A cross entropy-Lagrangean hybrid algorithm for the multi-item capacitated lot-sizing problem with setup times

The aim of this article is to introduce a hybrid algorithm for the multi-item multi-period capacitated lot-sizing problem with setups. In this problem, demands over a finite planning horizon must be met, where several items compete for space with limited resources in each period, and a portion of these resources is used by setups. The proposed scheme considers a Lagrangean relaxation of the problem and applies a cross entropy-based metaheuristic to the uncapacitated version of the original problem. A thorough experimental plan has been designed and implemented to test the effectiveness and the robustness of the algorithm: first, drawing inspiration from the response surface methodology, we calibrate the algorithm by identifying the optimal parameters value for any given instance size. Next, we carry out experiments on large scale instances, collecting information about solution quality and computational time, and comparing these results with those offered by a global optimizer.