A Lagrangian Relaxation based heuristic approach for steel grade assignment problem

This paper investigates the steel grade assignment problem daily encountered in the iron and steel industry, which involves the determination of which candidate steel grades to be employed in order to satisfy as many collective customer orders as possible such that the number of employing new steel grades and the desirable costs of satisfying the customer orders from the employed steel grade are minimized. The problem is formulated as a mixed integer programming model in which customer orders are optional. In addition, it displays the characteristic of the uncapacitated facility location problem. A midpoint-based method is proposed to obtain the desirable costs for the ability of steel grades to satisfy the requirements of orders. We develop a Lagrangian relaxation based (LR-based) heuristic approach with hybrid improvements including local search for the problem. The algorithm has been tested on instances collected from practical production data. Computational results demonstrate the effectiveness of the approach even for realistic problems with larger instances.