Nonlinear optimization to management problems of end-of-life vehicles with environmental protection awareness and damaged/aging degrees

Zhong Wan; Jingjing Liu; Jing Zhang

doi:10.3934/jimo.2019046

Article Contents

2020, Volume 16, Issue 5: 2117-2139. Doi: 10.3934/jimo.2019046

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Nonlinear optimization to management problems of end-of-life vehicles with environmental protection awareness and damaged/aging degrees

1.
School of Mathematics and Statistics, Central South University, Changsha 410083, China
2.
Experimental Teaching Center, Guangdong University of Foreign Studies, Guangzhou 510420, China

^* Corresponding authors: Zhong Wan and Jing Zhang
^* Corresponding authors: Zhong Wan and Jing Zhang

Received: October 31, 2018

Revised: November 30, 2018

Early access: May 2019

Published: August 2020

The first and second authors are supported by the National Science Foundation of China (Grant No. 71671190)

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Abstract

In the past one decade, an increasing number of motor vehicles necessarily results in huge amounts of end-of-life vehicles (ELVs) in the future. From the view point of environment protection and resource utilization, government subsidy and public awareness of environmental protection play a critical role in promoting the formal recycle enterprises to recycle the ELVs as many as possible. Different from the existing similar models, a mixed integer nonlinear optimization model is established in this paper to formulate the management problems of recycling ELVs as a centralized decision-making system, where damaged and aging degrees, correlation between the recycled quantity and take-back price of ELVs, and the public environmental protection awareness are considered. Unlike the results available in the literature, take-back prices of the ELVs are the endogenous variables of the model (decision variables), which affect the collected quantity of ELVs and the profit of recycling system. Additionally, due to distinct damaged and aging degrees of the ELVs, the refurbished or dismantled amounts of ELVs are also regarded as the decision variables so that the recycle system is more applicable. By case study and sensitivity analysis, validity of the model is verified and impacts of the governmental subsidy and environmental awareness are analyzed. By the proposed model, it is revealed that: (1) Distinct treatment of ELVs with different damaged and aging degrees can increase the profit of recycling ELVs; (2) Compared with the transportation cost, higher processing cost is a main obstacle to the profit growth. Advanced processing technology plays the most important role in improving the ELV recovery efficiency. (3) Both of government subsidy and environmental awareness seriously affect decision-making of recycle enterprises.

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Mathematics Subject Classification: Primary: 90B06, 62K05; Secondary: 68T37.

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Figure 1. Material flow of the ELV recovery network

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Figure 2. The map and the existent ELV recycling network in Hunan

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Figure 3. Effect of public environmental protection awareness

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Figure 4. Impacts of subsidy

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Figure 5. Impact of different types of costs on profit

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Figure 6. Impacts of different types of costs on the recycled quantities

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Table 1. Number of different types of nodes in ELV recovery network

$ I $	$ J $	$ O $	$ K $	$ L $	$ U $	$ S $	$ P $	$ Q $	$ R $	$ V $	$ W $	$ M $	$ N $
5	5	2	6	5	2	2	2	2	2	2	2	2	2

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Table 2. Distribution of nodes in ELV recovery network

	Changsha	Zhuzhou	Xiangtan	Hengyang	Shaoyang
Resource	1	2	3	4	5
Collection center	1	2	3	4	5
Repair center	1, 2	-	-	-	-
Dismantler	1	2, 3	4	6	5
Shredder	2	1	3	5	4
Landfill	2	-	1	-	-
Steel mill	1, 2	-	-	-	-
Non-ferrous smeltery	1	-	-	2	-
Oil factory	1, 2	-	-	-	-
Battery factory	1	-	-	2	-
Rubber factory	-	1	-	-	2
Glass factory	1, 2	-	-	-	-
Plastics factory	-	-	1	-	2

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Table 3. Distance between the nodes of network (km)

	Collection center
	1	2	3	4	5
Resources
1	10	67.4	46.9	152	148.3
2	49.8	20.2	26.9	117	133.6
3	43.7	27.2	13.4	111.4	122.1
4	147.6	100.7	104.8	6.1	75.5
5	170.2	170.5	146.8	109.9	43.5
Repair certer
1	29.4	40.9	28	131	137.6
2	155.9	133.2	120.6	51.8	26.9
Dismantler
1	21.8	59.8	46.4	150.9	153.1
2	60.2	13.8	36.3	116.4	138.7
3	49.8	22.9	31.9	122.2	139.2
4	124.9	64.8	81.8	48.8	105.1
5	148.8	143.3	121.6	84.3	15.5
6	144.2	107.3	103.6	16.6	53.3

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Table 4. Distance between the nodes of network (Continued Table 3)

