Metaheuristics for the multi-item capacitated lot-sizing problem with time Windows and setup times

In this paper, we address to the multi-item capacitated lot-sizing problem with production time windows and setup times under the non-customer specific case. This problem is known to be NP-hard. Two cooperative approaches are proposed for solving this problem by combining mathematical programming and metaheuristics based on a decomposition scheme. The algorithms use simultaneously the mathematical programming and heuristic procedures such that the local Search algorithm and Variable Neighborhood descent algorithm. The computational experiments show the effectiveness of our proposed algorithms according to the approaches already presented in the literature.