Multi-item, multi-stage, multi-facility lotsizing with general product structures

In this paper a heuristic approach for the dynamic multi-level multi-item lotsizing problem in general product structures with multiple constrained resources and setup times is proposed. With the help of Lagrangean relaxation the capacitated multi-level lotsizing problem is decomposed into several uncapacitated single-item lotsizing problems. From the solutions of these single-item problems lower bounds on the minimal objective value are derived. Upper bounds are generated by means of a heuristic finite scheduling procedure. The quality of the approach is tested with reference to various problems groups of differing sizes.