A Fuzzy Robust Programming Model for Sustainable Closed-Loop Supply Chain Network Design with Efficiency-Oriented Multi-Objective Optimization
Abstract
:1. Introduction
2. Literature Review
- Most recent researches pay attention to multi-objective optimization for seeking an excellent trade-off between economic and environmental performance. Few take into consideration social performance.
- For different kinds of uncertainty in the supply chain network, there are targeted uncertainty technologies for coping with them.
- For solving the multi-objective mathematical model, firstly, some studies convert the multi-objective optimization problem into a single-objective problem by ε-constraint and other methods. Secondly, some exact solution methods are applied, such as goal programming. Thirdly, metaheuristic approaches are utilized which adopt the concept of the Pareto optimal solution. However, when solving multi-objective SCLSC network optimization problems, metaheuristic algorithms are rarely applied.
3. Model Formulation
3.1. Problem Description
3.2. Social Factor Modeling
3.3. Notations
Index of raw material suppliers, | |
Index of production centers, | |
Index of distribution centers, | |
Index of recycling centers, | |
Index of repair centers, | |
Index of disposal centers, | |
Index of customers, | |
Index of products, | |
Index of raw materials, |
Demands of customer for product | |
Recycle quantity of customer for product | |
Demands of repair center for raw material | |
Transport cost of raw material per kg from raw material supplier to production center | |
Transport cost of product per kg from production center to distribution center | |
Transport cost of product per kg from distribution center to customer | |
Transport cost of raw material per kg from raw material supplier to repair center | |
Transport cost of product per kg from customer to recycling center | |
Transport cost of product per kg from recycling center to repair center | |
Transport cost of product per kg from repair center to distribution center | |
Transport cost of raw material per kg from recycling center to disposal center | |
Manufacturing cost of producing unit new product in production center | |
Repair cost of producing unit repaired product in production center | |
Testing cost of testing unit material in recycling center | |
Disassembly cost of disassembling unit recycled product in recycling center | |
Disposal cost of disposing unit component in disposal center | |
Purchasing cost of unit component from component supplier | |
Opening cost of production center | |
Opening cost of distribution center | |
Opening cost of repair center | |
Opening cost of recycling center | |
Opening cost of disposal center | |
Capacity of raw material supplier for material | |
Capacity of production center for material | |
Capacity of repair center for material | |
Capacity of recycling center for material | |
Capacity of production center for product , | |
Capacity of distribution center for product | |
Capacity of repair center for product | |
Capacity of recycling center for product | |
Solid waste emission of producing unit product in production center | |
Solid waste emission of repairing unit product in repair center | |
Solid waste emission of dismantling unit product in recycling center | |
Solid waste emission of disposing unit material in disposal center | |
Carbon emission of component per kg from raw material supplier to production center | |
Carbon emission of component per kg from production center to distribution center | |
Carbon emission of component per kg from distribution center to customer | |
Carbon emission of component per kg from raw material supplier to repair center | |
Carbon emission of component per kg from customer to recycling center | |
Carbon emission of component per kg from recycling center to repair center | |
Carbon emission of component per kg from repair center to distribution center | |
Carbon emission of component per kg from recycling center to disposal center | |
Numbers of lost working days caused by work damages during the opening of distribution center | |
Numbers of lost working days caused by work damages during the opening of repair center | |
Numbers of lost working days caused by work damages during the opening of recycling center | |
Maximum averages of lost working days caused by work damages during the opening of distribution center | |
Maximum averages of lost working days caused by work damages during the opening of repair center | |
Maximum averages of lost working days caused by work damages during the opening of recycling center | |
Weight of product | |
Weight of component | |
Utilization ratio of component per unit of product | |
Average disposal fraction of disposal center | |
Price of new product produced by production centers | |
Price of repaired product produced by repair centers |
Number of raw material transported from raw material supplier to production center | ||
Number of new product transported from production center to distribution center | ||
Number of product transported from distribution center to customer | ||
Number of raw material transported from raw material supplier to repair center | ||
Number of repaired products transported from repair center to distribution center | ||
Number of EOL product transported from customer to recycling center | ||
Number of recyclable product transported from recycling center to repair center | ||
Number of material transported from recycling center to disposal center | ||
Membership degree for the number of lost working days because of work damage for each worker in production center | ||
Membership degree for the number of lost working days because of work damage for each worker in repair center | ||
Membership degree for the number of lost working days because of work damage for each worker in recycling center | ||
{ | 1, if raw material supplier is selected; | |
0, otherwise | ||
{ | 1, if production center is opened | |
0, otherwise | ||
{ | 1, if distribution center is opened | |
0, otherwise | ||
{ | 1, if repair center is opened | |
0, otherwise | ||
{ | 1, if recycling center is opened | |
0, otherwise | ||
{ | 1, if disposal center is opened | |
0, otherwise |
3.4. Objective Functions
3.4.1. The First Objective Function: Economic Factor
3.4.2. The Second Objective Function: Environmental Factor
3.4.3. The Third Objective Function: Social Factor
3.5. Objective Functions
3.5.1. Flow Balance Constraints
3.5.2. Demand and Recycling Constraints
3.5.3. Carbon Cap Constraints
3.5.4. Capacity Constraints
3.5.5. Lost Working Days Constraints
3.5.6. Binary and Non-Negative
4. Fuzzy Robust Optimization Model
5. Efficiency-Oriented Multi-Objective Optimization
5.1. Meta-Heuristic Algorithms
5.1.1. Fast and Elite Non-Dominated Sorting Genetic (NSGA-II) Algorithm
5.1.2. Multi-Objective Particle Swarm Optimization (MOPSO) Algorithm
5.2. Efficiency Sorting Strategy
5.2.1. CCR Model
5.2.2. Secondary Goals-Based DEA Model
5.2.3. Indicator Selection
- (1)
- The indicators should be quantitative to avoid the influence of subjective preference.
