The application of non-linear bi-level programming to the aluminium industry

In this paper, a solution algorithm is presented for the bi-level non-linear programming model developed to represent the complete operations of an aluminium smelter. The model is based on the Portland Aluminium Smelter, in Victoria, Australia and aims at maximising the aluminium production while minimising the main costs and activity associated with the production of this output. The model has two variables, the power input measured in kilo-Amperes (kA) and the setting cycle (of the anode replacement [SC]). The solution algorithm is based on the vertex enumeration approach and uses a specially developed grid search algorithm. An examination of the special nature of the model and how this assists the algorithm to arrive at an optimal unique solution (where there exists one) is undertaken. Additionally, future research into expansion of the model into a multi-period one (i.e., in effect a ''staircase'' model) allowing the optimisation of the smelter operations over a year (rather than as is currently the case, one month) and the broadening of the solution algorithm to deal with a more general problem, are introduced.