Design of an environmental contract under trade credits and carbon emission reduction

Chong Zhang; Yaxian Wang; Haiyan Wang

doi:10.3934/jimo.2021141

Article Contents

2022, Volume 18, Issue 6: 3929-3951. Doi: 10.3934/jimo.2021141

This issue Previous Article Open-loop equilibrium mean-variance reinsurance, new business and investment strategies with constraints Next Article Coordinated optimization of production scheduling and maintenance activities with machine reliability deterioration

Design of an environmental contract under trade credits and carbon emission reduction

1.
School of Management, Nanjing University of Posts and Telecommunications, Nanjing, 210003 Jiangsu, China
2.
School of Economics & Managements, Southeast University, Nanjing, 210089 Jiangsu, China

^* Corresponding author: Yaxian Wang
^* Corresponding author: Yaxian Wang

Received: March 2021

Revised: May 2021

Early access: August 2021

Published: September 2022

The paper is supported by the 1311 Programs Foundation of Nanjing University of Posts and Telecommunications, the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (NY220212), the Key Research Base of Philosophy and Social Sciences in Jiangsu–Information Industry Integration Innovation and Emergency Management Research Center

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Abstract

Most of the previous literatures proposed a single coordination contract to increase the total profit of the supply chain, while this paper focuses on how to design environmental contracts to increase economic and environmental performance in the context of sustainable development. This paper designs the environmental contract based on cap-and-trade mechanism and trade credits which has rarely been studied before, especially the impact of trade credit on environmental performance. We consider a green supply chain, assuming that the demand rate is linear with retail prices, joint carbon emission reduction efforts and trade credit. Two models, a decentralized one and a centralized one, are compared; four contracts are proposed. Via numerous examples and sensitivity analysis, we gain some insight into how to select supply chain contracts to better improve environmental performance. The results reveal that the manufacturer sharing the retailer's revenue and cost contract obtains the highest profit. While revenue sharing contract between both parties is the optimal environmental contract, but it is difficult to increase the profit of supply chain. Furthermore, it is found that trade credit works well in protecting the environment and plays a significant role in achieving coordination.

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Mathematics Subject Classification: Primary: 90B50, 91B24; Secondary: 91A40.

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Figure 1. Effects of $ {W_e} $ on optimal solutions

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Figure 2. Effects of $ \varepsilon $ on optimal solutions

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Table 1. Summary of Related Literature

	Decision variables				Demand dependency				Contract
	(ⅰ)	(ⅱ)	(ⅲ)	(ⅳ)	(ⅰ)	(ⅱ)	(ⅲ)	(ⅳ)	(ⅴ)	(ⅵ)
[38]	$ \times $	$ \times $	$ \surd $	$ \times $	$ \times $	$ \times $	$ \surd $	$ \times $	$ \surd $	$ \times $
Krishnan et al.[25]	$ \times $	$ \times $	$ \times $	$ \surd $	$ \times $	$ \times $	$ \times $	$ \surd $	$ \surd $	$ \surd $
Tsao and Sheen [43]	$ \times $	$ \times $	$ \surd $	$ \times $	$ \times $	$ \times $	$ \surd $	$ \times $	$ \surd $	$ \times $
Ma et al.[28]	$ \times $	$ \times $	$ \surd $	$ \surd $	$ \times $	$ \times $	$ \surd $	$ \surd $	$ \surd $	$ \surd $
Xu et al. [48]	$ \times $	$ \surd $	$ \surd $	$ \times $	$ \times $	$ \surd $	$ \surd $	$ \times $	$ \surd $	$ \times $
Ji et al.[19]	$ \times $	$ \surd $	$ \surd $	$ \surd $	$ \times $	$ \surd $	$ \surd $	$ \surd $	$ \times $	$ \times $
Bai et al.[3]	$ \times $	$ \surd $	$ \surd $	$ \surd $	$ \times $	$ \surd $	$ \surd $	$ \surd $	$ \times $	$ \surd $
Heydari et al.[13]	$ \surd $	$ \times $	$ \times $	$ \times $	$ \surd $	$ \times $	$ \times $	$ \times $	$ \surd $	$ \times $
Zhou and Ye [53]	$ \times $	$ \surd $	$ \surd $	$ \surd $	$ \times $	$ \surd $	$ \surd $	$ \surd $	$ \surd $	$ \surd $
Yang et al.[50]	$ \times $	$ \surd $	$ \surd $	$ \times $	$ \times $	$ \times $	$ \surd $	$ \times $	$ \times $	$ \times $
Hosseini-Motlagh et al.[15]	$ \surd $	$ \times $	$ \times $	$ \surd $	$ \surd $	$ \times $	$ \times $	$ \surd $	$ \surd $	$ \times $
Pakhira et al.[29]	$ \surd $	$ \times $	$ \times $	$ \surd $	$ \times $	$ \times $	$ \times $	$ \surd $	$ \surd $	$ \times $
Phan et al.[32]	$ \times $	$ \times $	$ \times $	$ \surd $	$ \times $	$ \times $	$ \times $	$ \surd $	$ \surd $	$ \surd $
Tsao[42]	$ \surd $	$ \times $	$ \times $	$ \times $	$ \surd $	$ \times $	$ \times $	$ \times $	$ \surd $	$ \surd $
Ranjan and Jha[35]	$ \times $	$ \times $	$ \surd $	$ \surd $	$ \times $	$ \times $	$ \surd $	$ \surd $	$ \surd $	$ \times $
This paper	$ \surd $	$ \surd $	$ \surd $	$ \surd $	$ \surd $	$ \surd $	$ \surd $	$ \surd $	$ \times $	$ \surd $

