Optimal Pricing in Recycling and Remanufacturing in Uncertain Environments
Abstract
1. Introduction
2. Problem Description
3. An Uncertain Programming Model
4. Numerical Experiments
5. Conclusions and Future Research
Author Contributions
Funding
Conflicts of Interest
Appendix A. Uncertainty Theory
References
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: | Unit price of a new product, which is a decision variable. |
: | Unit price of a second-hand product, which is a decision variable. |
: | Unit price of recycling a used product, which is a decision variable. |
: | Unit cost for manufacturing a new product with virgin raw materials. |
: | Unit cost for manufacturing a new product with recycled raw materials. |
: | Unit cost for renewing a used product in good condition. |
: | Proportion of the used products that are in good condition, . |
Parameters | Linear | Zigzag | Normal | Expected Value |
---|---|---|---|---|
(5000,10000) | (5000,8000,9000) | (7500,200) | 7500 | |
(30,50) | (30,40,50) | (40,8) | 40 | |
(2500,5000) | (2500,3000,6500) | (3750,100) | 3750 | |
(40,60) | (40,50,60) | (50,4) | 50 | |
(50,100) | (50,80,90) | (75,6) | 75 | |
(100,200) | (100,150,200) | (150,9) | 150 | |
(5000,8000) | (5000,6500,8000) | (6500,120) | 6500 |
Distribution | ||||
---|---|---|---|---|
Linear | 108.7501 | 46.5202 | 11.9011 | 274,767.7100 |
Zigzag | 108.7503 | 40.8848 | 11.2037 | 272,293.4025 |
Normal | 108.7498 | 56.1929 | 11.9987 | 282,495.1945 |
Distribution | ||||||
---|---|---|---|---|---|---|
Linear | (31,49) | 27.0000 | 108.7476 | 46.5347 | 11.8987 | 274,767.7138 |
(30,50) | 33.3333 | 108.7501 | 46.5202 | 11.9011 | 274,767.7120 | |
(29,51) | 40.3333 | 108.7519 | 46.5380 | 11.9011 | 274,767.7115 | |
(28,52) | 48.0000 | 108.7531 | 46.5347 | 11.9987 | 274,767.7040 | |
Zigzag | (31,40,49) | 27.0000 | 108.7564 | 40.8623 | 11.1994 | 272,293.4822 |
(30,40,50) | 33.3333 | 108.7503 | 40.8848 | 11.2037 | 272,293.4025 | |
(29,40,51) | 40.3333 | 108.7540 | 40.8680 | 11.1944 | 272,293.3899 | |
(28,40,52) | 48.0000 | 108.7500 | 40.8653 | 11.1960 | 272,293.3799 | |
Normal | (40,7) | 49.0000 | 108.7500 | 56.1966 | 11.8987 | 282,495.1944 |
(40,8) | 64.0000 | 108.7498 | 56.1929 | 11.9987 | 282,495.1945 | |
(40,9) | 81.0000 | 108.7509 | 56.1928 | 11.9987 | 282,495.1978 | |
(40,10) | 100.0000 | 108.7494 | 56.1929 | 12.0000 | 282,495.3938 |
Distribution | ||||||
---|---|---|---|---|---|---|
Linear | (51,99) | 192.0000 | 108.7499 | 46.5122 | 11.9890 | 274,764.4382 |
(50,100) | 208.3333 | 108.7501 | 46.5202 | 11.9011 | 274,767.7120 | |
(49,101) | 225.3333 | 108.7582 | 46.5330 | 11.9909 | 274,770.9045 | |
(48,102) | 243.0000 | 108.7662 | 46.5397 | 11.9948 | 274,774.2556 | |
Zigzag | (51,80,89) | 128.6667 | 108.7498 | 40.8604 | 11.1983 | 272,290.4050 |
(50,80,90) | 141.6667 | 108.7503 | 40.8848 | 11.2037 | 272,293.4025 | |
(49,80,91) | 155.3333 | 108.7570 | 40.8944 | 11.2099 | 272,296.5589 | |
(48,80,92) | 169.6667 | 108.7580 | 40.8967 | 11.2102 | 272,299.6402 | |
Normal | (75,5) | 25.0000 | 108.7479 | 56.1877 | 11.8999 | 282,486.3327 |
(75,6) | 36.0000 | 108.7498 | 56.1929 | 11.9987 | 282,495.1945 | |
(75,7) | 49.0000 | 108.7500 | 56.1980 | 11.9326 | 282,504.0573 | |
(75,8) | 64.0000 | 108.7501 | 56.2032 | 11.9489 | 282,512.9213 |
Distribution | ||||||
---|---|---|---|---|---|---|
Linear | (5100,7900) | 653,333.3333 | 108.7501 | 46.5200 | 11.9009 | 274,767.7116 |
(5000,8000) | 750,000.0000 | 108.7501 | 46.5202 | 11.9011 | 274,767.7120 | |
(4900,8100) | 853,333.3333 | 108.7577 | 46.5347 | 12.0000 | 274,767.7135 | |
(4800,8200) | 963,333.3333 | 108.7740 | 46.5315 | 12.0000 | 274,767.7235 | |
Zigzag | (5600,6500,7400) | 653,333.3333 | 108.7487 | 40.8631 | 11.1981 | 272,293.3926 |
(5100,6500,7900) | 750,000.0000 | 108.7490 | 40.8848 | 11.2037 | 272,293.4025 | |
(4900,6500,8100) | 853,333.3333 | 108.7490 | 40.8626 | 11.2014 | 272,293.4838 | |
(4800,6500,8200) | 963,333.3333 | 108.7529 | 40.8660 | 11.1972 | 272,293.4930 | |
Normal | (6500,110) | 12,100.0000 | 108.7492 | 56.1929 | 11.9999 | 282,495.1942 |
(6500,120) | 14,400.0000 | 108.7498 | 56.1929 | 11.9987 | 282,495.1945 | |
(6500,130) | 16,900.0000 | 108.7614 | 56.1928 | 11.9980 | 282,495.1981 | |
(6500,140) | 19,600.0000 | 108.7500 | 56.1929 | 11.9980 | 282,495.1999 |
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Yan, G.; Ni, Y.; Yang, X. Optimal Pricing in Recycling and Remanufacturing in Uncertain Environments. Sustainability 2020, 12, 3199. https://doi.org/10.3390/su12083199
Yan G, Ni Y, Yang X. Optimal Pricing in Recycling and Remanufacturing in Uncertain Environments. Sustainability. 2020; 12(8):3199. https://doi.org/10.3390/su12083199
Chicago/Turabian StyleYan, Guangzhou, Yaodong Ni, and Xiangfeng Yang. 2020. "Optimal Pricing in Recycling and Remanufacturing in Uncertain Environments" Sustainability 12, no. 8: 3199. https://doi.org/10.3390/su12083199
APA StyleYan, G., Ni, Y., & Yang, X. (2020). Optimal Pricing in Recycling and Remanufacturing in Uncertain Environments. Sustainability, 12(8), 3199. https://doi.org/10.3390/su12083199