Formulation to obtain the most reliable aggregate mix with quantity and other constraints

The aggregate batch mixing problem determines the proportion (or relative masses) in which aggregate batches with different gradations are to be blended so as to achieve a target mix with a given gradation. As shown in previous studies, the gradation of a batch is not homogeneous and should be considered stochastic. Also, when batches are blended in the field there are random variations in the masses or proportions of individual batches in the mix. Assuming batch gradation and blend masses as stochastic implies that the notion of a mix (blend) satisfying the gradation of a target mix becomes stochastic. In such a framework, every mix has a reliability with which it satisfies the definition of the target mix. In addition, a mix is also required to satisfy various restrictions. This article presents an optimization formulation to determine the most reliable mix while satisfying restrictions on available quantity, budget, etc.