A unifying framework and a mathematical model for the Slab Stack Shuffling Problem

Abstract

The Slab Stack Shuffling Problem (SSSP) consists of retrieving slabs, stored in stacks in a warehouse, to efficiently satisfy a processing order. The problem is relevant in the steel industry as the slab yard serves as a storage buffer between the continuous casting stage and the rolling mill. Notably, the SSSP also arises in cutting/assembly centres within the shipbuilding supply chain, where already rolled slabs must undergo further production stages. The different slabs managed in these facilities confer the problem novel practical features, such as the existence of slabs' typologies and deadlines, i.e., a maximum time beyond which their quality certifications expire and are no longer usable. In such a context, the goals of the present paper are twofold: (i) providing a comprehensive taxonomy of the main aspects involved in the problem; (ii) proposing an original mathematical formulation for the SSSP. Specifically, the model is cast as a bi-objective multi-period program, seeking to minimise the number of shuffles and expired slabs. Computational tests on randomly generated instances prove the relevance of the trade-off between the above-mentioned objectives and the impact of the yard's configuration on the retrieval process, suggesting the most suitable storage strategy to adopt under different operational settings.