In this paper, we consider a single level single item production control quantity problem where the demand is represented by a stochastic and non-stationary variable. The update of the information is taken into account through a rolling horizon framework: the demand of a specific period t depends on all past information on hand at this time, and is updated through the dynamics of the forecast method used. We formulate the problem as a stochastic dynamic programming problem, and give an explicit optimal solution for a case where the production lead-time is reduced to zero. We finally compare the optimal results with classical production planning methods through a simulation.