Optimised Cell Batching for New Zealand Aluminium Smelters Ltd

New Zealand Aluminium Smelters Ltd operates a smelting facility at Tiwai Point near Invercargill. The smelter produces aluminium by the electrolytic reduction of alumina in 650 cells. The cells are laid out in long lines and are grouped into tapping bays. The purity of the aluminium varies from cell to cell depending on a number of factors including the age of the cell, the purity of the alumina feed and the manner in which the cell has been operated during its production life. High purity aluminium commands a premium price on the metals market. In the production process molten aluminium is tapped from the cells into crucibles that are used to transport the metal to furnaces from where finished product is cast in the form of billet or ingot. Each crucible taps the metal from three cells that are located within some specified limit of spread in the same a tapping bay. The spread limit is imposed to minimise the time taken to fill the crucible. This paper describes the development of a set partitioning optimisation model to batch or group triples of cells so that the total value of metal produced is maximised. The main aim is to minimise the dilution of high purity (high value) metal by low purity (low value) metal. The optimised batches tend to group high purity cells together and leave the lower purity cells to be batched with other lower purity cells. Numerical results show that significant improvements in excess of 10% can be achieved in the value of metal by carefully batching cells.