—In this paper, we consider a single item single level production planning problem with uncertain and dynamic demand. The uncertainties are modelled through the probability density function of the demand. The system is studied in a rolling-horizon framework, in which data is updated at each iteration and makes the demand non-stationary. In this context, we model a cost minimization problem using a stochastic dynamic programming approach, which allows to integrate the update of the demand density into the optimization process. We calculate the optimal production quantities in a specific case where linear regression is the forecasting method used and the production lead-time is equal to one period. We finally run a simulation to illustrate the optimality of the solution, and to show its efficiency compared to others classical production planning procedures.