Primal dual approach to the multilevel capacitated lot-sizing problem

Traditional lot-sizing in multilevel MRP systems follows an infinite loading approach which has to be complemented afterwards with a checking for the availability of the required resources. On the contrary, taking into account the capacity constraints allows the computation of realistic lead times and cost-effective production schedules. This paper addresses the lot-sizing problem in a multi-echelon system where a bottleneck exists. A Primal-Dual approach, which had been previously used for the single level case, is proposed. It is a steepest ascent method that converges to the Lagrangean optimum in a finite number of iterations. Computational experiences with the proposed method are presented.