The solution is discussed of the process synthesis problem for cryogenic air separation using techniques from process synthesis optimization. The mass and energy balances for the process are represented by a simplified algebraic model in which material stream flows and pressures appear as continuous variables and the various equipment choices for components of the air separation cycle are represented by binary variables. The resulting model corresponds to a mixed-integer nonlinear programming (MINLP) formulation and enables numerical optimization of the cycle. The two problems addressed are the selection of the optimal equipment set for a given product slate and the flexibility determination of the chosen cycle. The flexibility analysis is complemented with unique visual techniques that depict the feasible region and use of the recently proposed convex-hull approach. The calculations are illustrated for low-purity (95%) oxygen plants using the Lachmann cycle. (c) 2005 American Institute of Chemical Engineers