Z-Number-Based Maximum Expected Linear Programming Model with Applications
Abstract
:1. Introduction
1.1. Motivation
1.2. Literature Review
1.3. Contribution
1.4. Structure
2. Z-Number Theoretical Preparation
2.1. Methodology
2.2. Credibility Distribution of Z-Number
2.3. Operational Law of Z-Number
2.4. Expected Value of Z-Number
3. Maximum Expected Z-Number Programming Model
3.1. Chance-Constrained Z-Number Programming
3.2. Z-Number Crisp Equivalent Model
4. Example of Maximum Expected Z-Number Programming Model
4.1. Supplier Selection Problem
4.2. Optimal Portfolio Problem
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
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Decision Variable | |
---|---|
Number of installing production lines, | |
Parameters | |
Expense of machine of the i-th type | |
productions, | |
Covering area of the i-th type productions, | |
Production efficiency of the i-th type | |
productions, | |
Demand of the i-th type productions, | |
Margin provided by the i-th type productions, | |
Confidence level of the i-th type productions, | |
Expected Total profits, where | |
, |
Parameter | Value | Parameter | Value |
---|---|---|---|
0.7 | |||
0.7 | |||
0.7 | |||
7 | |||
9 | |||
8 | |||
9 | |||
11 | |||
10 | |||
a | 600 | b | 800 |
Decision Variable | |
---|---|
Portfolios of i-th type stocks. | |
Parameters | |
Returns of the i-th type stocks. | |
Current closing value for the i-th type stocks. | |
Closing value in the following year of the i-th type stocks. | |
Dividend of the i-th type stocks. | |
Invested amount of the i-th type stocks. | |
m | Total amount of purchased stocks. |
Sum of investment. | |
Total returns, where | |
, |
Stocks | Z-Number Returns |
---|---|
1 | (−0.3, 1.8, 2.3, 3.8) (3, 5, 7) |
2 | (−0.4, 2.0, 2.2, 4.0) (6, 7, 8) |
3 | (0.3, 1.0, 1.5, 2.3) (7, 8, 9) |
4 | (0.1, 1.5,1.8, 3.2) (5, 7, 9) |
Stocks | Expected Value | Invested Amount |
---|---|---|
1 | 4.2485 | 2100 |
2 | 5.1592 | 3000 |
3 | 3.6062 | 1500 |
4 | 4.3655 | 2300 |
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Yuan, M.; Zeng, B.; Chen, J.; Wang, C. Z-Number-Based Maximum Expected Linear Programming Model with Applications. Mathematics 2023, 11, 3750. https://doi.org/10.3390/math11173750
Yuan M, Zeng B, Chen J, Wang C. Z-Number-Based Maximum Expected Linear Programming Model with Applications. Mathematics. 2023; 11(17):3750. https://doi.org/10.3390/math11173750
Chicago/Turabian StyleYuan, Meng, Biao Zeng, Jiayu Chen, and Chenxu Wang. 2023. "Z-Number-Based Maximum Expected Linear Programming Model with Applications" Mathematics 11, no. 17: 3750. https://doi.org/10.3390/math11173750
APA StyleYuan, M., Zeng, B., Chen, J., & Wang, C. (2023). Z-Number-Based Maximum Expected Linear Programming Model with Applications. Mathematics, 11(17), 3750. https://doi.org/10.3390/math11173750