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Aluminum Production Modeling—A Nonlinear Bilevel Programming Approach

Author

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  • Miles G. Nicholls

    (Swinburne University of Technology, Hawthorn, Victoria, Australia)

Abstract

This paper develops a nonlinear bilevel programming model of an aluminium smelter that is capable of representing all the major production processes. The model encompasses all the areas of the smelter which operates in a multilevel way. However, as shown, it can be reduced quite simply to a bilevel programming problem. The problem specification involves nonlinearities with respect to the variables and the presence of ratios among the constraints. The problem is also characterized by a two-way material flow in the production process. A relatively simple solution algorithm that facilitates the attainment of the global optimum is developed. While the problem specification appears daunting, a number of simplifications can be made, due to nature of the problem, allowing its quick solution. While the model developed in this paper together with the solution algorithm appear simple, considerable effort was required to identify the fundamental relationships in the aluminium smelting process, quantify them, and then develop appropriate expressions to represent them. It is believed that the solution of this class of nonlinear bilevel programming problems will have implications for other applications.

Suggested Citation

  • Miles G. Nicholls, 1995. "Aluminum Production Modeling—A Nonlinear Bilevel Programming Approach," Operations Research, INFORMS, vol. 43(2), pages 208-218, April.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:2:p:208-218
    DOI: 10.1287/opre.43.2.208
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    Cited by:

    1. G Dutta & N Gupta & R Fourer, 2011. "An optimization-based decision support system for strategic planning in a process industry: the case of aluminium company in India," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 616-626, April.
    2. Ankur Sinha & Zhichao Lu & Kalyanmoy Deb & Pekka Malo, 2020. "Bilevel optimization based on iterative approximation of multiple mappings," Journal of Heuristics, Springer, vol. 26(2), pages 151-185, April.
    3. M G Nicholls & B J Cargill, 2008. "Determining best practice production in an aluminium smelter involving sub-processes based substantially on tacit knowledge: an application of Communities of Practice," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 13-24, January.

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