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Table 2. Symbols in this paper

Parameters
$ C $	The production cost per unit
$ W $	The wholesale price per unit
$ I $	The market interest rate
$ v $	The effectiveness of carbon reduction efforts on carbon emissions for making a unit, $v > 0$
$ \varepsilon $	The manufacturer's carbon emissions for making a product without efforts on carbon reduction
$ {C_M} $	The manufacturer's carbon pollution limit or cap
$ {W_e} $	The trading price of carbon emissions
$ {\eta _1} $	The investment cost coefficient on carbon reduction efforts, $ {\eta _1} > 0 $
$ {\eta _2} $	The investment cost coefficient on promotional efforts, $ {\eta _2} > 0 $
$ a $	Market scale parameter, $ a > 0 $
$ b $	Price influence on the demand rate, $ b > 0 $
$ {\gamma _1} $	Effect of carbon reduction effort on demand, $ {\gamma _1} > 0 $
$ {\gamma _2} $	Effect of promotional effort on demand, $ {\gamma _2} > 0 $
Decision variables
$ s $	The retailer's promotional efforts
$ P $	The retail price per unit
$ M $	The length of the trade credit period offered by the manufacturer in years. $ M > 0$ represents a credit payment, $M = 0$ represents an advance payment, and $ M < 0$ represents a cash payment
$ {\theta} $	The manufacturer's carbon reduction efforts
Functions
$ {\pi _i} $	The supply chain member i's profit per year; $i = s, r, sc$ refer to the manufacturer, the retailer and the supply chain, respectively
$ * $	Represents the optimal value of a decision variable

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Table 3. Optimal solutions for the example

Model	$ M $	$ P $	$ \theta $	$ s $	$ \pi_r $	$ \pi_m $	$ \pi_{sc} $	$ E(D) $
$ Centralized $	0.74	33.694	7.916	3.401	-	-	4094.153	171.326
$ Decentralized $	-0.39	37.683	3.402	1.389	228.357	762.078	990.434	94.911
$ Contract A\left[\rho_{1}, \lambda_{1}\right] $
$ [0.1,0.7] $	-0.14	37.961	3.821	5.469	407.49	796.88	1204.37	131.86
$ [0.1,0.6] $	-0.02	37.207	3.773	4.573	550.99	816.57	1367.55	156.29
$ [0.1,0.5] $	0.04	36.773	3.735	3.870	650.65	829.39	1480.03	172.24
$ [0.1,0.4] $	0.08	36.501	3.707	3.325	715.62	837.43	1553.04	182.32
$ [0.2,0.5] $	0.49	36.049	3.938	5.004	1724.03	967.01	2691.04	314.26
$ [0.3,0.5] $	0.92	35.660	4.104	6.088	4116.45	1227.64	5344.10	554.05

$ Contract B\left[\rho_{2}, \tau_{1}\right] $
$ [0.1,0.6] $	-0.73	35.846	3.611	0.804	86.24	740.29	826.54	63.78
$ [0.2,0.6] $	-0.25	34.136	3.864	1.387	327.23	788.97	1116.20	122.98
$ [0.3,0.6] $	0.21	33.440	3.985	1.953	953.53	884.78	1838.31	228.22
$ [0.4,0.6] $	0.68	33.087	4.060	2.519	2500.88	1077.13	3578.01	419.39
$ [0.2,0.5] $	-0.10	34.401	3.841	1.608	470.48	810.54	1281.02	148.85
$ [0.2,0.4] $	0.05	34.613	3.825	1.827	663.39	837.37	1500.75	180.05

