In this article, we address the optimal scheduling of continuous air separation processes with electricity purchased from the day-ahead market, for which we propose a generalized framework to represent different operating states. Specifically, a discrete-time mixed integer linear programming (MILP) model is developed based on this representation for operating states, which has proven to provide a tight LP relaxation for handling industrial-scale instances. The computational efficiency of the model is demonstrated with data from real industrial production. The response of the scheduling and production level is also tested with various interval lengths for the electricity pricing and length of the time horizon.