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Stackelberg pricing policy in dyadic capital-constrained supply chain considering bank's deposit and loan based on delay payment scheme
Application of a modified VES production function model
1. | School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, 215009, China |
2. | School of Business, Suzhou University of Science and Technology, Suzhou, 215009, China |
In the analyses on economic growth factors, researchers generally use the production function model to calculate the contribution rates of influencing factors to economic growth. The paper proposes a new modified VES production function model. As for the model's parameter estimation, the conventional optimization methods are complicated, generally require information like the gradient of objective function, and have the poor convergence rate and precision. The paper gives a modern intelligent algorithm, i.e., the cuckoo search algorithm, which has the strong robustness, can be realized easily, has the fast convergence rate and can be used flexibly. To enhance the convergence rate and precision, the paper improves the conventional cuckoo search algorithm. Using the new model, the paper gives a method calculating the contribution rates of economic growth influencing factors scientifically. Finally, the paper calculates the contribution rates of influencing factors to economic growth in Shanghai City, China.
References:
[1] |
A. Assad and K. Deep,
A Hybrid Harmony search and Simulated Annealing algorithm for continuous optimization, Information Sci., 450 (2018), 246-266.
doi: 10.1016/j.ins.2018.03.042. |
[2] |
V. O. Bohaienko and V. M. Popov, Optimization of operation regimes of irrigation canals using genetic algorithms, in International Conference on Computer Science, Engineering and Education Applications, Advances in Intelligent Systems and Computing, 754, Springer, Cham, 2019,224–233.
doi: 10.1007/978-3-319-91008-6_23. |
[3] |
M. A. Cardenete, M. C. Lima and F. Sancho,
An assessment of the impact of EU funds through productivity boosts using CES functions, Appl. Econ. Lett., 26 (2019), 872-876.
doi: 10.1080/13504851.2018.1508867. |
[4] |
J. Cheng, L. Wang, Q. Jiang and Y. Xiong,
A novel cuckoo search algorithm with multiple update rules, Appl. Intell., 48 (2018), 4192-4211.
doi: 10.1007/s10489-018-1198-y. |
[5] |
M. L. Cheng,
A generalized constant elasticity of substitution production function model and its application, J. Systems Sci. Info., 4 (2016), 269-279.
doi: 10.21078/JSSI-2016-269-11. |
[6] |
M. L. Cheng, A Grey CES production function model and its application in calculating the contribution rate of economic growth factors, Complexity, 2019 (2019), 8pp.
doi: 10.1155/2019/5617061. |
[7] |
J. Chongela, V. Nandala and S. Korabandi, Estimation of constant elasticity of substitution (CES) production function with capital and labour inputs of agri-food firms in Tanzania, African J. Agricultural Res., 8 (2013), 5082-5089. Google Scholar |
[8] |
F. Erdal,
A firefly algorithm for optimum design of new-generation beams, Engineering Optim., 49 (2017), 915-931.
doi: 10.1080/0305215X.2016.1218003. |
[9] |
H. Guo, J. Hu, S. Yu, H. Sun and Y. Chen,
Computing of the contribution rate of scientific and technological progress to economic growth in Chinese regions, Expert Systems Appl., 39 (2012), 8514-8521.
doi: 10.1016/j.eswa.2011.12.032. |
[10] |
Y. He, S. W. Gao and N. Liao,
An intelligent computing approach to evaluating the contribution rate of talent on economic growth, Comput. Econ., 48 (2016), 399-423.
doi: 10.1007/s10614-015-9536-1. |
[11] |
G. V. S. K. Karthik and S. Deb,
A methodology for assembly sequence optimization by hybrid cuckoo-search genetic algorithm, J. Adv. Manufacturing Systems, 17 (2018), 47-59.
doi: 10.1142/S021968671850004X. |
[12] |
Y. N. Kiselev, S. N. Avvakumov and M. V. Orlov,
Optimal control in the resource allocation problem for a two-sector economy with a CES production function, Comput. Math. Model., 28 (2017), 449-477.
doi: 10.1007/s10598-017-9375-0. |
[13] |
X. J. Meng, J. X. Chang, X. B. Wang and Y. M. Wang,
Multi-objective hydropower station operation using an improved cuckoo search algorithm, Energy, 168 (2019), 425-439.
doi: 10.1016/j.energy.2018.11.096. |
[14] |
S. K. Mishra,
A brief history of production functions, IUP J. Managerial Econ., 8 (2010), 6-34.
