Heuristics for the multi-item capacitated lot-sizing problem with lost sales

This paper deals with the multi-item capacitated lot-sizing problem with setup times and lost sales. Because lost sales, demands can be partially or totally lost. To find a good lower bound, we use a Lagrangian relaxation of the capacity constraints, when single-item uncapacitated lot-sizing problems with lost sales have to be solved. Each subproblem is solved using an adaptation of the O(T ) dynamic programming algorithm of (Aksen et al., 2003). To find feasible solutions, we propose a non-myopic heuristic based on a probing strategy and a refining procedure. We propose also some metaheuristic principles to improve solutions. Some computational experiments showing the effectiveness and limit of each approach are presented.