A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times

In this paper a heuristic approach for the dynamic multilevel multiitem lotsizing problem in general product structures with multiple constrained resources and setup times is proposed. With the help of Lagrangean relaxation the capacitated multilevel multiitem lotsizing problem is decomposed into several uncapacitated single-item lotsizing problems. From the solutions of these single-item problems lower bounds on the minimum objective function 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 problem groups of differing sizes.