021), 1485.  doi: 10.3934/jimo.2020031. [35] X. Zhou, B. Xu, F. Xie and Y. Li, Research on quality decisions and coordination with reference effect in dual-channel supply chain, Sustainability, 12 (2020), 2296. [36] W. Zhuo, H. Yang, L. E. Cárdenas-Barrón and H. Wan, Loss-averse supply chain decisions with a capital constrained retailer, J. Ind. Manag. Optim., 17 (2021), 711.  doi: 10.3934/jimo.2019131.
Relationship between $\lambda$ and ${e^*}$
Relationship between $p$ and ${e^*}$
Relationship between $s$ and ${e^*}$
Relationship between $s$ and $\Delta {p^*}$
Relationship between $\lambda$ and utility
Relationship between ${p_c}$ and utility
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 √ √ √ √ √ √
 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 √ √ √ √ √ √
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
 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
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
 $\left( {w, \varepsilon } \right)$ $\Delta p$ $e$ $EU\left( {{\pi _R}} \right)$ $EU\left( {{\pi _M}} \right)$ $EU\left( \pi \right)$ 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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