Skip to main content
SpringerLink
Log in

An Linear Programming Model for Batch Optimization in the Ecological Zinc Production

  • Published:
Environmental Modeling & Assessment Aims and scope Submit manuscript

Abstract

This paper presents a mathematical model for solving the blending composition problem used in the zinc smelting process. The model proposes an objective function maximizing profit in terms of the total income from the sale of zinc on the market and the cost of producing zinc. In addition to the constraints contained in the basic mathematical model, the constraints, which are in accordance with the specific production process of zinc and environmental requirements, are developed. This paper proposes a model that can align three contradictory demands (technological, economic, and environmental) present in zinc production. The results, obtained by numerical experiments, confirm the assumption that it is possible to assemble such an optimal batch that will “reconcile” all contradictory demands. This model can be applied to other similar processes of production with minor changes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Lineberry, G.T., & Gillenwater, E. L. (1987). Linear programming to improve raw coal blending: a new twist to an old tool. Coal Preparation, 4(3-4), 227–239. doi:10.80/07349348708945534.

    Article  Google Scholar 

  2. Van Drew, S.L., & Maurer, R.A. (1987). Coal preparation and blending technique based on linear programming. Chapter 11 - Mining engineering and operations. In Mineral Resource Management by Personal Computer, pp. 89–94. Society of Mining Engineerings of AIME. Lettleton, CO.

  3. Liu, C.M., & Sherali, H.D. (2000). A coal shipping and blending problem for an electric utility company. Omega–International Journal of Management Science, 28(4), 433—444. doi:10.1016/S0305-04839900067-5.

    Google Scholar 

  4. Kim, J., & Lewis, R.L. (1987). A large scale linear programming application to least cost charging for foundry melting operations. American Foundrymens. Society Transactions, 95, 735–744.

    Google Scholar 

  5. Ashayeri, J., van Eijs, A.G.M., & Nederstigt, P. (1994). Blending modelling in a process manufacturing: a case study. European Journal of Operational Research, 72(3), 460–468. doi:10.1016/0377-22179490416-2.

    Article  Google Scholar 

  6. Nikolić, Dj., Jovanović, I., Mihajlović, I., & Živković, Ž (2009). Multi-criteria ranking of copper concentrates according to their quality—an element of environmental management in the vicinity of copper Smelting complex in Bor, Serbia. Journal of Environmental Management, 91(2), 509–515. doi:10.1016/j.jenvman.2009.09.019.

    Article  Google Scholar 

  7. Saramak, D., Tumidajski, T., & Skorupska, B. (2010). Technological and economic strategies for the optimization of Polish electrolytic copper production plants. Minerals Engineering, 23(10), 757–764. doi:10.1016/j.mineng.2010.05.013.

    Article  CAS  Google Scholar 

  8. Saramak, D. (2011). Optimal production of electrolytic copper determined by the concentration and distribution of copper concentrates to smelters on the example of KGHM. Archives of Metallurgy and Materials, 56(3), 619–626. doi:10.2478/v10172-011-0067-z.

    Article  CAS  Google Scholar 

  9. Jovanović, I., & Stanimirović, P. (2012). A blending problem in copper production. Environmental Modeling and Assessment, 17(5), 495–503. doi:10.1007/s10666-012-9309-3.

    Article  Google Scholar 

  10. Jovanović, I., Stanimirović, P., & Živković, Ž (2013). Environmental and economic criteria in ranking of copper concentrates. Environmental Modeling and Assessment, 8(1), 73–83. doi:10.1007/s10666-012-9327-1.

    Article  Google Scholar 

  11. Savić, M., Mihajlović, I., & Živković, Ž (2013). An ANFIS-based air quality model for prediction of SO2 concentration in urban area. Serbian Journal of Management, 8(1), 25–38. doi:10.2139/ssrn.2257533.

    Article  Google Scholar 

  12. Kalina, J. (2013). Highly robust methods in data mining. Serbian Journal of Management, 8, 9–24. doi:10.5937/sjm8-3226.

    Article  Google Scholar 

  13. Djordjević, P., Mihajlović, I., & Živković, Ž (2010). Comparasion of linear and nonlinear statistics metods applied in industrial process modeling procedure. Serbian Journal of Management, 5(2), 189–198.

    Google Scholar 

  14. Djurić, I., Djordjević, P., Mihajlović, I., Nikolić, Dj., & Živković, Ž (2010). Prediction of Al2O3 leaching recovery in the Bayer process using statistical multilinear regression analysis. Journal Of Mining And Metallurgy Section B: Metallurgy, 46(2B), 161–169. doi:10.2298/JMMB1002161D.

