In Steel industry slab yard serves as a buffer between the continuous casting stage and the steel rolling stage. After a scheduled rolling turn is released, the collection of suitable candidate slabs for each rolling item in the turn is identified. Candidate slabs are stored in different stacks in the yard. Shuffling is needed when picking up a slab which is stored under the other slabs. The purpose is selecting appropriate slabs in the yard for a given rolling schedule so as to minimize the total number of shuffles. So far, several studies have been conducted in the literature but in all of these studies heuristic and meta-heuristic methods have been used to solve the problem and the proposed models are theatrical and non-liner. In this study, various mathematical models have been proposed to select appropriate slabs in the yard for a given rolling schedule so as to minimize the total number of shuffles. Proposed models can solve real-world problems at an acceptable time. In this research slab Stack-shuffling problem has been investigated with three strategies. First strategy is to follow the rolling schedule sequence so as to pick slabs from the stacks. A mathematical binary model and several lemmas are proposed which can obtain optimal solutions for instances up to 200 rolling Items. Similar article have solved these instances with Genetic algorithm only up to 150 items which shows this study offers an improvement over other studies. Second strategy is to not to follow the rolling schedule sequence and pick slabs in a sequence which leads to minimize the number of shuffles in the slab yard. For this strategy, a mathematical binary model is presented that can solve the generated instances up to 150 roll items optimally. Third strategy is relative order strategy. In this strategy a model has been proposed which can obtain optimal solution for instances with 120 rolling items. Finally a case study was conducted on the slab yard of Mobarakeh Steel Co. as an application background. Experimental results shows that proposed models can reduce number of shuffles by 22.7% on average in the slab yard.
