A single product, single Btage, multiperiod production smoothing problem is considered in this paper. Demands are monotonically increasing in successive periods, and in each period, they occur at a uniform rate. The important feature is that a production run can be started or ended at any time, and not necessarily at the start of any period. Considering production costs, costs due to change of production rate and inventory costs, unique optimal policies are derived. The special feature of the solution is that no iterative search procedure is needed to arrive at the optimal policy. On the other hand, a set of three conditions are derived. Once any one of these conditions is satisfied, the optimal policy is easily determined. Cost formulae are given for optimal policies derived. Three examples are solved to illustrate the optimal policies derived. Finally scope for application of the model is suggested.