A new method of optimizing the operation of distillation processes with uncertain inflow streams from upstream plants is discussed. The case considered is the streams that will be first accumulated in a tank before feeding to the column. To minimize the total amount of operating energy while keeping a stable column operation under these inflows, a novel decomposed optimization strategy consisting of two steps was used. For an optimal planning of the dynamic operation, a smooth feed flow policy to the column is developed in the first step by stochastic optimization under chance constraints by ensuring a predefined probability of holding the tank level inside the desired range. An easy-to-use method developed computes the maximum reachable probability of holding the constraints so that a feasible solution of the chance constrained problem can be guaranteed. Since the uncertainty in the inflow stream variability is absorbed in the stochastic optimization over the tank, the operation of the downstream distillation column is deterministic. Therefore, in the second step, the reflux and reboiler duty policies of the column are developed by deterministic dynamic optimization. The optimal overall strategy is obtained by the maximized smoothness of the feed flow to the distillation column. The approach is applied to a pilot column, and the developed operating policies are implemented on the real plant by experiment.