A common optimization problem in refineries is the operation of fractional distillation towers in different operating modes where the product split is changed by changing conditions of the column as well as energy use of the column. Additionally, different crude oils will produce different product mix for a given mode. Product mix here refers to how much gasoline, how much diesel, etc. The optimization problem is to decide how much of each type of crude to feed into the towers in each operating mode to maximize profit. For example, one final decision could be to feed all Crude 1 into Mode 1, and to split Crude 2 where 70% goes into Mode 1, and 30% goes into Mode 3