	Shredder					Secondary market
	1	2	3	4	5	1	2
Dismantler
1	123.2	25.1	39.1	194.6	42.0	10.2	2.3
2	75.3	50.7	33.4	182.8	21.9	39.5	46.7
3	85.8	42.6	27.2	183.0	17.8	28.8	36.1
4	40.4	129.2	87.1	145.2	80.1	111.6	119.8
5	160.2	185.1	128.4	31.7	134.1	155.2	160.8
6	100.7	165.6	110.9	87.1	110.3	140.1	147.7
Landfill
1	148.7	39.4	59.5	204.0	65.3	-	-
2	88.1	50.9	14.4	170.2	4.7	-	-
Steel mill
1	117.8	33.0	29.7	185.1	33.8	-	-
2	114.7	33.3	27.2	184.0	30.8	-	-
Non-ferrous smeltery
1	149.4	33.0	65.3	214.1	69.3	-	-
2	75.7	156.5	106.2	113.9	102.7	-	-

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Table 5. Distance between the nodes of network (Continued Table 4)

	Oil		Battery		Rubber		Glass		Plastics
	1	2	1	2	1	2	1	2	1	2
ND
1	12.8	8.7	6.6	177.7	36.1	200.6	7.6	5.5	43.3	164.6
2	53.4	53.8	42.7	143.54	17.3	191.5	40.6	51.3	29.0	144.2
3	42.8	43.6	32.1	149.3	9.8	191.2	30.1	41.0	24.5	146.3
4	121.9	129.2	115.2	72.9	85.6	157.5	115.3	126.2	81.0	98.2
5	153.6	171.4	157.5	86.9	142.9	39.9	161.9	168.5	128.1	31.5
6	145.1	158.6	143.4	30.7	118.5	100.2	145.7	155.4	107.1	39.8

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Table 6. Capacity (ton) and unit processing cost (yuan RMB/ton)

$ {ca}_{j} $	$ {ca}_{k} $	$ {ca}_{l} $	$ {ca}_{u} $	$ pc_{1o} $	$ pc_{2o} $	$ pc_k $	$ pc_l $	$ pc_u $
2000	2000	1500	500	2000	3000	1960	270	500

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Table 7. Unit transportation cost (yuan RMB/ton·km)

$tc_{ij}$	$ tc_{jo}$	$ tc_{jk}$	$ tc_{kl}$	$ tc_{lu}$	$tc_{ks}$	$ tc_{kp}$	$ tc_{lm}$	$ tc_{ln}$	$ tc_{kq}$	$ tc_{kr}$	$tc_{kv}$	$ tc_{kw}$
2	1	0.8	0.4	1	1.5	0.7	0.6	0.5	0.5	0.5	0.7	0.7

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Table 8. Unit selling prices of recyled components (×10³ yuan RMB/ton)

$ s$	$ s_{0}$	$ s_{1}$	$ s_{2}$	$ s_{3}$	$ s_{4}$	$ s_{5}$	$ s_{6}$	$ s_{7}$	$ z_{1}$	$z_{2}$
3000	50000	2400	12000	4000	600	150	450	6000	500	1500
$ s^{'}_{1}$	$ s^{'}_{2}$	$ s^{'}_{3}$	$ s^{'}_{4}$	$ s^{'}_{5}$	$ s^{'}_{6}$	$ s^{'}_{7}$	$ z^{'}_{1}$	$z^{'}_{2}$
27360	136800	45600	6840	17100	5130	68400	5700	17100

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Table 9. Weight percentages in the recycled ELVs

$alpha$	$beta_{1}$	$beta_{2}$	$beta_{3}$	$beta_{4}$	$beta_{5}$	$beta_{6}$	$beta_{7}$	$eta$	$eta_{1}$	$eta_{2}$
0.81	0.06	0.04	0.017	0.013	0.03	0.015	0.015	15/81	62/81	4/81

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Table 10. Optimal solution in case study