doi: 10.2139/ssrn.1020577. |
[15] |
Y. Nakamura,
Productivity versus elasticity: A normalized constant elasticity of substitution production function applied to historical Soviet data, Appl. Econ., 47 (2015), 5805-5823.
doi: 10.1080/00036846.2015.1058909. |
[16] |
S. Opuni-Basoa, F. T. Oduro and G. A. Okyere,
Population dynamics in optimally controlled economic growth models: Case of Cobb-Douglas production function, J. Adv. Math. Comput. Sci., 25 (2017), 1-24.
doi: 10.9734/JAMCS/2017/36753. |
[17] |
A. S. Pillai, K. Singh, V. Saravanan, A. Anpalagan, I. Woungang and L. Barolli,
A genetic algorithm-based method for optimizing the energy consumption and performance of multiprocessor systems, Soft Comput., 22 (2018), 3271-3285.
doi: 10.1007/s00500-017-2789-y. |
[18] |
F. E. Sarac, A general evaluation on estimates of Cobb-Douglas, CES, VES and Translog production functions, Bull. Econ. Theory Anal., 2 (2017), 235-278. Google Scholar |
[19] |
C. Takeang and A. Aurasopon,
Multiple of hybrid lambda iteration and simulated annealing algorithm to solve economic dispatch problem with ramp rate limit and prohibited operating zones, J. Electrical Engineering Tech., 14 (2019), 111-120.
doi: 10.1007/s42835-018-00001-z. |
[20] |
K. Thirugnanasambandam, S. Prakash, V. Subramanian, S. Pothula and V. Thirumal,
Reinforced cuckoo search algorithm-based multimodal optimization, Applid Intell., 49 (2019), 2059-2083.
doi: 10.1007/s10489-018-1355-3. |
[21] |
H. Wang, X. Zhou, H. Sun, X. Yu, J. Zhao, H. Zhang and L. Cui,
Firefly algorithm with adaptive control parameters, Soft Comput., 21 (2017), 5091-5102.
doi: 10.1007/s00500-016-2104-3. |
[22] |
D. Zha, A. S. Kavuri and S. Si,
Energy-biased technical change in the Chinese industrial sector with CES production functions, Energy, 148 (2018), 896-903.
doi: 10.1016/j.energy.2017.11.087. |
[23] |
C. Zhao, Y. Xu and Y. Feng, A study on contribution rate of management elements in economic growth, in International Conference on Information and Management Engineering, Communications in Computer and Information Science, 234, Springer, Berlin, Heidelberg, 2011,151–158.
doi: 10.1007/978-3-642-24091-1_21. |
show all references
References:
[1] |
A. Assad and K. Deep,
A Hybrid Harmony search and Simulated Annealing algorithm for continuous optimization, Information Sci., 450 (2018), 246-266.
doi: 10.1016/j.ins.2018.03.042. |
[2] |
V. O. Bohaienko and V. M. Popov, Optimization of operation regimes of irrigation canals using genetic algorithms, in International Conference on Computer Science, Engineering and Education Applications, Advances in Intelligent Systems and Computing, 754, Springer, Cham, 2019,224–233.
doi: 10.1007/978-3-319-91008-6_23. |
[3] |
M. A. Cardenete, M. C. Lima and F. Sancho,
An assessment of the impact of EU funds through productivity boosts using CES functions, Appl. Econ. Lett., 26 (2019), 872-876.
doi: 10.1080/13504851.2018.1508867. |
[4] |
J. Cheng, L. Wang, Q. Jiang and Y. Xiong,
A novel cuckoo search algorithm with multiple update rules, Appl. Intell., 48 (2018), 4192-4211.
doi: 10.1007/s10489-018-1198-y. |
[5] |
M. L. Cheng,
A generalized constant elasticity of substitution production function model and its application, J. Systems Sci. Info., 4 (2016), 269-279.
doi: 10.21078/JSSI-2016-269-11. |
[6] |
M. L. Cheng, A Grey CES production function model and its application in calculating the contribution rate of economic growth factors, Complexity, 2019 (2019), 8pp.
doi: 10.1155/2019/5617061. |
[7] |
J. Chongela, V. Nandala and S. Korabandi, Estimation of constant elasticity of substitution (CES) production function with capital and labour inputs of agri-food firms in Tanzania, African J. Agricultural Res., 8 (2013), 5082-5089. Google Scholar |
[8] |
F. Erdal,
A firefly algorithm for optimum design of new-generation beams, Engineering Optim., 49 (2017), 915-931.