$ Contract C\left[\varphi_{1}, \lambda_{2}\right] $
$ [0.5,0.5] $	-0.40	43.264	6.599	3.367	198.32	808.30	1006.62	42.36
$ [0.5,0.4] $	-0.35	42.287	6.753	2.925	236.66	819.58	1056.24	45.20
$ [0.5,0.3] $	-0.32	41.707	6.833	2.562	261.25	826.59	1087.83	46.95
$ [0.4,0.2] $	-0.35	41.603	5.377	2.148	247.94	842.09	1090.03	63.22
$ [0.5,0.2] $	-0.30	41.341	6.876	2.269	277.01	831.03	1108.03	48.07
$ [0.6,0.2] $	-0.22	40.962	9.507	2.473	315.25	795.62	1110.88	9.18

$ Contract D\left[\varphi_{2}, \tau_{2}\right] $
$ [0.6,0.05] $	-0.28	41.512	9.147	1.899	263.38	772.25	1035.63	13.98
$ [0.61,0.05] $	-0.27	41.459	9.511	1.921	266.65	774.34	1040.99	8.23
$ [0.62,0.05] $	-0.26	41.404	9.904	1.945	269.71	776.63	1046.34	1.66
$ [0.6,0.05] $	-0.28	41.512	9.147	1.899	263.38	772.25	1035.63	13.98
$ [0.6,0.04] $	-0.27	41.307	9.232	1.920	277.15	775.09	1052.24	13.03
$ [0.6,0.003] $	-0.25	41.105	9.316	1.941	291.41	778.01	1069.42	12.02

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Table 4. The increase rates with different contract coefficients

Parameter	$ \pi_r $	$ \pi_m $	$ \pi_{sc} $	$ E(D) $

$ Contract A\left[\rho_{1}, \lambda_{1}\right] $
$ [0.1,0.7] $	78.45%	4.57%	21.60%	38.93%
$ [0.1,0.6] $	141.28%	7.15%	38.08%	64.67%
$ [0.1,0.5] $	184.93%	8.83%	49.43%	81.48%
$ [0.1,0.4] $	213.38%	9.89%	56.81%	92.10%
$ [0.1,0.5] $	184.93%	8.83%	49.43%	81.48%
$ [0.2,0.5] $	654.97%	26.89%	171.70%	231.11%
$ [0.3,0.5] $	1702.6%	61.09%	439.57%	483.76%

$ Contract B\left[\rho_{2}, \tau_{1}\right] $
$ [0.2,0.5] $	106.02%	6.36%	29.34%	56.83%
$ [0.2,0.4] $	190.50%	9.88%	51.53%	89.71%
$ [0.2,0.3] $	303.66%	14.26%	80.99%	129.38%
$ [0.2,0.6] $	43.30%	3.53%	12.70%	29.57%
$ [0.3,0.6] $	317.56%	16.10%	85.61%	140.46%
$ [0.4,0.6] $	995.15%	41.34%	261.26%	341.89%

$ Contract C\left[\varphi_{1}, \lambda_{2}\right] $
$ [0.5,0.4] $	3.63%	7.55%	6.64%	-52.38%
$ [0.5,0.3] $	14.40%	8.46%	9.83%	-50.53%
$ [0.5,0.2] $	38.05%	4.40%	12.16%	-90.32%
$ [0.6,0.2] $	38.05%	4.40%	12.16%	-90.32%
$ [0.5,0.2] $	21.30%	9.05%	11.87%	-49.35%
$ [0.4,0.2] $	8.58%	10.50%	10.06%	-33.39%

$ Contract D\left[\varphi_{2}, \tau_{2}\right] $
$ [0.6,0.05] $	15.33%	1.34%	4.56%	-85.27%
$ [0.61,0.05] $	16.77%	1.61%	5.10%	-91.33%
$ [0.62,0.05] $	18.11%	1.91%	5.64%	-98.25%
$ [0.6,0.05] $	15.33%	1.34%	4.56%	-85.27%
$ [0.6,0.04] $	21.37%	1.71%	6.24%	-86.27%
$ [0.6,0.03] $	27.61%	2.09%	7.98%	-87.34%

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