An integrated batching problem for steel plate manufacturing with bi-strand casting

We consider an integrated batching problem for steel-making and continuous casting process of steel plate manufacturing. For steel-making, slab batching problem is defined to make charges from slabs, and for continuous casting, charge batching problem is defined to make casts from charges. Our batching problem is regarded as a combination of slab batching and charge batching problems. Since steel-making and continuous casting are processes that must be synchronised, two batching problems must be integratedly handled. However, because of their difficulties, most papers solved each batching problem sequentially. We deal with a batching problem under bi-strand casting environment where slabs are cast with two strands. We also consider practical aspects that were barely considered before such as slab length difference constraints between strands and casts having few charges. We propose two mixed integer programming models. The first one is to create frames to define the overall structure of the solution and the second one is to fill the created frames with slabs to concretise the solution. The proposed matheuristic algorithm solves the problem in an integrated manner and finds a near-optimal solution in a reasonable time. It outperforms the company's current practice, as shown in experiments with real and randomly generated data.