New integer programming models for slab stack shuffling problems

Abstract

In the steel industry, a slab yard is a buffer that receives the slabs from the continuous casting and sends them to the hot rolling mill based on the hot rolling schedule. When a hot rolling schedule is released, several slabs are available for each rolling item, stored in different stacks in the yard. If the required slab is not on top of the stack, its above slabs must be first shuffled. The main problem is the slab stack shuffling problem related to selecting an appropriate slab for each rolling item to minimize the total number of shuffles. The present study considers two different variants of the slab stack shuffling problem based on the situation of the slab yard. A new integer programming model is proposed for each variant. Based on the properties of the problem, a theoretical analysis is derived to accelerate the models’ execution procedures. Then, the proposed models are applied to various numerical instances. Based on the results, optimal solutions can be obtained for practical scale problems in less than a few minutes. Finally, a real case study was conducted on a slab yard of a steel production company. Experimental results show that the proposed model for the classic problem version can reduce the total number of shuffles by 22.7%, on average.