A class of mix design problems: Formulation, solution methods and applications

In this paper, we consider a linear program with only equality constraints but containing interval and random coefficients. We first address the linear program with interval coefficients, and establish some structural properties of this linear program. On this basis, a solution method is proposed. We then move on to consider the linear program with random coefficients. Using the chance constraint approach and a new approach, the satisfaction degree approach, we obtain the two respective deterministic equivalent formulations. Then the results and the numerical solution methods obtained for these two linear models are applied to the original linear problem which contains both interval and random coefficients. By way of illustration, we consider a practical problem, where the optimal mixing proportions need to be determined for the mix slurry in the production process of aluminium with sintering. This gives rise to a linear program with interval and random coefficients. Its deterministic equivalent formulations are presented. Preliminary numerical examples show that the proposed models and the solution methods are promising.