doi: 10.1080/0305215X.2016.1218003. |
[9] |
H. Guo, J. Hu, S. Yu, H. Sun and Y. Chen,
Computing of the contribution rate of scientific and technological progress to economic growth in Chinese regions, Expert Systems Appl., 39 (2012), 8514-8521.
doi: 10.1016/j.eswa.2011.12.032. |
[10] |
Y. He, S. W. Gao and N. Liao,
An intelligent computing approach to evaluating the contribution rate of talent on economic growth, Comput. Econ., 48 (2016), 399-423.
doi: 10.1007/s10614-015-9536-1. |
[11] |
G. V. S. K. Karthik and S. Deb,
A methodology for assembly sequence optimization by hybrid cuckoo-search genetic algorithm, J. Adv. Manufacturing Systems, 17 (2018), 47-59.
doi: 10.1142/S021968671850004X. |
[12] |
Y. N. Kiselev, S. N. Avvakumov and M. V. Orlov,
Optimal control in the resource allocation problem for a two-sector economy with a CES production function, Comput. Math. Model., 28 (2017), 449-477.
doi: 10.1007/s10598-017-9375-0. |
[13] |
X. J. Meng, J. X. Chang, X. B. Wang and Y. M. Wang,
Multi-objective hydropower station operation using an improved cuckoo search algorithm, Energy, 168 (2019), 425-439.
doi: 10.1016/j.energy.2018.11.096. |
[14] |
S. K. Mishra,
A brief history of production functions, IUP J. Managerial Econ., 8 (2010), 6-34.
doi: 10.2139/ssrn.1020577. |
[15] |
Y. Nakamura,
Productivity versus elasticity: A normalized constant elasticity of substitution production function applied to historical Soviet data, Appl. Econ., 47 (2015), 5805-5823.
doi: 10.1080/00036846.2015.1058909. |
[16] |
S. Opuni-Basoa, F. T. Oduro and G. A. Okyere,
Population dynamics in optimally controlled economic growth models: Case of Cobb-Douglas production function, J. Adv. Math. Comput. Sci., 25 (2017), 1-24.
doi: 10.9734/JAMCS/2017/36753. |
[17] |
A. S. Pillai, K. Singh, V. Saravanan, A. Anpalagan, I. Woungang and L. Barolli,
A genetic algorithm-based method for optimizing the energy consumption and performance of multiprocessor systems, Soft Comput., 22 (2018), 3271-3285.
doi: 10.1007/s00500-017-2789-y. |
[18] |
F. E. Sarac, A general evaluation on estimates of Cobb-Douglas, CES, VES and Translog production functions, Bull. Econ. Theory Anal., 2 (2017), 235-278. Google Scholar |
[19] |
C. Takeang and A. Aurasopon,
Multiple of hybrid lambda iteration and simulated annealing algorithm to solve economic dispatch problem with ramp rate limit and prohibited operating zones, J. Electrical Engineering Tech., 14 (2019), 111-120.
doi: 10.1007/s42835-018-00001-z. |
[20] |
K. Thirugnanasambandam, S. Prakash, V. Subramanian, S. Pothula and V. Thirumal,
Reinforced cuckoo search algorithm-based multimodal optimization, Applid Intell., 49 (2019), 2059-2083.
doi: 10.1007/s10489-018-1355-3. |
[21] |
H. Wang, X. Zhou, H. Sun, X. Yu, J. Zhao, H. Zhang and L. Cui,
Firefly algorithm with adaptive control parameters, Soft Comput., 21 (2017), 5091-5102.
doi: 10.1007/s00500-016-2104-3. |
[22] |
D. Zha, A. S. Kavuri and S. Si,
Energy-biased technical change in the Chinese industrial sector with CES production functions, Energy, 148 (2018), 896-903.
doi: 10.1016/j.energy.2017.11.087. |
[23] |
C. Zhao, Y. Xu and Y. Feng, A study on contribution rate of management elements in economic growth, in International Conference on Information and Management Engineering, Communications in Computer and Information Science, 234, Springer, Berlin, Heidelberg, 2011,151–158.
