Discrete deterministic and stochastic blending problems with two quality characteristics: aluminum blending

This research is motivated by the problem of assigning the output of electrolytic cells to oven batches in the production of aluminum, so as to maximize the expected revenue. Cell output cannot be split between batches, and the batch sizes are constrained. Each batch is classified into a revenue category based on the levels of two impurities. The impurity levels differ from cell to cell and additional random quantities of impurities are added during the oven process. We develop optimal and heuristic solution approaches for the deterministic version of the problem (known amount of impurities) and use them as the basis for a heuristic procedure for the stochastic version. Using data from a high-grade aluminum manufacturer, we demonstrate that our approach finds near-optimal solutions to the stochastic problem, with significant gains over solving deterministic versions in which the stochasticity is modeled only approximately.