Two-staged guillotine cut, two-dimensional bin packing optimisation with flexible bin size for steel mother plate design

This paper looks into the steel mother plate design problem. A slab, which is an intermediate work in process, is subsequently rolled into a mother plate with the specific dimensions of thickness, length, and width. The mother plate is then cut into customer order plates. As a slab is rolled into a mother plate through a series of horizontal and vertical rolling processes, different-sized mother plates can be generated from a single-slab type. This flexibility allows for the size of a mother plate to be determined according to the order plates assigned to it. Furthermore, when the order plates are cut from a mother plate, a guillotine cut is required to reduce the production cost. The steel mother plate design problem involves the placing of order plates on the mother plates in a guillotine cut pattern and determining the sizes of the mother plates with the objective of minimising the number of slabs; thus it may be considered as a two-staged guillotine cut, two-dimensional bin packing problem with flexible bin size. This paper introduces the problem, presents several mathematical models, and proposes an iterative two-phase heuristic method consisting of several algorithms to solve the problem. Computational results for the benchmark problems show the effectiveness of the proposed method.