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.

Joint optimization of steel plate shuffling and truck loading sequencing based on deep reinforcement learning

“…Within these areas, items are piled up on the stacks to enhance space utilization. If the item to be retrieved is not positioned at the top of the stack, the shuffling process must be initiated [11,12]. Therefore, the retrieval problem becomes one of the most critical factors affecting the efficiency of yard operations.…”

“…A two-phase model-based heuristic was developed to minimize the makespan in their work. Bruno et al [17] proposed a bi-objective mathematical model aiming to minimize the number of shuffles and expired slabs simultaneously in a generic cutting/assembly center.…”

“…Constraint (10) reveals the relationship between decision variables 𝑧 𝑡 𝑖𝓁𝑘𝜏 and 𝑦 𝑡 𝑖𝓁𝑘𝜏 . Constraint (11) emphasizes the movement sequence of orders, that is, an order cannot be moved from its slot unless the slot above it is empty. Constraints ( 12)-( 14) are a set of vital constraints in this paper, where…”

“…Following the model in [30], the transformations of the stack configuration can be expressed as constraints ( 15)-( 21). In constraint (15), the stack configuration is initialized utilizing the parameter ỹ𝑖𝓁𝑘 , and the configuration status of adjacent intervals and adjacent stages can be updated by constraints ( 16) and (17), respectively. Constraint (18) indicates that a slot can only hold one order.…”