- (2)
- The input indicators should be minimum indicators and the output indicators should be maximum indicators.
- (3)
- The indicators should comprehensively the supply chain performance including economic, environmental and social dimensions.
- (1)
- Cost indicators, including transportation cost, facility opening cost, ordering cost, and facility processing cost:
- (2)
- Environmental indicators, including carbon emission and solid waste emission:
- (1)
- Profit indicator:
- (2)
- Social indicators, including the lost working days measured:
6. Numerical Case
6.1. Case Description
6.2. Results and Discussion
6.3. Comparison of Algorithms
6.4. Robustness Analyses
7. Conclusions
- This article proposes a multi-objective mixed-integer programming model with targets of the minimum total cost, reduction in environmental damage, and maximum social responsibility.
- In order to deal with the uncertainty caused by the dynamic business environment, a fuzzy robust programming (FRP) approach is applied.
- An efficiency-oriented optimization methodology, hybridizing meta-heuristics and efficiency evaluation, is proposed to solve the developed multi-objective model as auxiliary decision-making.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Facility | Potential Nodes | Facility | Potential Nodes |
---|---|---|---|
Product | 1 | Raw material | 3 |
Raw materials supplier | 4 | Recycling center | 5 |
Manufacturing center | 3 | Disposal center | 3 |
Distribution center | 6 | Customer | 11 |
Remanufacturing center | 3 |
Parameters | ||||
---|---|---|---|---|
Unif (35, 40) | Unif (40, 45) | Unif (45, 50) | Unif (50, 55) | |
Unif (15, 20) | Unif (20, 25) | Unif (25, 30) | Unif (30, 35) | |
Unif (200, 250) | Unif (250, 300) | Unif (300, 350) | Unif (350, 400) | |
Unif (200, 240) | Unif (240, 280) | Unif (280, 320) | Unif (320, 360) | |
Unif (0.105, 0.110) | Unif (0.110, 0.115) | Unif (0.115, 0.120) | Unif (0.120, 0.125) |
Parameters | Value | Parameters | Value |
---|---|---|---|
Unif (100, 200) | Unif (100, 200) | ||
Unif (20, 30) | Unif (0.025, 0.030) | ||
Unif (4000, 6000) | Unif (0.00010, 0.00013) | ||
Unif (200, 400) | Unif (1, 3) | ||
Unif (1000, 1200) | Unif (0.5CM, 0.6CM) | ||
Unif (0.35, 0.55) | [10, 20, 10] | ||
[400] | [5, 15, 10] | ||
[4000] | [3000] |
DMU | Input | Output | Self | Cross | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Transport Cost | Opening Cost | Order Cost | Process Cost | Carbon Emission | Solid Emission | Revenue | Lost Working Days | |||
1 | 493,833 | 48,694 | 72,342 | 500,588 | 490.42 | 157.33 | 4,143,000 | 8.7363 | 1.0000 | 0.3029 |
2 | 473,933 | 55,637 | 72,756 | 489,989 | 476.91 | 149.78 | 4,029,000 | 8.0063 | 1.0000 | 0.4071 |
3 | 449,392 | 54,584 | 69,584 | 502,315 | 450.79 | 139.45 | 4,044,000 | 7.8401 | 1.0000 | 0.4018 |
4 | 441,943 | 52,596 | 67,272 | 512,510 | 440.43 | 149.58 | 3,960,000 | 7.8232 | 1.0000 | 0.4448 |
5 | 469,958 | 43,683 | 66,858 | 447,033 | 464.84 | 144.61 | 3,882,000 | 8.6007 | 1.0000 | 0.3823 |
6 | 492,450 | 44,425 | 71,065 | 493,695 | 481.23 | 142.11 | 4,119,000 | 8.6503 | 1.0000 | 0.3539 |
7 | 411,664 | 52,260 | 67,162 | 455,364 | 411.11 | 133.60 | 3,936,000 | 6.1792 | 1.0000 | 0.9286 |