doi: 10.1007/978-3-642-24091-1_21. |


Year | |||
1999 | 4222.30 | 1856.72 | 733.76 |
2000 | 4812.15 | 1869.67 | 745.24 |
2001 | 5257.66 | 1994.73 | 752.26 |
2002 | 5795.02 | 2187.06 | 792.04 |
2003 | 6762.38 | 2452.11 | 813.05 |
2004 | 8165.38 | 3084.66 | 836.87 |
2005 | 9365.54 | 3542.55 | 863.32 |
2006 | 10718.04 | 3925.09 | 885.51 |
2007 | 12668.12 | 4458.61 | 909.08 |
2008 | 14275.80 | 4829.45 | 1053.24 |
2009 | 15285.58 | 5273.33 | 1064.42 |
2010 | 17433.21 | 5317.67 | 1090.76 |
2011 | 19533.84 | 5067.09 | 1104.33 |
2012 | 20553.52 | 5254.38 | 1115.50 |
2013 | 22257.66 | 5647.79 | 1137.35 |
2014 | 24060.87 | 6016.43 | 1197.31 |
2015 | 25643.47 | 6352.70 | 1361.51 |
2016 | 28178.65 | 6755.88 | 1365.24 |
2017 | 30632.09 | 7246.60 | 1372.65 |
2018 | 32679.87 | 7623.42 | 1430.82 |
Year | |||
1999 | 4222.30 | 1856.72 | 733.76 |
2000 | 4812.15 | 1869.67 | 745.24 |
2001 | 5257.66 | 1994.73 | 752.26 |
2002 | 5795.02 | 2187.06 | 792.04 |
2003 | 6762.38 | 2452.11 | 813.05 |
2004 | 8165.38 | 3084.66 | 836.87 |
2005 | 9365.54 | 3542.55 | 863.32 |
2006 | 10718.04 | 3925.09 | 885.51 |
2007 | 12668.12 | 4458.61 | 909.08 |
2008 | 14275.80 | 4829.45 | 1053.24 |
2009 | 15285.58 | 5273.33 | 1064.42 |
2010 | 17433.21 | 5317.67 | 1090.76 |
2011 | 19533.84 | 5067.09 | 1104.33 |
2012 | 20553.52 | 5254.38 | 1115.50 |
2013 | 22257.66 | 5647.79 | 1137.35 |
2014 | 24060.87 | 6016.43 | 1197.31 |
2015 | 25643.47 | 6352.70 | 1361.51 |
2016 | 28178.65 | 6755.88 | 1365.24 |
2017 | 30632.09 | 7246.60 | 1372.65 |
2018 | 32679.87 | 7623.42 | 1430.82 |
Method | Conventional CS | Improved CS |
4.9963 | 3.9414 | |
0.0450 | 0.0433 | |
1.1503 | 1.4430 | |
4.9788 | 6.6868 | |
4.9940 | 5.0012 | |
3.2084 | 3.1064 | |
0.1988 | 0.1497 | |
0.8231 | 0.8293 | |
Number of Iteration | 252 | 54 |
1.0319e |
9.9439e |
|
0.9935 | 0.9937 |
Method | Conventional CS | Improved CS |
4.9963 | 3.9414 | |
0.0450 | 0.0433 | |
1.1503 | 1.4430 | |
4.9788 | 6.6868 | |
4.9940 | 5.0012 | |
3.2084 | 3.1064 | |
0.1988 | 0.1497 | |
0.8231 | 0.8293 | |
Number of Iteration | 252 | 54 |
1.0319e |
9.9439e |
|
0.9935 | 0.9937 |
Year | ||||||
1999 | 1.2536 | 6.5002 | -9.275e-5 | -13.7e-4 | -5.69e-5 | 1.2364e-7 |
2000 | 1.2387 | 6.2050 | -7.511e-5 | -11.8e-4 | -9.53e-5 | 7.9713e-8 |
2001 | 1.2487 | 6.1583 | -6.335e-5 | -10.9e-4 | -1.15e-4 | 5.5835e-8 |
2002 | 1.2665 | 6.1774 | -5.439e-5 | -9.92e-4 | -1.23e-4 | 3.8894e-8 |
2003 | 1.2922 | 6.2664 | -4.787e-5 | -9.33e-4 | -1.27e-4 | 2.8559e-8 |
2004 | 1.3090 | 6.3446 | -3.959e-5 | -8.48e-4 | -1.21e-4 | 1.8918e-8 |
2005 | 1.3397 | 6.4705 | -3.565e-5 | -7.93e-4 | -1.19e-4 | 1.4196e-8 |
