Column generation algorithms for mother plate design in steel plants

Abstract

This paper investigates the mother plate design (MPD) problem which is a typical problem in the production planning of steel plants. The MPD problem refers to a variant of the two-dimensional variable-sized bin packing problem in which the height of a bin is in a given finite set and the width of each bin is continuous in an interval. The problem is first formulated as a mixed integer nonlinear programming model and then linearized into a mixed integer programming model. We present a column generation-based (CG-based) algorithm to approximately solve the MPD problem, in which a height combination scheme is devised to decrease the dimensions of the pricing sub-problem. We present an accelerated CG (ACG) algorithm with improved performance which adopts two heuristic accelerating strategies in the pricing process. We use practical instances collected from a Chinese steel plant to test the performance of the proposed algorithms. The results indicate that the ACG algorithm is suitable for solving real-world instances.