$ 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 |
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.
Citation: |
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 |
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 |
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 |
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 | - | - |
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 |
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 |
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 |
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 |
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 |
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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Material flow of the ELV recovery network
The map and the existent ELV recycling network in Hunan
Effect of public environmental protection awareness
Impacts of subsidy
Impact of different types of costs on profit
Impacts of different types of costs on the recycled quantities