Successive LP Approximation for Nonconvex Blending in MILP Scheduling Optimization Using Factors for Qualities in the Process Industry

We develop a linear programming (LP) approach for nonlinear (NLP) blending of streams to approximate nonconvex quality constraints by considering property variables as constants, parameters, or coefficients of qualities that we call factors. In a blend shop, these intensive properties of streams can be extended by multiplying the material flow carrying out these amounts of qualities. Our proposition augments equality balance constraints as essentially cuts of quality material flow for each property specification in a mixing point between feed sources and product sinks. In the LP factor formulation, the product blend quality is replaced by its property specification and variables of slacks and/or surpluses are included to close the balance; these are called factor flows and are well known in industry as product giveaways. Examples highlight the usefulness of factors in successive substitution by correcting nonlinear blending deltas in mixed-integer linear models (MILP) and to control product quality giveaways or premium specifications in blend shops.