Optimizing chemical processes with discontinuous function — A novel formulation

Abstract This paper introduces a novel formulation of modeling discontinuous functions, named Multi-M formulation. The new formulation is quite similar to the famous big-M formulation. Instead of subtracting a big value (M) from each cost segment when the solution does not fall into, the Multi-M formulation disaggregates the big M into smaller M values for each pair of cost segments. By doing so, problem relaxation is significantly improved without increasing the number of variables and constraints. Examples will be used to illustrate the effectiveness of Multi-M formulation in comparison with the Big-M and Convex-Hull formulations.