Aluminium production modeling – a nonlinear bilevel programming approach

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.