# American Institute of Mathematical Sciences

July  2020, 16(4): 1943-1965. doi: 10.3934/jimo.2019037

## Impact of risk aversion on two-echelon supply chain systems with carbon emission reduction constraints

 1 Institute of Operations Research, School of Management, Qufu Normal University, Rizhao, Shandong 276826, China 2 Department of Health Services and Outcomes Research, National Healthcare Group, 138543, Singapore

* Corresponding author

Received  June 2018 Revised  November 2018 Published  May 2019

Fund Project: The research is partly supported by the National Natural Science Foundation of China under grant 71771138, Humanities and Social Sciences Youth Foundation of Ministry of Education of China under grant 17YJC630004, Natural Science Foundation of Shandong Province, China under Grant ZR2017MG009, and Special Foundation for Taishan Scholars of Shandong Province, China under Grant tsqn201812061

This study examines a two-echelon supply chain consisting of two competing manufacturers and one retailer that has the channel power, in which one manufacturer is engaged in sustainable technology to curb carbon emissions under the cap-and-trade regulation while the other one operates its business as usual in a traditional manner. Two different supply chain configurations concerning risk attributes of the agents are considered, that is, (ⅰ) two risk-neutral manufacturers with one risk-averse retailer; and (ⅱ) two risk-averse manufacturers with one risk-neutral retailer. Under the mean-variance framework, we use a retailer-leader game optimization approach to study operational decisions of these two systems. Specifically, optimal operational decisions of the agents are established in closed-form expressions and the corresponding profits and carbon emissions are assessed. Numerical experiments are conducted to analyze the impact of risk aversion of the underlying supply chains. The results show that each risk-averse agent would benefit from a low scale risk aversion. Further, low carbon emissions could be attainable if risk aversion scale of the underlying manufacturer is small or moderate. In addition, the carbon emissions might increase when risk aversion of the traditional manufacturer or the retailer is of small or moderate scale.

Citation: Qingguo Bai, Fanwen Meng. Impact of risk aversion on two-echelon supply chain systems with carbon emission reduction constraints. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1943-1965. doi: 10.3934/jimo.2019037
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##### References:
Effects of $\lambda_{r}$ on DM$_{1}$
Effects of $\lambda_{m_{1}}$ on DM$_{2}$
Effects of $\lambda_{m_{2}}$ on DM$_{2}$
The optimal solutions for DM$_{1}$
 Decentralized Model 1 $w^{*}_{1}$ $w^{*}_{2}$ $s^{*}$ $p^{*}_{1}$ $p^{*}_{2}$ $C = 9000$ 422.5471 207.3770 8.0263 483.9910 297.6065 $C = 12569$ 422.5471 207.3770 8.0263 483.9910 297.6065 $C = 15000$ 422.5471 207.3770 8.0263 483.9910 297.6065
 Decentralized Model 1 $w^{*}_{1}$ $w^{*}_{2}$ $s^{*}$ $p^{*}_{1}$ $p^{*}_{2}$ $C = 9000$ 422.5471 207.3770 8.0263 483.9910 297.6065 $C = 12569$ 422.5471 207.3770 8.0263 483.9910 297.6065 $C = 15000$ 422.5471 207.3770 8.0263 483.9910 297.6065
The optimal profits and carbon emissions for DM$_{1}$
 Decentralized Model 1 $U^{*}(\pi_{r})$ $E^{*}(\pi_{m_{1}})$ $E^{*}(\pi_{m_{2}})$ $J(s^{*})$ $C = 9000$ 17,627 57,170 31,166 12,569 $C = 12569$ 17,627 67,877 31,166 12,569 $C = 15000$ 17,627 75,170 31,166 12,569
 Decentralized Model 1 $U^{*}(\pi_{r})$ $E^{*}(\pi_{m_{1}})$ $E^{*}(\pi_{m_{2}})$ $J(s^{*})$ $C = 9000$ 17,627 57,170 31,166 12,569 $C = 12569$ 17,627 67,877 31,166 12,569 $C = 15000$ 17,627 75,170 31,166 12,569
The optimal solutions for DM$_{2}$
 Decentralized Model 2 $w^{**}_{1}$ $w^{**}_{2}$ $s^{**}$ $p^{**}_{1}$ $p^{**}_{2}$ $C = 9000$ 298.4721 67.4862 2.1871 506.5056 311.8028 $C = 11416$ 298.4721 67.4862 2.1871 506.5056 311.8028 $C = 15000$ 298.4721 67.4862 2.1871 506.5056 311.8028
 Decentralized Model 2 $w^{**}_{1}$ $w^{**}_{2}$ $s^{**}$ $p^{**}_{1}$ $p^{**}_{2}$ $C = 9000$ 298.4721 67.4862 2.1871 506.5056 311.8028 $C = 11416$ 298.4721 67.4862 2.1871 506.5056 311.8028 $C = 15000$ 298.4721 67.4862 2.1871 506.5056 311.8028
The optimal profits and carbon emissions for DM$_{2}$
 Decentralized Model 2 $E^{**}(\pi_{r})$ $U^{**}(\pi_{m_{1}})$ $U^{**}(\pi_{m_{2}})$ $J(s^{**})$ $C = 9000$ 66,868 31,809 5617.9 11,416 $C = 11416$ 66,868 39,057 5617.9 11,416 $C = 15000$ 66,868 49,809 5617.9 11,416
 Decentralized Model 2 $E^{**}(\pi_{r})$ $U^{**}(\pi_{m_{1}})$ $U^{**}(\pi_{m_{2}})$ $J(s^{**})$ $C = 9000$ 66,868 31,809 5617.9 11,416 $C = 11416$ 66,868 39,057 5617.9 11,416 $C = 15000$ 66,868 49,809 5617.9 11,416
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