DV	OS	DV	OS	DV	OS	DV	OS	DV	OS
$ \rho_{1,1} $	15000	$ A_{3,1,3} $	119	$ E_{3,2,5} $	468.2	$ Q3_{3,1} $	92.8	$ Q6_{2,1} $	8.7
$ \rho_{1,2} $	15000	$ A_{3,2,2} $	578	$ E_{3,3,5} $	442.3	$ Q3_{5,1} $	106.4	$ Q6_{3,1} $	8.2
$ \rho_{1,3} $	15000	$ A_{3,2,3} $	9	$ E_{3,5,3} $	507.1	$ Q3_{6,1} $	111.5	$ Q6_{5,1} $	9.4
$ \rho_{1,4} $	15000	$ A_{3,3,3} $	418	$ E_{3,6,3} $	531.4	$ Q3^{'}_{1,2} $	34	$ Q6_{6,1} $	9.9
$ \rho_{1,5} $	14900	$ A_{3,4,4} $	656	$ F_{3,2} $	352.7	$ Q3^{'}_{2,1} $	34	$ Q6^{'}_{1,2} $	3
$ \rho_{2,1} $	10000	$ A_{3,5,5} $	626	$ F_{5,2} $	228.4	$ Q3^{'}_{3,1} $	34	$ Q6^{'}_{2,1} $	3
$ \rho_{2,2} $	10000	$ B_{1,1,1} $	150	$ Q1_{1,2} $	40.3	$ Q3^{'}_{6,1} $	34	$ Q6^{'}_{3,1} $	3
$ \rho_{2,3} $	10000	$ B_{1,2,1} $	150	$ Q1_{2,1} $	34.7	$ Q4_{1,1} $	8.7	$ Q6^{'}_{6,1} $	3
$ \rho_{2,4} $	10000	$ B_{1,3,1} $	150	$ Q1_{3,1} $	32.8	$ Q4_{2,1} $	7.5	$ Q7_{1,1} $	10.1
$ \rho_{2,5} $	9950	$ B_{1,4,2} $	150	$ Q1_{5,1} $	37.6	$ Q4_{3,1} $	7.1	$ Q7_{2,1} $	8.7
$ \rho_{3,1} $	501.4	$ B_{1,5,2} $	149	$ Q1_{6,1} $	39.4	$ Q4_{5,2} $	8.1	$ Q7_{3,1} $	8.19
$ \rho_{3,2} $	577.1	$ B_{2,5,2} $	199	$ Q1^{'}_{1,2} $	12	$ Q4_{6,2} $	8.5	$ Q7_{5,2} $	9.4
$ \rho_{3,3} $	600	$ C_{2,1,1} $	200	$ Q1^{'}_{2,1} $	12	$ Q4^{'}_{1,1} $	2.6	$ Q7_{6,2} $	9.84
$ \rho_{3,4} $	474.3	$ C_{2,2,2} $	200	$ Q1^{'}_{3,1} $	12	$ Q4^{'}_{2,1} $	2.6	$ Q7^{'}_{1,1} $	3
$ \rho_{3,5} $	435.7	$ C_{2,3,3} $	200	$ Q1^{'}_{6,1} $	12	$ Q4^{'}_{3,1} $	2.6	$ Q7^{'}_{2,1} $	3
$ A_{1,1,1} $	150	$ C_{2,4,6} $	200	$ Q2_{1,2} $	26.9	$ Q4^{'}_{6,2} $	2.6	$ Q7^{'}_{3,1} $	3
$ A_{1,2,2} $	150	$ C_{3,1,1} $	672	$ Q2_{2,1} $	23.1	$ Q5_{1,1} $	20.16	$ Q7^{'}_{6,2} $	3
$ A_{1,3,3} $	150	$ C_{3,2,2} $	578	$ Q2_{3,1} $	21.8	$ Q5_{2,1} $	17.3	$ Q8_{3,2} $	1210.8
$ A_{1,4,4} $	150	$ C_{3,3,3} $	546	$ Q2_{5,1} $	25.0	$ Q5_{3,1} $	16.4	$ Q8_{5,2} $	696.5
$ A_{1,5,5} $	149	$ C_{3,4,6} $	656	$ Q2_{6,1} $	26.2	$ Q5_{5,2} $	18.8	$ Q8^{'}_{3,2} $	247.9
$ A_{2,1,1} $	200	$ C_{3,5,5} $	626	$ Q2^{'}_{1,2} $	8	$ Q5_{6,2} $	19.7	$ Q8^{'}_{5,2} $	247.9
$ A_{2,2,2} $	200	$ E_{2,1,3} $	162	$ Q2^{}_{2,1} $	8	$ Q5^{'}_{1,1} $	6	$ Q9_{3,1} $	79.1
$ A_{2,3,3} $	200	$ E_{2,2,5} $	162	$ Q2^{'}_{3,1} $	8	$ Q5^{'}_{2,1} $	6	$ Q9_{5,1} $	45.5
$ A_{2,4,4} $	200	$ E_{2,3,5} $	162	$ Q2^{'}_{6,1} $	8	$ Q5^{'}_{3,1} $	6	$ Q9^{'}_{3,1} $	16.2
$ A_{2,5,5} $	199	$ E_{2,6,3} $	162	$ Q3_{1,2} $	114.2	$ Q5^{'}_{6,2} $	6	$ Q9^{'}_{5,1} $	16.2
$ A_{3,1,1} $	672	$ E_{3,1,3} $	544.3	$ Q3_{2,1} $	98.3	$ Q6_{1,2} $	10.1

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