In this paper, we suggest a production planning approach that takes the finite capacity of the manufacturing system into account. The approach is based on a reduced level of detail modeling of the process flows. We consider explicitly only bottleneck steps. A mixed integer programming (MIP) formulation is suggested to determine completion time targets for the bottleneck steps of the lots. A Lagrange relaxation technique is applied to solve the MIP approximately. We present some preliminary results of computational experiments that demonstrate some promising features of the suggested approach with respect to solution quality and time needed for computation.