Integer linear programming can help find the answer to a variety of real-world problems. Now researchers have found a much faster way to do it. It's for when you need to optimize for problems involving whole-number amounts. What good is a factory optimization plan that manufactures 500.7 couches? For this, researchers often turn to a variant of linear programming called integer linear programming (ILP). It’s popular in applications that involve discrete decisions, including production planning, airline crew scheduling, and vehicle routing. “Basically, ILP is the bread and butter of operations research both in theory and practice,” said Santosh Vempala, adjunct professor in the School of Mathematics and the H. Milton Stewart School of Industrial and Systems Engineering, and Frederick G. Storey Chair in Computing and professor in the College of Computing.