2006 | 1.3780 | 6.6312 | -3.337e-5 | -7.56e-4 | -1.18e-4 | 1.1381e-8 |
2007 | 1.4150 | 6.7923 | -3.086e-5 | -7.15e-4 | -1.14e-4 | 8.9777e-9 |
2008 | 1.4472 | 6.9094 | -2.805e-5 | -6.34e-4 | -1.06e-4 | 6.5751e-9 |
2009 | 1.4950 | 7.1239 | -2.709e-5 | -6.20e-4 | -1.06e-4 | 5.6539e-9 |
2010 | 1.5549 | 7.3862 | -2.754e-5 | -6.24e-4 | -1.09e-4 | 5.2946e-9 |
2011 | 1.6274 | 7.7058 | -2.929e-5 | -6.53e-4 | -1.17e-4 | 5.4122e-9 |
2012 | 1.6907 | 7.9924 | -2.949e-5 | -6.59e-4 | -1.20e-4 | 5.0563e-9 |
2013 | 1.7496 | 8.2616 | -2.888e-5 | -6.48e-4 | -1.19e-4 | 4.5043e-9 |
2014 | 1.8078 | 8.5239 | -2.803e-5 | -6.28e-4 | -1.17e-4 | 3.9252e-9 |
2015 | 1.8582 | 8.7431 | -2.631e-5 | -5.82e-4 | -1.10e-4 | 3.1723e-9 |
2016 | 1.9281 | 9.0661 | -2.625e-5 | -5.83e-4 | -1.11e-4 | 2.9566e-9 |
2017 | 1.9985 | 9.3922 | -2.600e-5 | -5.81e-4 | -1.11e-4 | 2.7283e-9 |
2018 | 2.0695 | 9.7171 | -2.563e-5 | -5.71e-4 | -1.10e-4 | 2.4778e-9 |
Year | ||||||
1999 | 1.2536 | 6.5002 | -9.275e-5 | -13.7e-4 | -5.69e-5 | 1.2364e-7 |
2000 | 1.2387 | 6.2050 | -7.511e-5 | -11.8e-4 | -9.53e-5 | 7.9713e-8 |
2001 | 1.2487 | 6.1583 | -6.335e-5 | -10.9e-4 | -1.15e-4 | 5.5835e-8 |
2002 | 1.2665 | 6.1774 | -5.439e-5 | -9.92e-4 | -1.23e-4 | 3.8894e-8 |
2003 | 1.2922 | 6.2664 | -4.787e-5 | -9.33e-4 | -1.27e-4 | 2.8559e-8 |
2004 | 1.3090 | 6.3446 | -3.959e-5 | -8.48e-4 | -1.21e-4 | 1.8918e-8 |
2005 | 1.3397 | 6.4705 | -3.565e-5 | -7.93e-4 | -1.19e-4 | 1.4196e-8 |
2006 | 1.3780 | 6.6312 | -3.337e-5 | -7.56e-4 | -1.18e-4 | 1.1381e-8 |
2007 | 1.4150 | 6.7923 | -3.086e-5 | -7.15e-4 | -1.14e-4 | 8.9777e-9 |
2008 | 1.4472 | 6.9094 | -2.805e-5 | -6.34e-4 | -1.06e-4 | 6.5751e-9 |
2009 | 1.4950 | 7.1239 | -2.709e-5 | -6.20e-4 | -1.06e-4 | 5.6539e-9 |
2010 | 1.5549 | 7.3862 | -2.754e-5 | -6.24e-4 | -1.09e-4 | 5.2946e-9 |
2011 | 1.6274 | 7.7058 | -2.929e-5 | -6.53e-4 | -1.17e-4 | 5.4122e-9 |
2012 | 1.6907 | 7.9924 | -2.949e-5 | -6.59e-4 | -1.20e-4 | 5.0563e-9 |
2013 | 1.7496 | 8.2616 | -2.888e-5 | -6.48e-4 | -1.19e-4 | 4.5043e-9 |
2014 | 1.8078 | 8.5239 | -2.803e-5 | -6.28e-4 | -1.17e-4 | 3.9252e-9 |
2015 | 1.8582 | 8.7431 | -2.631e-5 | -5.82e-4 | -1.10e-4 | 3.1723e-9 |
2016 | 1.9281 | 9.0661 | -2.625e-5 | -5.83e-4 | -1.11e-4 | 2.9566e-9 |
2017 | 1.9985 | 9.3922 | -2.600e-5 | -5.81e-4 | -1.11e-4 | 2.7283e-9 |
2018 | 2.0695 | 9.7171 | -2.563e-5 | -5.71e-4 | -1.10e-4 | 2.4778e-9 |
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Bahaaeldin Abdalla, Thabet Abdeljawad. Oscillation criteria for kernel function dependent fractional dynamic equations. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020443 |
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