An Application of Bilevel Programming Problem in Optimal Pollution Emission Price

ABSTRACT

Charging for the pollution is one of the ways to enhance the environmental quality. The appropriate price of the pollution emission is the most important question of the research on how to charge for the pollution. So, by constructing a bilevel programming model, we provide a novel way for solving the problem of charging for the pollution. In our model, the government (or the social regulation) chooses the optimal price of the pollution emission with consideration to firms’ response to the price. And the firms choose their optimal quantities of the production to maximize their profits at the given price of the pollution emission. Finally, a simple example is illustrated to demonstrate the feasibility of the proposed model.

Charging for the pollution is one of the ways to enhance the environmental quality. The appropriate price of the pollution emission is the most important question of the research on how to charge for the pollution. So, by constructing a bilevel programming model, we provide a novel way for solving the problem of charging for the pollution. In our model, the government (or the social regulation) chooses the optimal price of the pollution emission with consideration to firms’ response to the price. And the firms choose their optimal quantities of the production to maximize their profits at the given price of the pollution emission. Finally, a simple example is illustrated to demonstrate the feasibility of the proposed model.

Cite this paper

nullG. Wang, L. Ma and L. Li, "An Application of Bilevel Programming Problem in Optimal Pollution Emission Price,"*Journal of Service Science and Management*, Vol. 4 No. 3, 2011, pp. 334-338. doi: 10.4236/jssm.2011.43039.

nullG. Wang, L. Ma and L. Li, "An Application of Bilevel Programming Problem in Optimal Pollution Emission Price,"

References

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[10] M. A. Amouzegar and S. E. Jacobsen, “A Decision Support System for Regional Hazardous Waste Management Alternatives,” Journal of Applied Mathematics and Decision Sciences, Vol. 2, No. 1, 1998, pp. 23-50. doi:10.1155/S1173912698000029

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[13] J. Bracken and J. M. McGill, “Mathematical Programs with Optimization Problems in the Constraints,” Operations Research, Vol. 21, No. 1, 1973, pp. 37-44. doi:10.1287/opre.21.1.37

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[16] S. Dempe, “Annotated Bibliography on Bilevel Program- ming and Mathematical Programs with Equilibrium Con- straints,” Optimization, Vol. 52, No. 3, 2003, pp. 333-359. doi:10.1080/0233193031000149894

[17] B. P. Colson, P. Marcotte and G. Savard, “Bilevel Programming: A Survey,” A Quarterly Journal of Operations Research, Vol. 3, No. 2, 2005, pp.87-107.

[18] G. M. Wang, Z. P. Wan and X. J. Wang, “Bibliography on Bilevel Programming,” Advances in Mathematics, Vol. 36, No. 5, 2007, pp. 513-529.

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[20] L. Vicente, G. Savard and J. Judice, “Descent Approaches for Quadratic Bilevel Programming,” Journal of Optimization Theory and Applications, Vol. 81, No. 2, 1994, pp. 379-399. doi:10.1007/BF02191670

[21] G. Z. Ruan, F. M. Yang and S. Y. Wang, “A Simplex Algorithm to Solve Bilevel Linear Price Control Problem,” Systems Engineering Theory and Practice, Vol. 16, No. 12, 1996, pp. 38-43.

[22] C. X. Teng, Z. H. Li and L. Li, “Basic Properties and Continuity of the Solution Sets of Price Control Problem,” Systems Engineering Theory and Practice, Vol. 17, No. 2, 1997, pp. 45-49.

[23] H. Y. Liu and S. Y. Liu, “A Note on Bilevel Linear Price Control Problem,” Systems Engineering Theory and Practice, Vol. 19, No. 4, 1999, pp. 141-143.

[24] J. P. Dussault, P. Marcotte, S. Roch and G. Savard, “A Smoothing Heuristic for a Bilevel Pricing Problem,” European Journal of Operational Research, Vol. 174, No. 3, 2006, pp.1396-1413. doi:10.1016/j.ejor.2004.07.076

[25] Y. B. Lv, T. Hu and Z. P. Wan, “A Penalty Function Method for Solving Weak Price Control Problem,” Applied Mathematics and Computation, Vol. 186, No. 2, 2007, pp. 1520-1525. doi:10.1016/j.amc.2006.07.151

[1] Y. G. Zhu, L. Wang, Z. J. Wang, et al., “China Steps up Its Efforts in Research and Development to Combat Environmental Pollution,” Environmental Pollution, Vol. 147, No. 2, 2007, pp. 301-302. doi:10.1016/j.envpol.2006.10.001

[2] H. D. Kan, W. Huang, B. H. Chen, et al., “Impact of Out- door Air Pollution on Cardiovascular Health in Mainland China”, CVD Prevention and Control, Vol. 4，No. 1, 2009, pp. 71-78.