8 | 431,381 | 56,304 | 67,413 | 439,684 | 424.69 | 145.45 | 3,702,000 | 7.6559 | 1.0000 | 0.7506 |
9 | 422,890 | 58,326 | 67,996 | 454,897 | 421.51 | 137.75 | 4,017,000 | 6.8180 | 1.0000 | 0.5625 |
10 | 442,712 | 49,122 | 68,477 | 494,147 | 443.78 | 144.98 | 3,906,000 | 7.8323 | 1.0000 | 0.4670 |
11 | 452,111 | 48,808 | 66,688 | 493,070 | 453.01 | 144.21 | 3,585,000 | 7.9384 | 1.0000 | 0.9936 |
12 | 508,657 | 53,535 | 73,019 | 531,301 | 499.69 | 160.32 | 4,035,000 | 8.1373 | 1.0000 | 0.4049 |
13 | 470,983 | 50,411 | 62,587 | 452,363 | 464.57 | 144.52 | 3,990,000 | 8.6279 | 1.0000 | 0.3504 |
14 | 449,112 | 56,309 | 67,119 | 426,297 | 452.17 | 146.83 | 3,918,000 | 7.8681 | 1.0000 | 0.4737 |
DMU | Input | Output | Self | Cross | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Transport Cost | Opening Cost | Order Cost | Process Cost | Carbon Emission | Solid Emission | Revenue | Lost Working Days | |||
1 | 659600 | 41706 | 90544 | 602750 | 662.05 | 178.82 | 5154000 | 8.0000 | 1.0000 | 0.4783 |
2 | 660157 | 47820 | 80967 | 622465 | 654.91 | 192.03 | 5460000 | 5.0000 | 1.0000 | 0.5215 |
3 | 668984 | 63755 | 89688 | 594961 | 658.19 | 185.84 | 5415000 | 5.0000 | 1.0000 | 0.5546 |
4 | 647114 | 45897 | 89168 | 569337 | 648.26 | 184.84 | 5361000 | 4.0000 | 1.0000 | 0.5762 |
5 | 637212 | 55192 | 81012 | 581502 | 629.52 | 184.04 | 5334000 | 4.0000 | 1.0000 | 0.5907 |
6 | 629990 | 55464 | 78168 | 577766 | 634.30 | 170.93 | 5235000 | 7.0000 | 1.0000 | 0.4919 |
7 | 634105 | 30294 | 81457 | 564696 | 625.68 | 181.94 | 5391000 | 5.0000 | 1.0000 | 0.4904 |
8 | 636202 | 65939 | 87761 | 570562 | 637.24 | 178.48 | 5379000 | 4.0000 | 1.0000 | 0.5941 |
9 | 650233 | 49591 | 89003 | 586320 | 648.95 | 178.53 | 5190000 | 1.0000 | 1.0000 | 0.9286 |
10 | 663550 | 42467 | 90761 | 562545 | 660.41 | 172.19 | 5184000 | 7.0000 | 1.0000 | 0.4995 |
11 | 640400 | 51161 | 89049 | 551701 | 645.92 | 177.46 | 5160000 | 3.0000 | 1.0000 | 0.7086 |
12 | 657757 | 55069 | 89149 | 575980 | 666.43 | 171.38 | 5142000 | 6.0000 | 1.0000 | 0.5684 |
13 | 470384 | 49496 | 61902 | 455024 | 472.66 | 144.42 | 3990000 | 8.6279 | 1.0000 | 0.7254 |
14 | 449346 | 60702 | 63633 | 455676 | 445.69 | 144.80 | 3918000 | 7.8681 | 1.0000 | 0.9826 |
Facility | SG-NSGA-II | SG-MOPSO |
---|---|---|
Raw materials supplier | 4 | 1, 2, 3, 4 |
Manufacturing centers | 1, 2 | 3 |
Distribution centers | 2, 4, 5, 6 | 1, 4, 5, 6 |
Remanufacturing centers | 1, 3 | 1 |
Recycling centers | 5 | 2 |
Disposal centers | 1, 2 | 2, 3 |
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Guo, Y.; Shi, Q.; Guo, C. A Fuzzy Robust Programming Model for Sustainable Closed-Loop Supply Chain Network Design with Efficiency-Oriented Multi-Objective Optimization. Processes 2022, 10, 1963. https://doi.org/10.3390/pr10101963
Guo Y, Shi Q, Guo C. A Fuzzy Robust Programming Model for Sustainable Closed-Loop Supply Chain Network Design with Efficiency-Oriented Multi-Objective Optimization. Processes. 2022; 10(10):1963. https://doi.org/10.3390/pr10101963
Chicago/Turabian StyleGuo, Yurong, Quan Shi, and Chiming Guo. 2022. "A Fuzzy Robust Programming Model for Sustainable Closed-Loop Supply Chain Network Design with Efficiency-Oriented Multi-Objective Optimization" Processes 10, no. 10: 1963. https://doi.org/10.3390/pr10101963