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 of 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 $O(T^2)$ dynamic programming algorithm of Aksen et al. . To find feasible solutions, we propose a non‐myopic heuristic based on a probing strategy and a refining procedure. We also propose a metaheuristic based on the adaptive large neighborhood search principle to improve solutions. Some computational experiments showing the effectiveness and limitation of each approach are presented.