[3] S. Managi and S. Kaneko, “Environmental Performance and Returns to Pollution Abatement in China,” Ecological Economics, Vol. 68, No. 6, 2009, pp.1643-1651. doi:10.1016/j.ecolecon.2008.04.005

[4] H. F. Cheng and Y. N. Hu, “Lead (Pb) Isotopic Fingerprinting and Its Applications in Lead Pollution Studies in China: A Review,” Environmental Pollution, Vol. 158, No. 5, 2010, pp. 1134-1146. doi:10.1016/j.envpol.2009.12.028

[5] D. D. Cao, G. B. Jiang, Q. F. Zhou, et al., “Organotin Pollution in China: An Overview of the Current State and Potential Health Risk,” Journal of Environmental Man- agement, Vol. 90, No. 1, 2009, pp. 16-24. doi:10.1016/j.jenvman.2008.06.007

[6] J. H. Dales, “Pollution Properly and Price,” Toronto Uni- versity Press, Toronto, 1968.

[7] United States Environmental Protection Agency (USEPA), Office of Water, “A Summary of U.S. Effluent Trading and Offset Projects, US,” Environmental Pro- tection Agency, Washington DC, 1999.

[8] E. Woerdman, “Implementing the Kyoto Protocol: Why JI and CDM Show More Promise than International Emissions Trading,” Energy Policy, Vol. 28, No. 1, 2000, pp. 29-38. doi:10.1016/S0301-4215(99)00094-4

[9] M. A. Amouzegar and K. Moshirvaziri, “Determining Optimal Pollution Control Policies: An Application of Bilevel Programming,” European Journal of Operational Research, Vol. 119, No. 1, 1999, pp. 100-120. doi:10.1016/S0377-2217(98)00336-1

[10] M. A. Amouzegar and S. E. Jacobsen, “A Decision Support System for Regional Hazardous Waste Management Alternatives,” Journal of Applied Mathematics and Decision Sciences, Vol. 2, No. 1, 1998, pp. 23-50. doi:10.1155/S1173912698000029

[11] X. J. Wang and S. Y. Feng, “The Optimality Theory of Bilevel System,” The Science Press, Cape Town, 1995.

[12] Z. Hu, C. Fu and X. Wang, “Property Rights Disposition and Management of Water Resources,” The Science Press, Cape Town, 2003.

[13] J. Bracken and J. M. McGill, “Mathematical Programs with Optimization Problems in the Constraints,” Operations Research, Vol. 21, No. 1, 1973, pp. 37-44. doi:10.1287/opre.21.1.37

[14] H. V. Stackelberg, “The Theory of the Market Economy,” Oxford University Press, Oxford, 1952.

[15] J. F. Bard, “Practical Bilevel Optimization: Algorithms and Applications,” Kluwer Academic Publishers, Dordre- cht, 1998.

[16] S. Dempe, “Annotated Bibliography on Bilevel Program- ming and Mathematical Programs with Equilibrium Con- straints,” Optimization, Vol. 52, No. 3, 2003, pp. 333-359. doi:10.1080/0233193031000149894

[17] B. P. Colson, P. Marcotte and G. Savard, “Bilevel Programming: A Survey,” A Quarterly Journal of Operations Research, Vol. 3, No. 2, 2005, pp.87-107.

[18] G. M. Wang, Z. P. Wan and X. J. Wang, “Bibliography on Bilevel Programming,” Advances in Mathematics, Vol. 36, No. 5, 2007, pp. 513-529.

[19] J. F. Bard, “Some Properties of the Bilevel Linear Pro- gramming,” Journal of Optimization Theory and Applica- tions, Vol. 68, No. 2, 1991, pp. 371-378. doi:10.1007/BF00941574

[20] L. Vicente, G. Savard and J. Judice, “Descent Approaches for Quadratic Bilevel Programming,” Journal of Optimization Theory and Applications, Vol. 81, No. 2, 1994, pp. 379-399. doi:10.1007/BF02191670

[21] G. Z. Ruan, F. M. Yang and S. Y. Wang, “A Simplex Algorithm to Solve Bilevel Linear Price Control Problem,” Systems Engineering Theory and Practice, Vol. 16, No. 12, 1996, pp. 38-43.

[22] C. X. Teng, Z. H. Li and L. Li, “Basic Properties and Continuity of the Solution Sets of Price Control Problem,” Systems Engineering Theory and Practice, Vol. 17, No. 2, 1997, pp. 45-49.

[23] H. Y. Liu and S. Y. Liu, “A Note on Bilevel Linear Price Control Problem,” Systems Engineering Theory and Practice, Vol. 19, No. 4, 1999, pp. 141-143.

[24] J. P. Dussault, P. Marcotte, S. Roch and G. Savard, “A Smoothing Heuristic for a Bilevel Pricing Problem,” European Journal of Operational Research, Vol. 174, No. 3, 2006, pp.1396-1413. doi:10.1016/j.ejor.2004.07.076

[25] Y. B. Lv, T. Hu and Z. P. Wan, “A Penalty Function Method for Solving Weak Price Control Problem,” Applied Mathematics and Computation, Vol. 186, No. 2, 2007, pp. 1520-1525. doi:10.1016/j.amc.2006.07.151