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

Qingguo Bai; Fanwen Meng

doi:10.3934/jimo.2019037

Article Contents

2020, Volume 16, Issue 4: 1943-1965. Doi: 10.3934/jimo.2019037

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

Qingguo Bai^1, and
Fanwen Meng^2, ,

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
^* Corresponding author

Received: June 2018

Revised: November 2018

Early access: May 2019

Published: May 2020

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

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 90B60, 91A05; Secondary: 90C46.

Citation:

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Figure 1. Effects of $ \lambda_{r} $ on DM$ _{1} $

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Figure 2. Effects of $ \lambda_{m_{1}} $ on DM$ _{2} $

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Figure 3. Effects of $ \lambda_{m_{2}} $ on DM$ _{2} $

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Table 1. 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

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Table 2. 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

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Table 3. 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

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Table 4. 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

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