Linear programming (LP) models for Supply Chain Operations Planning are widely used in Advanced Planning Systems. The solution to the LP model is a proposal for order releases to the various production units (PU) in the supply network. There is a non-linear relationship between the work-in-process in the PU and the lead time that is difficult to capture in the LP model formulation. We propose a two-step lead time anticipation (LTA) procedure where the LP model is first solved irrespective of the available production capacity and is subsequently updated with aggregate order release targets. The order release targets are generated by a local smoothing algorithm that accounts for the evolution of the stochastic workload in the PU. A solution that is both feasible with respect to the planned lead time and meets the material requirements may not exist. By means of discrete event simulation, we compare a conservative strategy where the production quantities are reduced to an optimistic strategy where the planned lead time constraint is allowed to be violated.