This work aims at quantifying the minimum utility cost necessary to complete a given separation task using vapor liquid equilibrium (distillation) operations. The Infinite DimEnsionAl State-space (IDEAS) process is introduced as a new paradigm for this process synthesis activity. The IDEAS conceptual framework includes all possible process configurations, and yields mathematical programs that are convex (linear), thereby guaranteeing the global optimality of the obtained solution. A case study, on nitrogen/oxygen mixture separation, is employed to illustrate the power of the proposed approach. The obtained IDEAS designs are compared with the corresponding McCabe-Thiele (conventional) minimum utility designs, and are shown to be as much as 50% more thermodynamically and economically efficient.