A Bi-level Multi-objective Optimization Model of Multiple Items for Stone Industry Under Fuzzy Environment

  • Muhammad Nazim
  • Abid Hussain Nadeem
  • Muhammad Hashim
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 185)


Traditionally, stone industry is produced essential materials for the construction industry but stone industry is always debated as a high emission industry for stone dust and waste water. This emission has an adverse impact on environment, humans, agriculture and ground water. This paper focuses on how to optimize the stone industry. The government is considered as the leader level which will make a strategy to plan the exploring amount of every stone plant and sustainable development in stone industry to create employment opportunity and economic growth. The stone plants are considered as the lower-level decision-makers which optimize their objective functions under the constraint of leader. The stone plants have individual objectives of maximizing the profit and produce different product according to the demand constraints under the limited exploring amount. Due to the lack of historical data, some emission coefficients are considered as fuzzy numbers according to experts advices. Therefore, a bi-level multi-objective optimization model with possibilistic and predetermined constraints under the fuzzy environment is developed to control the pollution and get sustainable development in stone industry. For some special fuzzy coefficients, the equivalent model is obtained. At the end, a practical case is proposed to show the efficiency of the proposed model.


Bi-level multi-objective programming Possibilistic constraint Stone industry Fuzzy simulation 


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  1. 1.
    Al-Jabri M, Sawalh H (2002) Treating stone cutting waste by flocculation-sedomentation. In: Proceeding of the Sustainable Enviromental Sanitation and Water Services Conference, 28th WEDC conference, Calcutta, India.Google Scholar
  2. 2.
    Nasserdine K, Mimi Z, Bevan B et al. (2009) Environmental management of the stone cutting industry. Journal of Environmental Management 90:466–470.Google Scholar
  3. 3.
    Almeida N, Branco F, Santos JR (2007) Recycling of stone slurry in industrial activities: Application to concrete mixtures. Building and Environment 42:810–819.Google Scholar
  4. 4.
    CH2MHILL (2002) Herbon industerial waste water controle and pretreatment fesibility study. Task 10, unpublisheed report.Google Scholar
  5. 5.
    Montero MA, Jordan MM, Almendro-Candel MB et al. (2009) The use of a calcium carbonate residue from the stone industry in manufacturing of ceramic tile bodies. Applied Clay Science 43:186–189.Google Scholar
  6. 6.
    Ammary BY (2007) Clean production in stone cutting industries. International Journal of Enviroment and Waste Managment 1:106–112.Google Scholar
  7. 7.
    Algin HM, Turgut P (2008) Cotton and limestone powder wastes as brick material. Construction and Building Materials 22:1074–1080.Google Scholar
  8. 8.
    Hebhoub H, Aoun H, Belachia M et al. (2011) Use of waste marble aggregates in concrete. Construction and Building Materials 25:1167–1171.Google Scholar
  9. 9.
    Pearce DW, Warford JJ (1993) World without end: Economics, environment and sustainable development. Oxford University Press/World Bank, Oxford.Google Scholar
  10. 10.
    Grossman GM, Krueger AB (1991) Environmental impacts of a North American free trade agreement. Discussion Paper No. 158,WoodrowWilson School, Princeton University, Princeton, NJ.Google Scholar
  11. 11.
    Ryu JH, Dua V, Pistikopoulos EN (2004) A bi-level programming framework for enterprisewide process networks under uncertainty. Computers and Chemical Engineering 2:1121–1129.Google Scholar
  12. 12.
    Takama N, Umeda T (1980) Multi-level, multi-objective optimization in processing engineering. Chemical Engineering Science 36:129–136.Google Scholar
  13. 13.
    TeresaW, Som S, Mengqi H (2011) The application of memetic algorithms for forearm crutch design: A case study. Mathematical Problems in Engineering, Doi: 10.1155/2011/162580.
  14. 14.
    Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Management Science 17:141–164.Google Scholar
  15. 15.
    Shih HS, Lai YJ, Lee ES (1996) Fuzzy approach for multi-level programming problems. Computers and Operations Research 23:73–91 1060 M. Nazim & A. Nadeem & M. Hashim.Google Scholar
  16. 16.
    Singh A, Lou HH (2006) Hierarchical Pareto optimization for the sustainable development of industrial ecosystems. Industrial and Engineering Chemistry Research 45:3265–3279.Google Scholar
  17. 17.
    Arora SR, Gupta R (2009) Interactive fuzzy goal programming approach for bi-level programming problem. European Journal of Operational Research 194:368–376.Google Scholar
  18. 18.
    Dubois D, Prade H (1978) Operations on fuzzy numbers. International Journal of System Sciences 9:613–626.Google Scholar
  19. 19.
    Lim SR, Park JM (2008) Cooperative water network system to reduce carbon footprint. Environmental Science and Technology 42:6230–6236.Google Scholar
  20. 20.
    World Commission on Environment and Development (WCED) (1987) Our common future. Oxford University Press, New York.Google Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Muhammad Nazim
    • 1
  • Abid Hussain Nadeem
    • 1
  • Muhammad Hashim
    • 1
  1. 1.Uncertainty Decision-Making LaboratorySichuan UniversityChengduPeople’s Republic of China

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