Lagrangian-based solutions for the multi-level production-inventory problem in iron and steel production with reverse logistics

This research deals with the production-inventory problem originating from the ironmaking production system in Shanghai Baoshan Iron and Steel Complex. A mixed integer programming (MIP) model based on the minimisation of total related costs including production/purchasing costs, inventory costs and setup costs is proposed to determine the production and inventory quantities of all materials in each time period under material-balance and capacity constraints. To solve the problem, a decomposition approach based on Lagrangian relaxation (LR) is developed. A solution property is introduced to speed up the solving process. Heuristic strategies are applied to improve the upper bound. In order to further improve the quality of the solutions, an alternative Lagrangian relaxation algorithm based on variable splitting is derived. A detailed numerical evaluation based upon the actual production data from Baosteel is performed. The computational results reveal that the proposed algorithms can obtain good quality solutions within a reasonable time. [Submitted: 6 February 2023; Accepted: 25 February 2024]