    Article  Google Scholar 

  15. Queiroz, C.A.R., Carvalho, R.J., & Moura, F.J. (2005). Oxidation of zinc sulphide concentrate in a fluidized bed reactor, Part.2. The influence of experimental variables and kinetics. Brazilian Journal of Chemical Engineering, 22(1), 127–133. doi:10.1590/S0104-66322005000100013.

    Article  CAS  Google Scholar 

  16. Balarini, J.C., de Oliveira Polli, L., Miranda, T.L.S., de Castro, R.M.Z., & Salum, A. (2008). Importance of roasted sulphide concentrates characterization in the hydrometallurgical extraction of zinc. Minerals Enginering, 21(1), 100–110. doi:10.1016/j.mineng.2007.10.00.

  17. WHO–World Health Organization. (2001). Air quality guidelines for Europe (2nd edition WHO regional publications). Copenhagen: Regional Office for Europe.

    Google Scholar 

  18. EU, 1999/30/CE 1999. Council Directive relating to limit values for sulphur dioxide, nitrogen dioxide and oxide of nitrogen, particulate matter and lead in ambient air. The Council of the European Union.

  19. EU, 2004/107/CE 2004. Council Directive relating to arsenic, cadmium, mercury, nickel and polycyclic aromatic hydrocarbons in ambient air. The Council of the European Union.

  20. Habachi, F. (1998). Principles of extractive metallurgy. Vol. 4, Amalgam Electrometallurgy Metallurgie Extractive Quebec. Canada: Quebec.

    Google Scholar 

  21. Habachi, F. (2009). Recent trends in extractive metallurgy. Journal of Mining and Metallurgy Section B: Metallurgy, 45B(1), 1–13. doi:10.2298/JMMB0901001H.

    Article  Google Scholar 

  22. Dutrizac, J.E. (2010). Comparative rates of precipitation of ammonium jarosite and sodium jarosite in ferric sulphate–sulphuric acid media. The Canadian Metallurgical Quarterly, 49(2), 121– 130.

    Article  CAS  Google Scholar 

  23. Chen, T.T., & Dutrizac, J.E. (2004). Mineralogical changes occurring during the fluid-bed roasting of zinc sulfide concentrates. Journal of Metals / JOM, 56(12), 46–51. doi:10.1007/s11837-004-0235-y.

    CAS  Google Scholar 

  24. Dimitrov, R.I., Moldovanska, N., Bonev, I.K. & Živković, Ž. (2000). Oxidation of marmatite. Thermochimica Acta, 362(1-2), 145–151. doi:10.1016/S0040-6031(00)00582-7.

    Article  CAS  Google Scholar 

  25. Wolfram, S. (2003). The Mathematica Book, 5th edn. Champaign: Wolfram Media/Cambridge University Press.

    Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge support from the Research Projects TR34023, financed by The Ministry of Education and Science of the Republic of Serbia.

Author information

Authors and Affiliations

  1. Technical Faculty in Bor, University of Belgrade, 12 Vojske Jugoslavije, Bor, Serbia

    Ivan Jovanović, Marija Savić & Živan Živković

  2. Department of Chemical Technology, University of Plovdiv, 24 Tsar Asen, Plovdiv, Bulgaria

    Bojan S. Boyanov & Alexander Peltekov

Authors
  1. Ivan Jovanović
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marija Savić
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Živan Živković
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bojan S. Boyanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Alexander Peltekov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ivan Jovanović.

Additional information

The results shown in this paper are part of the research of the TR34023 project, financed by The Ministry of Education and Science of the Republic of Serbia.

Appendix: Implementation in MATHEMATICA

Appendix: Implementation in MATHEMATICA

This section describes the mathematica code for computing values max F(x). List P defines the contents of all 19 components contained in 10 separate concentrates. The 19th concentrate component is the “miscellaneous” group.

figure a

The initial data are defined as follows:

figure b

The objective function is defined as the following:

figure c

Constraints are defined as follows:

figure d

When you have defined all the necessary parameters, it is possible to calculate the value max F(x). To obtain an optimal solution for the first numerical experiment, it is necessary to apply step A. For the second numerical experiment, step B is applied, and step C for the third.

Step A. Calculation for the first numerical experiment (only Zn):

figure e

Step B. Calculation for the second numerical experiment (Zn + S + As):

figure f

Step C. Calculation for the third numerical experiment (Zn + all elements):

figure g

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jovanović, I., Savić, M., Živković, Ž. et al. An Linear Programming Model for Batch Optimization in the Ecological Zinc Production. Environ Model Assess 21, 455–465 (2016). https://doi.org/10.1007/s10666-015-9485-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10666-015-9485-z

Keywords

Search

Navigation