In this paper the stochastic dynamic lot sizing problem with multiple items and limited capacity under two types of fill rate constraints is considered. It is assumed that according to the static-uncertainty strategy of Bookbinder and Tan, the production periods as well as the lot sizes are fixed in advance for the entire planning horizon and are executed regardless of the realisation of the demands. We propose linear programming models, where the non-linear functions of the expected backorders and the expected inventory on hand are approximated by piecewise linear functions. The resulting models are solved with a variant of the Fix-and-Optimize heuristic. The results are compared with those of the column generation heuristic proposed by Tempelmeier.